Hey Jake - I'm struggling with this question from my maths textbook: "A rectangular box is to have a square base and no top. If it's volume is 500cm^{3}, find the least area of sheet metal of which it can be made." I'm not understanding how all this maximum and minimum stuff is applied to these kind of questions, I thought it just had to do with graphs? Thanks!! :)
Hey Jake - I'm struggling with this question from my maths textbook: "A rectangular box is to have a square base and no top. If it's volume is 500cm^{3}, find the least area of sheet metal of which it can be made." I'm not understanding how all this maximum and minimum stuff is applied to these kind of questions, I thought it just had to do with graphs? Thanks!! :)
Hey Liiz! I see that HPL has already posted an answer, but I'll throw mine in as well in case any of the methodology is different. Hope it helps, and thanks for the questions!
(http://i.imgur.com/NubpZ8v.png?1)
(http://i.imgur.com/0beu0z5.png?1)
Thanks for your post!
If anyone else wants to ask or answer questions, I would really appreciate the contribution! Before you can ask a question, you'll have to make an ATAR Notes account here. Once you've done that, a little 'reply' button will come up when you're viewing threads, and you'll be able to post whatever you want! :)
Great work Jake, I think it was a really good idea for you to first state the equation of how to calculate the volume of the rectangular box (cant believe l forgot to include that) and to state that x does not equal to 0 which is the condition which must be met despite obvious in this case. Great combined effort and a really good question Liiz!!!You have the best handwriting I've ever seen.
You have the best handwriting I've ever seen.
Hi,
Okay, so I've got a (possibly silly) question to ask, but I actually - GENUINELY - do not have any idea and need help:
How does one study for Maths?
I seem to have a really consistent system for each of my subjects as to approaching study in the most efficient way possible, but I can not seem to find an effective way of studying for Maths. I've tried everything I can think of. Please help.
Thank you
Hello HSC Math geniuses :D
I have a math differentiation and integration assessment soon and was just wondering if you could help me on how to set answers out, especially with lengthy questions. Here is one question I have recently, recived the correct answers but was not sure on how to structure my answer exactly:
A magazine advertisement is to contain 50cm^2 of lettering with clear margins of 4cm each at the top and bottom and 2cm at each side. Find the overall dimensions if the total area of the advertisement is to be a minimum.
Thank you so much for your help!!!!!!
;D ;D ;) :D :)
Hey Caninesandy!
This was actually quite a difficult question, which required me to draw the picture in order to figure out what was going on! My general tips for these questions are
1. Figure out the equations that you have
2. Sub in the equations, so that you have a differentiatable one
3. Differentiate, and find the required minimum
4. Sub the found value into the original, to find the solution.
Here is the solution I came up with. Hope it helps! This is exactly how I would set out any question similar to this :)
(http://i.imgur.com/hY8GLxv.png?1)
(http://i.imgur.com/hQTKRDX.png?1)
Jake
Sorry to challenger your authority jake, but did you mean h = 50/(x-4) + 8??? (Is it a transcription error?)
Sorry to challenger your authority jake, but did you mean h = 50/(x-4) + 8??? (Is it a transcription error?)
Hi!
At the moment I'm doing HSC Trigonometry and I'm really confused about when to change the calculator's mode to Degrees or Radians. How can i be able to tell when to change the mode?
Thank You.
And by personal experience there will definitely be cases where you would forget to change from radian mode to degrees modes and this is gonna be very disastrous. So some of my friends decided to bring two calculators, one labelled degrees and another labelled radians. If you are struggling to remember to change to radian mode then you might like to consider that method.
Hi!
At the moment I'm doing HSC Trigonometry and I'm really confused about when to change the calculator's mode to Degrees or Radians. How can i be able to tell when to change the mode?
Thank You.
Hey jake, having trouble integrating this.
Integrate (4-(x-8)^2)^(1/2)
I know its a semicircle and the limits are 10 to 6, but I keep getting zero.
Is there a special way to integrate a semicircle and find the area? (Other than (pi*r^2)/2 )
Hey jake, having trouble integrating this.
Integrate (4-(x-8)^2)^(1/2)
I know its a semicircle and the limits are 10 to 6, but I keep getting zero.
Is there a special way to integrate a semicircle and find the area? (Other than (pi*r^2)/2 )
Could someone please help with question 10a of the 2003 2u mathematics hsc paper :)
Hey Jake, I just got my results back for my first 2u exam for year 12. It was on sequence and series, applications of calculus, integration and logs and exponentials. I got a 55/78 because I didn't finish the last section (logs and expos) of the exam. My teacher did say I smashed the first three parts though.
Firstly I wasn't super strong on logs and exponentials from the beginning, and secondly I spent way too long trying to work out a question earlier in the exam that i was sure I could get. It was a question where you had to find the equation of a parabola given its vertex and x intercepts.
Based on all this, how do you think I should move on. What can I learn from this experience, and just because I got a 70% on this exam, does that mean i'm doomed to around a 70 for the rest of my 2u math career? Like, this is the real thing now, is it still possible to recover?
Hey Jake, I just got my results back for my first 2u exam for year 12. It was on sequence and series, applications of calculus, integration and logs and exponentials. I got a 55/78 because I didn't finish the last section (logs and expos) of the exam. My teacher did say I smashed the first three parts though.
Firstly I wasn't super strong on logs and exponentials from the beginning, and secondly I spent way too long trying to work out a question earlier in the exam that i was sure I could get. It was a question where you had to find the equation of a parabola given its vertex and x intercepts.
Based on all this, how do you think I should move on. What can I learn from this experience, and just because I got a 70% on this exam, does that mean i'm doomed to around a 70 for the rest of my 2u math career? Like, this is the real thing now, is it still possible to recover?
cos(2x+pie/6)=1/root2 -pie<=x<=pie
how do i find the angles in a simple way without getting the angles confused?
how do you do this ques thanks ;D
a man in a rowing boat is presently 6km from the nearest point A on the shore. He wants to reach as soon as possible a point B that is further 20km down the shore from A. If he can row at 8km/hr and run at 10km/hr , how far from A should he land? ans: 8km
how do you do this ques thanks ;D
a man in a rowing boat is presently 6km from the nearest point A on the shore. He wants to reach as soon as possible a point B that is further 20km down the shore from A. If he can row at 8km/hr and run at 10km/hr , how far from A should he land? ans: 8km
how do you do this ques thanks ;D
a man in a rowing boat is presently 6km from the nearest point A on the shore. He wants to reach as soon as possible a point B that is further 20km down the shore from A. If he can row at 8km/hr and run at 10km/hr , how far from A should he land? ans: 8km
Assumed we wanted to minimise time:
(http://uploads.tapatalk-cdn.com/20160227/37fd2b8c68f2b54865edec0515867baf.jpg)
P.S. Woah Jake what are you doing with the trig!
I'm not sure if this was meant to be an unanswered question but here's a solution
Pick an arbitrary point (a,0) to be the first vertex of the rectangle. By default (a, e^(-a^2)) is also on the rectangle. But because it HAS TO BE A RECTANGLE and we have an even function
(-a,0) and (-a, e^(-a^2)) must lie on the rectangle. This is most easily shown with a diagram.
(http://i.imgur.com/fzE9TxN.png)
So the breadth and length of the triangle are:
Hence we can combine these to give an expression for area:
Set dA/dx=0 to maximise:
Reject x=0 though, because if x=0 we have no rectangle (we can't have a width of 0).
So just show that the remaining value gives a maxima using a table of values or the second derivative. Note that because the curve is an even function, the negative term can be ignored.
I would've used latex but I'm thoroughly lazy to on a phone (Hello, Jamon here, I went through and added LaTex ;D)
I was wondering how to draw the x-intercepts and vertex??? For Y= 3-2xsquared
LEGEND! Thanks RuiAce! I went through and added LaTex and a diagram for you, cheers for the solution! Jake has been on holiday and I've been trying to keep an eye on all his forums, I must have missed this, you are a champion ;D
Hey :)
This is a Geometrical Applications of Calculus question I'm stuck on (I've attached a photo of the question and answer). I know the quotient and product rules, but for some reason I keep ending up with some ridiculous answer. A step by step explanation would be hugely helpful :)
Hey Jake, so i got my 2u half yearly tomrrow and not sure what i'm supposed to be doing this very moment wether its past papers of relaxing haha, any advice would be great
Hello, needing some help to integrate this: x / 2x^{2} - 3
Thankyou!
Loan Repayments Question
The smith family buys a car for $38 000, paying a 10% deposit and taking out a loan for the balance. if the loan is over 5 years with interest of 1.5% monthly, find the amount of each monthly (a) loan repayment the total amount that the (b) smith family paid for the car.
Answer:
(a) $592.00 (b) $39 319.89
I didn't forget you imtrying! I'm just not at my desk at the moment, I need to write out the series for your question (I think), so I'll tackle it tonight once I have some desk space! Unless someone else would like to have a crack ;D
Loan Repayments Question
The smith family buys a car for $38 000, paying a 10% deposit and taking out a loan for the balance. if the loan is over 5 years with interest of 1.5% monthly, find the amount of each monthly (a) loan repayment the total amount that the (b) smith family paid for the car.
Answer:
(a) $592.00 (b) $39 319.89
Hey Liiz! Sure thing!
Okay, so this question takes a bit of experience to spot the trick for. The integral of this will be a logarithm.
Remember, the derivative of the log of some function is:
For your question, we almost have the derivative of the bottom on top of the fraction, which is what is required. To make it work, we multiply by 4 on the numerator, then multiply the integral by a quarter, thus balancing everything out. You could also think of it as taking out a factor of 1/4:
This isn't super easy to spot, it might take some practice to see it quickly! Hope this helps ;D
I've got a question that was on my exam and I got it wrong after literally 10 attempts.
The question is: Find the area bounded by y=sin x and y=cos 2x for π/6 ≤ x ≤ 5π/6
Thanks!
hey
can u please help me with how to differentiate this...i really don't know how to...
i'd really appreciate it :)
Can't see your image. If your integral was something along the lines of this then in NSW it belongs under MX2.yes that is the integral...and d/dx belongs in front of it...sorry...
Also, you said differentiate? Did you mean you wanted to put d/dx in front of that integral? (or d/dt inside it?)
Hello y'all. How do I solve this question:
Find the point T(a,lna) on y=lnx where the tangent passes through the origin, i.e. find the value of a.
Hi,
So currently for Maths 2U and for Ext 1 maths, i am using the maths in focus textbook (Margaret Grove) but i want to purchase another textbook as this one is not that great. I was wondering if you could give suggestions as to what textbook is really good. I'm debating between the Fitzpatrick book and Cambridge book. Please help!
Thank you :)
Hi,
So currently for Maths 2U and for Ext 1 maths, i am using the maths in focus textbook (Margaret Grove) but i want to purchase another textbook as this one is not that great. I was wondering if you could give suggestions as to what textbook is really good. I'm debating between the Fitzpatrick book and Cambridge book. Please help!
Thank you :)
Hi guys!, I seem to struggle with this integration question.Can you explain why the answer is 1/6(2x-1)^{3/2} + 1/2(2x-1)^{1/2} + C ?. Thank you!
I need help with a rates and finance question.
For the AP: 100 + 97 + 94 + ...
Show that 68 is the minimum number of terms in which S_{n} is negative.
Hey Guys,
Some help with this question please?
https://goo.gl/3ZYQOC
Hey Jake,
Thanks for the help! But i'm a little confused, isn't there another intersection at -3pi/8? Which is before the endpoint at -pi/2...
No worries Jake, yeah I used your method and was able to get a solution I believe to be right. You had the right idea, just missed one little thing. No problem, HAPPY BIRTHDAY BY THE WAY!
No problem Jake, another question for you. I can do up to part iii, but part IV I am stuck.
https://goo.gl/photos/wTkpMHqM6dVkFfSr7
Hey Jake, wondering if we could revisit this question. For the final part, (the tan inequality) I seem to be getting different results from different places. The one I am currently thinking is correct is -pi/2<=x<=-3pi/8, -pi/4<x<=pi/8, pi/4<x<=pi/2
https://goo.gl/Hg97px
hey
can someone please explain how to do this question for me?
Q: Police set up a road block to check cars for seatbelt use. From experience, they estimate that 80% of drivers wear seat belts. Use this estimate to determine what the probability is that the second unbelted driver is in the 8th car stopped?
there is a second part of this question that i know how to do...but i don't know how to do this part..
any help will be much appreciated :)
hey
can someone please explain how to do this question for me?
Q: Police set up a road block to check cars for seatbelt use. From experience, they estimate that 80% of drivers wear seat belts. Use this estimate to determine what the probability is that the second unbelted driver is in the 8th car stopped?
there is a second part of this question that i know how to do...but i don't know how to do this part..
any help will be much appreciated :)
Looks like Rui beat me too it :)
Ninjas. Ah sorry :)
But yeah I basically also considered the binomial probability distribution. I just didn't exactly apply it since this question wasn't posted under the Extension 1 section of the forum.
Looks like Rui beat me too it :)
thank you both of you :)
i am doing binomial distribution but since I'm on the opposite side of the country as you guys i didn't know where to put which question :)
sorry ???
but thank you again :)
A man takes out a $250 000 mortgage. Interest is 7.2% per annum, compounded monthly. Repayments are $3 000 monthly.
a) Find a formula for the balance on the loan after n months
b) How many years does it take to repay the loan
Thank you!
Struggling to understand how to do this!Inserted an edit to make Jamon's point a bit clearer. Let A=P_{0}
- a population in a certain city is growing at a rate proportional to the population itself. after 3 years the population increases by 20%. How long will it take for the population to double?
Optionally, you can add a comment about the fact that a $250 000 dollar mortgage is totally unrealistic for first home buyers in Sydney ;)
Totally kidding, though it might give the marker a laugh.
Topic: Applications of Calculus to the Physical World
Sub-topic: ￼Exponential growth and decay
Formulas: ￼Q = Ae^kt, dQ/dt = kQ
Can you help with this question please? not having obvious numbers to substitute into the formula is really throwing me off ???
The half-life of radium is
1600 years.
(a) Find the percentage of radium that will be decayed after 500 years.
(b) Find the number of years that it will take for 75% of the radium to decay.
Thank you! :) :)
Hey! This is a standard method for exponential growth/decay questions that don't give you actual numbers, but rather percentages. You need to just LET Q equal something at time t=0 (eg. 100, like I used, or 1, which is what I usually used). Then, as time progresses, you just use an appropriate percentage of your original value. The explanation in the answer below should explain what I mean; once you've seen it once, you'll be able to do it again in a heartbeat!
(http://i.imgur.com/7MoE2dZ.jpg)
Jake
PLEASE HELP!! THANK YOU!
Find, correct to 2 decimal places, the area enclosed by the curve
y = log2 x, the x-axis and the lines x = 1 and x = 3 by using simpson’s rule with 3 function values.
Hey Jake, sorry to bother you but we got this massive revision booklet for my test recently, but we are not allowed to ask our teachers for awnsers or anything and there are a few questions (a lot) that I'm really struggling to Understand?
1 b ii
8 a iii
10 b
14 c ii
16 b iii
17 iii Iv
18 b i ii
20
22 a iii d ii e i ii iii
I understand there are heaps so please just pick one or two that suit you best?
Here are thre questions; sorry about my dodgy af collage.
Hey Jake, sorry to bother you but we got this massive revision booklet for my test recently, but we are not allowed to ask our teachers for awnsers or anything and there are a few questions (a lot) that I'm really struggling to Understand?
1 b ii
8 a iii
10 b
14 c ii
16 b iii
17 iii Iv
18 b i ii
20
22 a iii d ii e i ii iii
I understand there are heaps so please just pick one or two that suit you best?
Here are thre questions; sorry about my dodgy af collage.
Hey!Or maybe just a larger collage.
Unfortunately I can't decipher the questions you've sent over, they are way too blurry. If you could either send higher quality pictures, or just type up the important ones, that would be great! I'm happy to help with things that you're struggling with, but maybe do try to limit the questions to like one of each type. That way, hopefully I can help explain the general way to solve those kinds of questions, and then you can figure out the others yourself.
Jake
Hey Jake, sorry to bother you but we got this massive revision booklet for my test recently, but we are not allowed to ask our teachers for awnsers or anything and there are a few questions (a lot) that I'm really struggling to Understand?
Must be a pretty dodgy teacher if ur not allowed to ask them questions
Must be a pretty dodgy teacher if ur not allowed to ask them questions
You got that right, surely that's just their entire job?Yep. People like them should be fired.
Yep. People like them should be fired.I thank the moon, stars and whatever the hell else is up there that i have the best maths teacher ever who puts in so much effort for her students. ;D
I thank the moon, stars and whatever the hell else is up there that i have the best maths teacher ever who puts in so much effort for her students. ;D
The difference between teachers can really make or break a subject IMO
I thank the moon, stars and whatever the hell else is up there that i have the best maths teacher ever who puts in so much effort for her students. ;D
The difference between teachers can really make or break a subject IMO
Let me retype my question above
How do I find the domain of y=(3-x)squareroot of x
Also how do I type up maths questions on this forum?
How do I find the domain of y=(3-x)?
I want to do it without inspection
Also how do I answer people's maths questions if I were to answer them?
:-\
It's great to here that you want to answer maths questions! When you see something you want to take a crack at, just hit "reply" on their post, and type out a response. You can hand write an answer and attach it using the mona lisa button in the toolbar (you'll need to upload the image to Imgr, as you need a hyperlink, but that doesn't take too long) or use LaTeX to type using maths, as I've explained above!
Looking forward to seeing more of you on the forum :)
Jake
Hey! So first, I'll answer your Maths question. To find the domain of
We just need to consider which values of x are essentially 'not allowed'. Generally, to do this we just set whatever is in the square root to be greater than zero (noting that the square root of a negative number does not exist!). So, this one turns out the be easy; the (3-x) bit doesn't do anything, but the square root of x means that x must be greater than 0! In maths;
Not too difficult!
Now, to answer your second question, you started on the right track (using the LaTeX button in the toolbar). However, various functions have various codes attributable to them. Check out Rui's incredible guide HERE to find out how to use it! I'm pretty shit at it, but Rui and Jamon are pros.
Jake
Once again thanks
So basically (3-x) has no effect on the domain? If so why?
Precisely! Because 3-x has no restrictions, we can put anything into it and it makes sense. It's only the square root term that causes issues (think Math error on your calculator) ;D
Absolutely this. And the thing is, it's not just intelligence. I've had lecturers who were absolute wizards, knew their shit like absolutely nothing I've ever seen, but I still didn't like them as a lecturer. Then I have had tutors who know their course content really well and not too much beyond that, but holy crap they just knew how to explain it!! Being able to explain something well is just so important, something which I fear is overlooked in favour of pure academic skill.Theres that famous saying that goes along the lines of "If you cant explain it to a 6 year old in simple terms, you don't know it well enough" ahah
The best teachers in my experience are the ones who love their job, because it shows ;D
Theres that famous saying that goes along the lines of "If you cant explain it to a 6 year old in simple terms, you don't know it well enough" ahah
Try explaining linear algebra to a 6 year old
Coordinates are steps to the left or right, or up and down. If you wanted the parametric version of a line you could explain it in terms of walking to a starting point, then walking so many steps in a given direction. Mappings would be taking longer steps, shorter steps, swapping the direction, etc. Vector spaces would be like the map of the park where you are walking. Etc.
Of course none of this would give them any actual useful skills, but kind of fun to think about!! ;) I'm a big believer than you can teach anyone, anything (albeit at a very simple level) provided they have the right dedication. Of course, this relies on 6 year olds having the dedication to try and understand linear algebra... So maybe not ;) anyway, back to the math!! ;D
Im not sure if this is the right place to ask this but eh...
Everywhere i look at Maths resources, i find study notes of maths... which is not something i want. Ive looked all over the place and i cant seem to find simple formula sheets of the stuff in the course. Unfortunately, this is something i really suck at doing. Ive written study notes for all my subjects but for maths I prefer a simple, clear list of formulas. Any idea where i can find something like this?
You're literally given a formula sheet by BOSTES now for the exam.sure, but theres way too many things missing from it.
sure, but theres way too many things missing from it.
sure, but theres way too many things missing from it.
Totally agree! If there is nothing out there, I'll make it my business to get one of these formula sheets written in the next week or two and uploaded to the site! Great idea ;DWhat's missing that you guys want to see so badly?
What's missing that you guys want to see so badly?
It's not something I'd want to see in an exam scenario (well this is given since I did without) but even with my tutoring students off the top of my head some missing ones:Well I guess the HSC basically just gave you all the simplified formulae that you need cause
- Area of a Secant
- Multiple Applications of Trapezoidal/Simpson's Rule
- General Forms of the Trig Expansions
I'm sure there are more ;D it's like Physics and Chem where you definitely have enough to get by, but it's nice to have something comprehensive around that covers absolutely everything!! And in a form that is easier to study from (I'm thinking this is a study resource more than anything) ;D
Well I guess the HSC basically just gave you all the simplified formulae that you need cause
Area of a segment = Area of a sector minus area of a triangle
Trap/Simpson's rule can just be done recursively (tbh, the general Simpson's rule depends on if you start counting at x_{0} or x_{1})
Trig is idk I just know it
But yeah fair enough if you want sophistication I can see where you're coming at. But at least they give you the building blocks in the HSC now instead of just an integrals sheet!
For trigonometry limits, why do we have to multiply by the fraction?
Hi at school we've started trigonometry identities proofsBe clearer about the word "illegal". Only certain things are illegal and it always depends on what you're trying to prove and restrictions.
I was wondering if i could get help in understanding what i can and can not do to prove trig identities
and how i should interpret the proofs
I also seem to do illegal steps in getting one side equal the other and never seem to understand how I should 'visualise' and understand what to do when given a proof
Hi at school we've started trigonometry identities proofs
I was wondering if i could get help in understanding what i can and can not do to prove trig identities
and how i should interpret the proofs
I also seem to do illegal steps in getting one side equal the other and never seem to understand how I should 'visualise' and understand what to do when given a proof
What exactly do you mean by 'illegal'?Not necessarily in the HSC. Concepts such as L'Hopital's rule that used to get abused by students are now strictly forbidden and subject to being penalised.
If it means doing something that is mathematically wrong like dividing by zero on both sides on a equation, or assuming what you are trying to prove, then that's a big no no.
However if you're using theorems, results and formulas that are outside of the syllabus and not taught covered in school, that's a big yes as it shows you have the initiative to learn more than you're expected to.
I apologize for not being clear about what I meant by 'illegal'The rule that everything is not a mathematical mistake or misuse in assumption? Show me an example of where you messed up and did something "illegal" for a better idea.
I was referring to my habit of constantly doing something that is mathematically wrong/not possible.
How do you know what you can and can not do in regards to the trig identities?
Are there particular rules that must be followed when proving trig identities?
Not necessarily in the HSC. Concepts such as L'Hopital's rule that used to get abused by students are now strictly forbidden and subject to being penalised.
I apologize for not being clear about what I meant by 'illegal'
I was referring to my habit of constantly doing something that is mathematically wrong/not possible.
How do you know what you can and can not do in regards to the trig identities?
Are there particular rules that must be followed when proving trig identities?
Damn didn't realize the use L'Hopital rule got caught on, it's such a useful theorem to use though ;D Yeah I agree with you though, be mindful of what concepts you can't use too.Yep
Yep
One of the more minor reasons as to why I wanted to do uni maths already was just to abuse the crap out of L'H ;D
But the HSC is just the way it is. Always try to use what's in the syllabuses. I think one of the most lenient things they do is allow implicit differentiation in Ext 1...when it's really just properly taught in Ext 2.
Okay so I am having trouble with "quadratic identities"
I don't seem to understand things like x^2+x+1=a(x-1)^2+b(x-1)+c
How is a=1 c=3 b=3 in this case
Same with this case 3x^2-5x-2=a(x-1)^2+b(x+1)+c
How is a=3 c=-6 and b=1
If anyone here is good at explaining clearly then could you please help me
Thanks ;D
Would like to say that L'Hopital was my favourite thing in first year math, now it's probably Cauchy-Goursat's Theorem for use in complex contour integration (beautiful math) ;)
Oh that's such a sweet result :-* I'd say my the Residue Theorem's (again from Complex Analysis) my favorite, and how it can be used to find really nasty integrals and find inverse Laplace Transforms so efficiently.
Need help with the following questions:The others are lecturing right now and I'm afraid I don't have paper on me at this moment. Have you tried drawing diagrams?
6. A motorbike and car leave a service station at the same time. The motorbike travels on a bearing of 080 degrees and the car travels for 15.7km on a bearing of 108 degrees until the bearing of the motorbike from the car is 310 degrees. How far, correct to 1 decimal place, has the motorbike travelled?
7. A plane flies from Dubbo on a bearing of 139 degrees for 852 km then turns and flies on a bearing of 285 degrees until it is due west of Dubbo. How far from Dubbo is the place, to the nearest km?
8. Stig leaves home and trave;s on a bearing of 248 degrees for 109.8 km. He then tuens and travels for 271.8 km on a bearing of 143 degrees. Stif then turns and travels home on a bearing of "a"
a. How far does he travel on the final part of his journey?
b. Evaluate a
9. Two cars leave an intersection at the same time, one travelling at 70km/h along one road and he other car travelling at 80 km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection?
Need help with the following questions:
6. A motorbike and car leave a service station at the same time. The motorbike travels on a bearing of 080 degrees and the car travels for 15.7km on a bearing of 108 degrees until the bearing of the motorbike from the car is 310 degrees. How far, correct to 1 decimal place, has the motorbike travelled?
7. A plane flies from Dubbo on a bearing of 139 degrees for 852 km then turns and flies on a bearing of 285 degrees until it is due west of Dubbo. How far from Dubbo is the place, to the nearest km?
8. Stig leaves home and trave;s on a bearing of 248 degrees for 109.8 km. He then tuens and travels for 271.8 km on a bearing of 143 degrees. Stif then turns and travels home on a bearing of "a"
a. How far does he travel on the final part of his journey?
b. Evaluate a
9. Two cars leave an intersection at the same time, one travelling at 70km/h along one road and he other car travelling at 80 km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection?
I have question 9... I'm not sure about the others though
I have question 9... I'm not sure about the others though
Thanks for that answer happy_turtle, and welcome to the forums!! Absolute legend ;D conic I'll definitely come and give you an explanation of this style of question tomorrow, just need to finish this lecture series first ;) I'll run through one besides Question 9 ;D
Okay cheersJust going to highlight that you can post multiple qs in the same comment and avoid a warning. You can also edit your comment by clicking modify. You don't need to post consecutively to ask multiple qs :)
I need someone to comment below so then I can post a couple of new questions down here. If I post consecutively, it will be labelled spam and I may get a warning
Just going to highlight that you can post multiple qs in the same comment and avoid a warning. You can also edit your comment by clicking modify. You don't need to post consecutively to ask multiple qs :)Can I just say, on a person note I really do not wish to be bombarded by a continuous streak of questions especially of the same topic. It begins to feel like a chore, instead of a generous act, in helping.
Can I just say, on a person note I really do not wish to be bombarded by a continuous streak of questions especially of the same topic. It begins to feel like a chore, instead of a generous act, in helping.
Well, I asked only like 4 questions here. Also you seem to spend a lot of time on this online forum. May I ask but why is that the case? Whenever I'm online (supposedly trying to increase my post count in order to qualify for more free essays/creatives to mark) I tend to see you online here as well?It's becoming pushy when it's the same trigonometry based questions. If your diagram is wrong, then you don't make any progress altogether.
I need someone to comment below so then I can post a couple of new questions down here. If I post consecutively, it will be labelled spam and I may get a warning
Well, I asked only like 4 questions here. Also you seem to spend a lot of time on this online forum. May I ask but why is that the case? Whenever I'm online (supposedly trying to increase my post count in order to qualify for more free essays/creatives to mark) I tend to see you online here as well?
For a graph like x^3 if you were to differentiate it, it would be 3x^2 however whenever graphed here: https://www.desmos.com/calculator it doesn't seem to be the caseNothing changes about differentiating cubic functions compared to any other power functions. I don't know exactly what you graphed, but the two graphs should be the same.
Whenever you differentatiate, you are finding the gradient of the tangent/finding the rate of change, right?
For a graph like x^3 if you were to differentiate it, it would be 3x^2 however whenever graphed here: https://www.desmos.com/calculator it doesn't seem to be the case
Can someone here help me understand the concept of differnetiation and when it comes to cubic equations like this
Thanks
Nothing changes about differentiating cubic functions compared to any other power functions. I don't know exactly what you graphed, but the two graphs should be the same.
Whenever you differentatiate, you are finding the gradient of the tangent/finding the rate of change, right?
For a graph like x^3 if you were to differentiate it, it would be 3x^2 however whenever graphed here: https://www.desmos.com/calculator it doesn't seem to be the case
Can someone here help me understand the concept of differnetiation and when it comes to cubic equations like this
Thanks
x^3 is a cubic and 3x^2 is a parabola. They are two separate graphs that do not touch each other except for when they touch each other at the originYes x^3 and 3x^2 are indeed different graphs. When you differentiate x^3 you get 3x^2.
Just in case I am confusing, I hope this helps everyone outEDIT by Jamon: Ensure all discussion is civil and respects others right to ask questions.
Just in case I am confusing, I hope this helps everyone outTHe original equation is different from the first differentiation.
I told you, do NOT relate the y-coordinates of the derivative, to the y-coordinates of the original function.
Draw a tangent on y=x^{3}. The GRADIENT of the TANGENT, is the y-coordinate on the derivative.
Using this: http://www.teacherschoice.com.au/Maths_Library/Calculus/tangents_and_normals.htmAccording to the website you gave, the derivative is a measure of the GRADIENT of the TANGENT at the point (to the curve). Anything else?
According to the website you gave, the derivative is a measure of the GRADIENT of the TANGENT at the point (to the curve). Anything else?
Obviously the gradient of the tangent at the point does not have to resemble that of the actual curve. The tangent to y=x^{2} at (1,1) is 2. What does that have to do with the original curve? Nothing.
Okay I think I am very confusingOk. Let's clear one thing up.
ANyways, going back to basics, if you were to differentaite y=x, you would get y=1 right? This is finding the gradient of the tangent (i.e. the rate of change). As you can see, the gradient of the tangent is "visible" on this graph
For the example I posted originally, it was y=x^3 and if that was differentiated (i.e. the rate of change was found) it was y=3x^2 and that did not touch the graph at all except for the origin. Is this case shouldn't of 3x^2 of had been the gradient of the tanngent to x^3
If I am very confusing then just forget about this because I feel bad making all of you guys do this to me
Ok. Let's clear one thing up.
x is not necessarily a number. x is a variable. We have to let x = a certain number, to get the gradient of the tangent, at that number.
The plot of the derivative shows the gradient of the tangent, EVERYWHERE on the original curve.
It is not immediately obvious that 3x^{2} is the derivative of x^{3}. The reason why this is the case is that
Oh....Right, I get it now thank you thank you thank you ;DGlad that we eventually got there
Sorry for making you go through the pain in answering this :'(
Question: "A radioactive substance decays by 10% after 80 years. By how much will it decay after 500 years?"
My working:
T_{0} = 100
T_{80} = 90
T_{n}=T_{0}e^(kn)
T_{80} = T_{0}e^(80k)
90 = 100e^(80k)
k = (ln(0.9))/80
T_{500} = 100e^500k
T_{500} = 51.72655
Therefore the substance will decay by 51.7% in 500 years?
Permit k to be negative in your working out.
Edit: No never mind. This is exactly what happens when you try to rush.
51.76...% of the original mass is whatever is left behind.
100% - 51.76%... of the original mass is what has actually decayed.
Hey Jake!When you do past papers, do you struggle on questions? Because doing past papers "ineffectively" is the same thing as ineffective studying habits.
I have like 2 and a bit weeks to trials and have been pumping our past 2U papers but my marks in each has not improved at all!!
I've done the whole, do extra revision on stuff you get wrong but IT ISN'T WORKING!!! :(
What do I do? I'm usually a band 6 student in maths, so this is really annoying me!!
Thank you!!
Hey Jake!
I have like 2 and a bit weeks to trials and have been pumping our past 2U papers but my marks in each has not improved at all!!
I've done the whole, do extra revision on stuff you get wrong but IT ISN'T WORKING!!! :(
What do I do? I'm usually a band 6 student in maths, so this is really annoying me!!
Thank you!!
How do I do part (b) of this question?
Hey!
Firstly, welcome to the forums! Nice job studying for trials; sounds like you're really putting the hours in.
Firstly, two and a bit weeks is ages. You could learn the entire Maths curriculum from scratch in that time.
It looks like you've identified what areas you are weak in, because you have tried doing revision for topics that you lose marks in. What kind of sections are you struggling with? At the end of the day, if there is a section you're not very confident with, and you just do a billion questions of that type, you might not improve at all. That's because, in those sections, it might come down to UNDERSTANDING, before repetition. If you struggle to understand a concept, doing it wrong 100 times won't improve your mark.
Past papers is really all you can do. Write out questions you get incorrect, and redo them once a day for a few days until you can do them with ease. This will solidify the methodology in your mind, and make sure that none of your time is wasted. Again, if you let us know where you are specifically struggling with, maybe we can help!
Keep at it. You have so much time left, and doing past papers DOES help even if it feels like it doesn't. There's no like secret trick or anything, nothing I can tell you right now that will get you 100% in every paper you do. But past papers helps you improve, and identifying areas of weakness will help you improve. If you have any specific questions, post them here, and we can talk them through with you in a way that will hopefully help you understand the fundamental underlying mathematics as well as the answer itself.
You'll be fine! Keep at it.
Jake
Thank you! I will definitely keep doing questions, it's my nerdy form of procrastination! By the way, your chem lecture was great!
Just wondering but how do you graph lines (without plotting the points) for the following (I don't remember learning this at school):You can do it by letting x or y =0 and then find the intercepts.
x+y, x-y, x-y+3, y-3, x-6, etc (using no graphing calculator)
Thanks
Just wondering but how do you graph lines (without plotting the points) for the following (I don't remember learning this at school):
x+y, x-y, x-y+3, y-3, x-6, etc (using no graphing calculator)
Thanks
You can also use the gradient-intercept form for a line if it happens to be in the correct form, or is easy to get there. If we have an equation that looks like this:
Then it is just a line with a y-intercept of b, and a gradient of m (remember gradient is just rise over run) ;D
So for the equations, I plotted above you just assume they're all equal to 0
E.g. x-y+3, does this mean x-y+3=0?
We wouldn't assume it in all cases, but it is very common for equations to be expressed with everything on the left hand side equal to zero, called the general form. So that's how nerd1 interpreted it above ;D
So if it's an equation like graph x+3 then would it be x+3=0 or y=x+3 because in the original question there's no y value?
The question itself is flawed, they'd say which, but I'd interpret it as y=x+3 in that case :)
@conic
Let's just clear one thing up. If in the exam they wanted you to graph, something is always EQUAL to something.
Otherwise, as Jamon said, the question is flawed.
Has anyone here learnt a topic called the unit circle where you know the exact values of the trig ratios and where you learnt the fundamental formula (I.e. +k360)
Yep I think I can help there ;D if/when you have questions let me know!!Oh ok :P
Oh ok :P
I can now anyway! I went to a pretty decent 2U lecture on Trigonometry on Monday, lecturer was pretty good, think his name was James, or, Jameen, or something... ;)
Anyone here know how to solve this trigonometry equation:
Anyone here know how to solve this trigonometry equation:
Damm, it required that much working out. Woah, you guys are awesome. Cheers ;DThat would've made the factorisation process suck
COuldn't of you have divided by 3 first?
Jake what is that typing program you use to type up the answer to the question?
It's a nifty little program called Word; I suck at LaTeX (at least when it comes to slightly more complicated stuff, or typing quickly), so I prefer to use Word, screenshot, upload to Imgur and attach it here. Totally impractical, but I'm an idiot when it comes to coding-related languages.
You mean microsoft word?Uh huh.
How do I upload photos to this forum when the file is too big?
I tried to upload an image from my phone but it won't let me :(
You might have to do what I do, and upload the file to Imgur. I'm not super techy though, so I'll leave it to someone else to answer properly
Do you need a imgur account?
Also if anyone can help me with these Q's it would be great:
4. g(x)=2x-1.find x if
a. g(x+1)=3
b. [g(x)]^2=3
The second one could've been done by quadratic formula
Also, no.
ThanksBefore tackling these questions, can I ask about if you've revised how functions actually work?
Also sorry for the overburdening of questions:
5. a. g(x)= x +(1/x)
Prove that g(x)g(x+(1+x))=g(x^2)+3
b. f(x)= (a^x+a^(-x))/2
Show that f(2x)=2[f(x)]^2-1
c.g(x)=log((1+x)/(1-x) .Show that g(2x/(1+x^2 ))=2g(x)
d. f(x)=log((x+1)/x)
Show that:
I. F(1)+f(2)+f(3)=log4
II. F(1)+f(2)+…+f(n)=log(n+1)
The second one could've been done by quadratic formula
Also, no.
Before tackling these questions, can I ask about if you've revised how functions actually work?
I did it last term for school but these were unanswered questions from a while ago which I found out today. The reason why it was unanswered was because I wasn't sure of how to do it back thenSo have you tried looking over your resources and figuring how to do them now instead of blindly giving us your unfinished homework?
So have you tried looking over your resources and figuring how to do them now instead of blindly giving us your unfinished homework?
I did back then. Just curious but do these questions seem easy to you all?
I did back then. Just curious but do these questions seem easy to you all?That's because we have all studied it before.
Hi! So i was wondering what the difference between a solution and a root is.
For example, when the discriminant = 0, it says theres one solution but two real equal roots and i have a diagram and all but i dont really understand that.
Hi! So i was wondering what the difference between a solution and a root is.Alternative solution/explanation to rui's, but I think it is more friendly to beginners.
For example, when the discriminant = 0, it says theres one solution but two real equal roots and i have a diagram and all but i dont really understand that.
Hi! So i was wondering what the difference between a solution and a root is.
For example, when the discriminant = 0, it says theres one solution but two real equal roots and i have a diagram and all but i dont really understand that.
Hi, at school we have started probability. I was wondering would anyone have tips on how to remember whether event A and B are independent or mutually exclusive. I am confused about the probability rules in general. There are so many so how would you know which rule to use? TTT ^ TTTGenerally, you can use your intuition to determine if multiple events are mutually exclusive or not. If two events are mutually exclusive, they cannot occur at the same time (simultaneously). If you want, you can provide some examples and I will attempt to explain which are and which are not.
I have tried to answer this question but i didnt understand how to do it
solve 2e^2x -7e^x +3I can assume you meant e^(2x) but more importantly is the expression equal to 0?
i let u = e^x then found u but cant remember where to go from here Thanks
solve 2e^2x -7e^x +3
i let u = e^x then found u but cant remember where to go from here Thanks
Hey, this may be a simple question but i cant seem to grasp the idea of domain and range, for example a common question would be the multiple choice ones where it says find the value for x that satisfy this equation ( sorry dont have one on me ) i can solve it but i wont know what the domain is e.g 4<= x <= 2, 4< x while x> 2etcFind the values for x that satisfy this equation sounds like just solving something such as 5x+3>5, i.e. an equation (or inequality)
Thanks
Is anyone else struggling with Applications of Calculus?? Does anyone have any tips on how to do those describe the motion of a particle questions??I'll just go through what I know from SACE, it may be a little different for you, but I'm sure that the fundamentals are still there.
Is anyone else struggling with Applications of Calculus?? Does anyone have any tips on how to do those describe the motion of a particle questions??
Oh alright, just different notation between the states :)
Oh alright, just different notation between the states :)Yep. All good here; I'm not entirely why sure why x, r and s get juggled to represent displacement. (Incidentally the latter two are found in the HSC physics courses.)
Hey,
This question might be super simple, but I've been having some trouble with this question, mainly part ii.
Could someone please explain how to do it?
For part (i) just gotta be careful when factorising by completing the square. In point gradient form the tangent has equation
y-(t-b)^2 = 2(t-b)(x-t)
So y = (t-b)(t-b)+(t-b)(2x-2t)
So y=(t-b)(t-b+2x-2t)
=(t-b)(2x-t-b)
Hey was looking for help with a couple questions ive been stuck on
Part ii for the area under the curve questions
Thanks!
What does it mean by "magnitude" in maths?
I searched it up and it said that "magnitude is the size of a mathematical object" but then, I'm thinking, what? This is so confusing
Thanks :D
Hi! just wondering how you would go about graphing
dv/dt=1−(√2)sin(πt/60)
between 0<=t<=120
Hi, I'm just having trouble working through methodology of this question. By substitution i can assume the answer, but I want to know how to actually work it out.
Find the radius of the circle that has its centre at the origin and a tangent with equation given by 4x - 3y - 5 =0
I think this question requires the use of the distance between a line and a point formula! Since the radius will be the line perpendicular to the tangent, to the origin, you can literally plug in the values and a radius should pop out.
(http://images.tutorcircle.com/cms/images/108/formula-of-distance-from-a-point-to-line.png)
Where A=4, B=-3, C=-5, x=0 and y=0
I think the radius turns out to be 1!
Jake
Why is cos theta not equal to zero at the beginning of the question?
Thanks I get it nowFor the first one your solution is actually the same as the answer. But the answer makes it tidier, which is good practice that you should be getting use to.
In this equation: (x-3)(x+5)=<0 I got x=<5 and x>=-3 as the answer but the answer says -3=<x=<5. What am I doing wrong?
For this question 4x^2-12x+10>0 how is the answer all real x
Thanks guys ;D
For the first one your solution is actually the same as the answer. But the answer makes it tidier, which is good practice that you should be getting use to.
Note how x≤5 can stay as x≤5. But x≥-3 can become -3≤x.
Just combine them together to get -3≤x≤5.
This answer is tidier because you have an enclosed domain, not one that's going on infinitely and forever. It shows that x is between two things where possible.
Thanks
How do you do the question I attached below:
I know it involves substituting in the function but I find it confusing and very hard to understand
Thanks
How do you do the question I attached below:
I know it involves substituting in the function but I find it confusing and very hard to understand
Could you please elaborate further for what I have attached below because I don't seem to understand thatApplied the definition of a function?
Thanks ;D
Hey,
I'm just having a bit of trouble with this question. Could someone please give me an explanation of how to do this. Thank you!!!
Let g(t) be another function defined for all t ≥ 0. The gradient function is given by g′(t) = 33/10 te^{−kt }.
It is given that g′(t) attains the greatest value at t = 7.5 and g(0) = 0. g′(t)
where k is a positive constant. The diagram below shows a sketch of g′(t) against t.
(i) Show that k = 2/15
(ii) Use the trapezoidal rule with four sub-intervals to estimate the shaded area in the diagram above.
(iii) Explain why your answer to (ii) is an estimate for g(12).
Hey there, wondering whether someone could please help me out with part b) of this question that I've attached. Not quite sure how to approach it! Thanks so much :))
2U Question. Halp.This does not look like a 2U question given that I do not believe spirals are so easy to analyse. However this is the best I could come up with.
2U Question. Halp.
How do I differentiate this?
Heyyy :) :)
I need some help with how i should approach the following;
The parabola P has the equation y^2=8(x+2).
i) write down the coordinates of the vertex of P.
ii) find the coordinates of the focus of P.
iii) write down the equation of the directrix of P.
iv) sketch the parabola P showing the features found above, as well as any x or y intercepts.
cheers
Hey there!! No worries I'll give you a hand! ;D
Before we do, we notice that the equation is in the typical form of a 'sideways' parabola:
If we consider it this way, we can immediately read off the coordinates of the vertex (h,k) as (-2, 0):
We can also determine the focal length:
Now, remember that the focus is 'a' units away from the vertex. This is a right facing parabola (try some random points to check), so it is 2 units to the right of the vertex:
The directrix is 2 units the other way (remember, in this case, the directrix is a vertical line since the parabola is sideways):
All of this should help you sketch ;D does that help?
If they a function is monotonic increasing does that mean f(x)>0 or f(x)>=0? If so why, I can't seem to distinguish between the twof'(x)≥0
f'(x)≥0
Don't forget the dash
A stationary point doesn't necessarily impede it being "monotonic" increasing. f(x)>0 still satisfies monotonic increasing but more specifically it means strictly increasing.
I don't get it. Could you please elaborate on f'(x)>0 and f'(x)>=0 (and try to give me examples)
Thanks
I don't get it. Could you please elaborate on f'(x)>0 and f'(x)>=0 (and try to give me examples)
Thanks
Finally this cleared things up for me ;D
Thanks
When would you actually use it (with an example question)
Can someone explain 'b)' and 'c)'?
Thank you!
Can someone explain 'b)' and 'c)'?
Thank you!
For (b), you'll have to differentiate for the velocity as a function of time. Then solve for zeros.
For (c), you'll have to use a definite integral. Assuming $t$ can only be positive, $x$ is defined over the interval \([0, 7]\), so 'altogether' means from t=0 to t=7.
These are standard procedures in kinematics :)
Can someone explain 'b)' and 'c)'?
Thank you!
Need help with this Q
Let's start by simplifying some stuff
By difference of two squares. But, p+q=1, so
Now, let's use sum of two cubes
As p+q=1
As required
Thanks Jake
How would I do question iii and iv
How do I differentiate each function with respect to x?
Sorry, but I haven't become familiar with LaTeX yet, but I will do soon.
Could someone assist me with the integral of (e^{2x-1} +3)^{2} dx?
Thankyou
Alright, did it a different way, would you always recommend expanding?
Alright, did it a different way, would you always recommend expanding?
How do I find the deriative of the following?
How do I find the deriative of the following?
Hey Conic,This.
A lot of your questions appear to be fairly normal applications of the Chain Rule, Product rule or Quotient rule. The rules are described below.
(http://mathcs.slu.edu/history-of-math/images/history/thumb/7/7f/Pqr-rules.jpg/350px-Pqr-rules.jpg)
I don't think that it is very helpful if we just keep answering your questions, because that doesn't seem to be helping you very much. Rather, I think I would prefer if you post up your attempt at a solution, so that we can correct you and help you as you go. My main advice is to (for product/quotient) identify u, v, u' and v', write it all down then simply apply the formula. Give these questions a go; will be happy to help once I can see that you've made an attempt!
(http://i.imgur.com/CTH9ycL.jpg)
Oh yeah I was meant to use the product rule. Apologies.Here's my feedback:
Anyways here is my working to the questionSpoiler(http://i.imgur.com/EqDdbz2.jpg)
(http://i.imgur.com/zGV36Yr.jpg)
Someone please correct me if I am wrong
Moderator edit: Put images in spoiler
Hey guys-
Can anyone help me understand this question?
Help with iv and v
Need help for sketching the following:
y= -x^3/6 + x^2/3 - x/6
I did y' and got -3x^2/6 +4x/6 -1/6=0 and when I try to solve for the x intercepts, I can't seem to find them
Also I'm having trouble drawing a y dash table in order to graph it, like what are the steps to doing that and how do I fill it in?
Thanks guys :D
(http://i.imgur.com/oDcI5Ll.jpg)Nice, but I have a few comments.
(http://i.imgur.com/oDcI5Ll.jpg)Mod edit: Swapped over the quote.
thank you for the help :D
I was wondering how exactly did the surds disappear to equal 2/8?
I also wanted to ask how do you know when to use a plus or minus sign? I've only learnt that its only for when the power is to 2?
Mod edit: Took out the quote. I'm not the one who deserves the thanks here.
I was also wondering how would you do these 2 questions? I am not sure how to approach them
You might make both a bit easier by making a substation for yourself!
In the first:
Have a go at a similar thing in the second one! Make a substitution to turn it into a quadratic equation, and see if you can follow the same procedure as me ;D let me know if you need more of a hand with it ;D
thank you for the help conic curve :D
I was wondering how exactly did the surds disappear to equal 2/8?
I also wanted to ask how do you know when to use a plus or minus sign? I've only learnt that its only for when the power is to 2?Mod edit: Swapped over the quote.
Thank you for your help :D i was able to get the answer for the second one by following your example.
I also wanted to ask for a question like this how should you approach it? Im not sure where i should and how to begin ???
How do you know that lim a^x = 2?This does get forgotten by heaps of 2U students to be fair but it's absolutely crucial.
I have never used or hear about lim before
This does get forgotten by heaps of 2U students to be fair but it's absolutely crucial.
The exponential a^x (doesn't have to specifically be e^x) has a horizontal asymptote at y=0, for very large NEGATIVE x. We say that the limit as x goes to negate infinity is therefore 0.
Because fact is if you raise a number to a really negative number it just goes down to 0
However, if you've never heard of what a limit is, then there's something that you weren't taught that belongs in 2U. I do suspect you're a VCE student but in here I use anything that belongs to the 2U course.
Another world is a WACE student ;D you can think about limits intuitively without the notation! Like, for the limit of something as x approaches infinity, you mean, What happens as you pop in MASSIVE values of x. It's just a formal notation for saying, when x is HUGE, or x is HUGELY NEGATIVE (-infinity), or (less important for you), when x is REALLY CLOSE to some other value :)Hmm. Yeah I thought that VCE also do have limits.
Hmm. Yeah I thought that VCE also do have limits.
But I had a look in the WACE courses. There's an explicit reference to limits in relation to the definition of the derivative in the methods course.
Got a foolish question.
Indefinite integral of (3)^(2x-1)
Thanks guys
ah - more complicated than I thought but I got it. Awesome, you're a legend Rui!
Yeah that was definitely not a foolish question (not that there are any foolish questions, but that one is actually pretty tough to do unless you know the trick) ;D
Yeah 100% - that is one of those things to look out for when you are stuck I guess. Goes into the list of:
-equations reducible to quadratics
-factoring
-simultaneous equations
-the limiting sum
-graphing the problem
etc etc
That being said, I have another question for probability:
a) Given a standard deck of cards, a player is dealt five cards. What is the probability that 4 aces are drawn?
b) Dealt five cards, what is the probability of all cards being of the same suit?
I've been trying a four of a kind +1 kind of approach but it hasn't worked.
Cheers guys
The point: When ordering isn't specified, the number of favourable outcomes is changed. (I had a feeling my answer was wrong but I couldn't see where so blindly.)
Hey guys i was wondering how to effectively study maths in the sense that i do past hsc papers and review my mistakes but i feel like it isnt necessarily improving my maths skills. Like even doing maths everyday i manage to forget small details and concepts of questions, im not sure how to explain it but an example would be like one of my maths exams i did well in, when i sat the same exam again 2 months later i manage to forget how to do some of the questions despite doing at least 30mins to 2 hours of maths everyday.
Also, when a question asks for maximum velocity e.g attached how would i do part (ii)
Thanks
Hey guys i was wondering how to effectively study maths in the sense that i do past hsc papers and review my mistakes but i feel like it isnt necessarily improving my maths skills. Like even doing maths everyday i manage to forget small details and concepts of questions, im not sure how to explain it but an example would be like one of my maths exams i did well in, when i sat the same exam again 2 months later i manage to forget how to do some of the questions despite doing at least 30mins to 2 hours of maths everyday.
Also, when a question asks for maximum velocity e.g attached how would i do part (ii)
Thanks
@Jamon, ah i assumed you had to differentiate since it said maximum however i had never seen a question like this so i was confused on what to do
I havent touched the topics individually since ive been taught them so i guess it does make sense, should probably get down with the basics before doing the HSC papers to be more effective?
@Jake, Thanks, but i suck with inequalities so ill stick with Jamon's way
Specifically iii) please!
This one is a series/probability one, not sure how to get to the answer.
Thanks!
@Jake, Thanks, but i suck with inequalities so ill stick with Jamon's way
Hey! This is a fairly common ace up the sleeve for BOSTES, the same style of question was at the end of my MX1 exam:This looks good (y)
First question is fairly easy, remember that there are 36 possible outcomes for throwing two dice, and only one yields a win!
For the second bit, remember that for Pat to have a second turn, Chandra must not roll a double six on her turn, otherwise she would win, AND Pat must not roll a double six on his first turn either. This creates the following:
Now we get technical. For Pat to eventually win the game, we need to consider an infinite number of turns. After all, the game could go on forever, couldn't it? Let's look at the series for just the 1st-3rd turns:
Notice what's inside the brackets? An infinite series! We can find it's sum using the formula:
Note that we are allowed to use this formula because the common ratio is less than 1 ;D
Using that formula should get the answer you need! ;D
Hi i was wonering how do I solve these questions?
I'll just help you out with the first, one, because once you've done one you can definitely figure out the rest yourself! You need to start with the relevant formula for the type of sequence (ie. geometric or arithmetic). For arithmetic sequences;
Where n is the term number, a is the first term, and d is the difference between subsequent terms. So, we know two pieces of information.
We can quickly subtract one equation from the other (to eliminate the a term)
So, subbing back into an equation above
Giving us the final formula
We've already found the first term (a=2000). The 51st term will be
The same approach (simultaneous equations to fill in the relevant equation) should be taken for your other questions. If you can't get them, post up your attempt at a solution and I'll help you out!
Jake
thank you for your help with Q29 but for Q30 I'm not sure how to do it. I got a really large number that is completely off the correct answer
I found why I was getting it wrong yay ;D
(http://uploads.tapatalk-cdn.com/20160903/9c8e20f1a0050a56205d57886442b93f.jpg)
Hey guys im not very good at doing probability qs can someone help me out with this one?
Thanks !
[IMG]http://uploads.tapatalk-cdn.com/20160903/9c8e20f1a0050a56205d57886442b93f.jpg[/IMG
Hey guys im not very good at doing probability qs can someone help me out with this one?
Thanks !
(http://uploads.tapatalk-cdn.com/20160908/fbd35324c152443c57020f766686223e.jpg)
Hey guys im not really sure how to do question i) , i got out cos(pi on 6) = -1/2 but not really sure where to go from there..
Thanks !
(http://uploads.tapatalk-cdn.com/20160911/db59b46aafce63ccd1e9b1a018625847.jpg)
Hello again :), i was wondering how to get the equation for example 10.. dont really know what the question is asking. Thanks !!
Im not sure if this is past hsc
How do you do this question
(http://i.imgur.com/DiZub5k.jpg)
This is what I gotYou didn't understand what Jake said.
I think it may be wrong
(http://i.imgur.com/gOFmDSR.jpg)
This is what I got
I think it may be wrong
(http://i.imgur.com/gOFmDSR.jpg)
As an example, I've plotted the first two derivatives of the basic cubic graph. Can you see what's going on?
(http://i.imgur.com/tK6XbBG.png)
Jake
Nah not really. Which one would be f'(x)?
They interesect at the originNot the point.
Not the point.
Here I might have a favouritism towards the graphs I suggested (Jake picked the most coincidental) but read the above posts 5 times.
Where f(x) is INCREASING, f'(x) is ABOVE THE X-AXIS etc.
Know what you're comparing. To know what you're comparing, read all of the above posts 5 times. Read and compare simultaneously
So imagine f'(x) was the cubic in the image I have attached aboveFor the sake of this question, STOP considering f"(x).
Is it the fact that f(x), f'(x) and f''(x) are all monotonic increasing
Also for this question below, for 16 and 17 I know how to do it in my head but am not sure how to geometrically prove it
Also for 18, the answer is 6,6 but I got 3
(http://i.imgur.com/W3VpSJs.jpg)
To prevent confusion I decided to redo the question given the information you and Jake gave meHow you labelled your +,s and -'s are correct but the graph you ended up drawing makes no sense.
If it is above the x axis, it is monotonic increasing and if it is below the x axis, it is monotonic decreasing
(http://i.imgur.com/bAbUgni.jpg)
WHat is the answer to thisWell what was your attempt?
Well what was your attempt?
I found the domain first and got x is not equal to 4 and subbed back in to the original equation in order to find the range but then I get 1/0 as the range (which is infinity which is all y)That's only a part of the answer.
Am I right?
Hey! So I was wondering if it is worth buying a Mathomat or Math-Aid to take into the exam? (btw they're permitted by BOSTES)They are most certainly permitted and I bought one in for each of my maths exams.
How am I supposed to do vi)
Answer for v) is (40)^1/2
Thanks
How many past papers shpuld we complete before hsc?
I think that depends on the person! I personally did over 20, but that was probably excessive, do however many you think you need to!! Your aim should be to be able to know how to do almost any question on sight ;D
Just curious but how do I change my username?
How do i attempt this question? Havent done anything like it before. Dumb brain immediately thought of pythag to work out the slope lol
__________________________
__________________________
Answers to the 2015 HSC can be found here.
Alternatively (or, rather, using the exact same method but without the actual integration), you can remember that the area under the curve is the change in displacement. Assuming that, prior to t=4, the particle continues to move away from the origin, you can easily find the area under the curve (16) and add that to the original displacement (2). I would have done Rui's way, and they're exactly the same.I was going to do it that way, but then I remembered the original displacement was 2 and that's just a bugger. Don't feel safe just adding 2 on for most questions.
__________________________
__________________________
Answers to the 2015 HSC can be found here.
Hi, I was just wondering how you find the limit approaching infinity (I get how to do it for the limit approaching an actual number). E.g. Idk just a simple equation like lim x->infinity (x+1)/x
Ok, thanks!
How is this done?
Like Jamon says, it's as many as you think works. That being said, if you did two past papers a day (for different subjects), 5 days a week, for two weeks, that's already 20 past papers. You've got way more than two weeks for most of your subjects, so plenty of time to do heaps of papers!
I'm confused on how they found c in the tangent equation, please help.Derivative of y at x=a will give you the gradient of the tangent. Subbing x=a back into y will give you a point, that the tangent will also pass through. Subbing this point into your tangent equation will give you c.
Determine the equation of the tangent to the graph of y = x^(2)e^(x) + 1, x ≥ 0 at any point where x = a
I'm confused on how they found c in the tangent equation, please help.
Determine the equation of the tangent to the graph of y = x^(2)e^(x) + 1, x ≥ 0 at any point where x = a
Hi jamonwindeyer and jakeisloveYour textbook for mathematics doesn't matter at the end of the day, because you're going to be glued to past papers.
I just wanted to know what text books you used for physics (jacaranda?) and maths (cambridge?)
Thanks
Your textbook for mathematics doesn't matter at the end of the day, because you're going to be glued to past papers.
Though with that out of the way, in general Cambridge is the recommended textbook. This is due to its wide range of coverage and its suitability in addressing all levels of student capability. It starts off nice and easy for people to start grasping the basics and still has a range of challenging problems for the very keen student.
In general, I do advocate for it. But I didn't use it. I used Fitzpatrick for 2U and Maths in Focus (this textbook is actually strongly advised against under normal situations) for 3U.
Note that every textbook has its pros and cons. An answer cannot be made definitively as it is entirely based off personal preference. Cambridge just happens to be the stronger option in general.
With physics, Jacaranda and Physics in Focus are the two recommended. Not the place to be discussing it though.
Jake's surname is "Silove"
Hi jamonwindeyer and jakeislove
I just wanted to know what text books you used for physics (jacaranda?) and maths (cambridge?)
Thanks
Hey all.
Quick question here
Evaluate lim θ -> 0
Of (sin2θ)/3θ
Im not sure how to arrive at the final answer.
Any help would be appreciated.
cheers :^)
Can you explain how sin2θ/2θ = 1
Since sinx/x = 0, i still don't understand the above
Can you explain how sin2θ/2θ = 1My apologies, I made a mistake in typing. That 0 is meant to be a 1. I will fix that now
Since sinx/x = 0, i still don't understand the above
for the limit of sin(x)/(x), is x approaching 0?Yes. x goes to 0.
I check with wolframalpha the limit is =1 too: https://www.wolframalpha.com/input/?i=lim+x-%3E+0+sin(x)%2F(x)
I'd appreciate if someone could help me with this one:
Thanks!
Hey! So, essentially, we need to find a value for k such that the area under the curve from -6 to 4 equals the area under the curve from 4 to k (that way, the negative and positive areas cancel out!ok, thanks :)
You can find the area under the first section in many ways; there's a formula, which I don't know, so I'll divide it into a triangle and a rectangle. The rectangle has area 10*2, and the triangle has area 10*(1/2)*3, so the total area will be 35 units squared.
The area of the second section can be found in the same way; the rectangle will have area (k-4)(4) and the triangle will have area (1/2)(k-4)(2). So, the total area will be (k-4)(4)+(1/2)(k-4)(2). Now, we need these two areas to be the same, so
As required.
Jake
Hi again :PYes that last step wouldn't be required. Still a rational denominator.
So concerning the attachment (the question is express with a rational denominator), for my answer i got the second last line: 8(2-sqrt7)/3 (which is just factorised from the final answer). If i left it in the factorised form, would i still get full marks?
Yes that last step wouldn't be required. Still a rational denominator.
Hey guys,
How does (d-6)^2 - 4 < 0
become 4 < d < 8 ?
im confused with the individual steps
Hey guys,
How does (d-6)^2 - 4 < 0
become 4 < d < 8 ?
im confused with the individual steps
Hey guys,
How does (d-6)^2 - 4 < 0
become 4 < d < 8 ?
im confused with the individual steps
Please help me on this question. So I managed to get the mean and standard deviation correct, but i didn't understand why they made certain choices.Statistics is not in the HSC mathematics course.
The probability of a seventeen year old boy having a part-time job while at school is 0.4
In a sample of 80 seventeen year old boys, what is the probability that between 20 and 25 of them have a part-time job.
The answer key says the answer is 0.07
Hey! There are heaps of ways of going about this, but this is how I generally work through these kinds of questions. Let me know if you don't understand any steps!
Now, I usually work out inequalities by first solving an equation. As such,
So, we now have two solutions for d. The range will either be OUTSIDE (ie. d>8, d<4) or INSIDE (ie. 4<d<8 ). You can figure this out in a number of ways; the easiest is to sub in a point to the original equation. Let's say that d is equal to 5.
Clearly, the relationship is true for d=5, which is between 4 and 8. Therefore, the solution for d is
As required!
Jake
Ignore method 1 if it makes no sense and focus on method 2. Because it is the exact same as Jake's method
Hi guys! I'm a bit confused with this question:
A piece of wire of length 50 cm is cut into two sections. One section is used to construct a rectangle whose
dimensions are in the ratio 3 : 1; the other section is used to construct a square. Find the dimensions of the
rectangle and the square so that the total enclosed area is a minimum.
I'm confused with the 3:1 ratio and how am I going to incorporate this in another similar question that talks about ratio? Thank you :)
A particle is moving in a straight life, starting from the origin. At time t seconds the particle has a displacement of x metres from the origin and a velocity v m s^-1. the displacement is given by x=2t - 3ln(t+1). Find the distance travelled by the particle in the first 2 seconds. (HSC Paper 2000).
Can someone please help me out
What has been the main topic that they have assessed from the prelim course in the hsc exam?
I had a look: The question actually asks for the first THREE seconds. This will mean that my final answer won't match with the actual answer since you said two seconds (presumably a typo). Also, please indicate any previous parts if there happens to be some in the future.
From what ive seen, locus & parabola. Also, just basic algebra and quadratics too.
Alright thank you! Do you know anywhere that I can find a whole bunch of locus questions from past papers (other than going through every past paper)?
I had a look: The question actually asks for the first THREE seconds. This will mean that my final answer won't match with the actual answer since you said two seconds (presumably a typo). Also, please indicate any previous parts if there happens to be some in the future.
in regards to this question, for case one, it is t(1/2) - t(0) & you got 3ln(3/2) - 1. how did you get that because im getting 1 - 3ln(3/2).The absolute value brackets are there for a reason.
Hey guys so i was just curious as to how to study for the finance (money) area of maths because i am terrible at understanding the question and answering them and i find that theres alot of finance based questions in the exams so please any advice would be grateful!! :)Effectively, every finance question is just the same thing in different words.
also i do so so so many practice questions and i still struggle in understanding them!
Hey guys! I'm having trouble with this question. Thank you! :DThe question asks to list the possibilities, hence you should. However I'll structure my answers as though they weren't listed
Two dice with their faces numbered 1 to 6 are tossed.
i. By listing the possible outcomes find the probability of
a) one die showing a 6 with other showing at least 4
b) one die showing a 6 with the other showing 3 or less
ii) Deduce from the results in part (i) the probability that neither die shows a 6.
Guys I have no Idea how to answer this question at all. Its question 15 b) from the 2015 paper.
(http://i63.tinypic.com/106mzac.png)
I would say for:
i) (triangle)ACB = (triangle)DCF
AC=DC (Given)
(angle)ACB=(angle)DCF (Angles bisect/intesect at 90' - Given)
- SAS somehow??
I dont know what else...
i
AC is not equal to DC either. AD is equal to DC.
And a hint for part (ii) - you were given a pair of similar triangles in part (i). You'd be crazy to not use it.
AC is not equal to DC either. AD is equal to DC.
And a hint for part (ii) - you were given a pair of similar triangles in part (i). You'd be crazy to not use it.
Guys I have no Idea how to answer this question at all. Its question 15 b) from the 2015 paper.
(http://i63.tinypic.com/106mzac.png)
I would say for:
i) (triangle)ACB = (triangle)DCF
AC=DC (Given)
(angle)ACB=(angle)DCF (Angles bisect/intesect at 90' - Given)
- SAS somehow??
I dont know what else...
i
(http://uploads.tapatalk-cdn.com/20161007/58acb99cb53b5093233aba2f8a357806.jpg)
Can someone help me with 15) ii. Im not sure about it
(http://uploads.tapatalk-cdn.com/20161007/58acb99cb53b5093233aba2f8a357806.jpg)
Can someone help me with 15) ii. Im not sure about it
Which ii) did you need help with? There are two in the image you've postedI just noticed that lol
Hello, I am sort of having trouble with geometry, for similar triangles etc. How many proofs do we need for each?? ???What do you mean by "each"? You only prove two triangles are similar at a time, not three or four at a time.
What do you mean by "each"? You only prove two triangles are similar at a time, not three or four at a time.
Instead, there are three tests that you need to know:
- Equiangular: Two angles in both triangles are equal
- All three sides in proprotion
- Two sides in proportion, included angle equal
(Note: There is a similar one for RHS but it is not needed)
The similarity tests can be matched up with a congruence test
Equiangular VS AAS
3 sides in prop VS SSS
2 sides in prop + inc. angle VS SAS
Okay Thanks! What I meant by 'how many proofs for each' was similar triangles, congruent triangles, alternate etc :)These can be found in any textbook. They stem down from properties of the geometric figure we're interested in.
Hey Mathematicians,
Do any of you have any tips (besides practice as it doesn't seem to work) on doing geometry-related questions such as Question 10, B from the 2006 HSC exam (http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_06.pdf)?
I often struggle to see the connections between what has been given and what is being asked.
Much appreciated. :P
Hey Mathematicians,
Do any of you have any tips (besides practice as it doesn't seem to work) on doing geometry-related questions such as Question 10, B from the 2006 HSC exam (http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_06.pdf)?
I often struggle to see the connections between what has been given and what is being asked.
Much appreciated. :P
Hi,
Can you please explain how the the solution to question 14 (d) is obtained and how exactly the graph is interpreted [2013 HSC] http://boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf
Hey guys,
Could someone please help me with this question?
I'm not sure where to start and have been blankly staring at it for a while now.
Thanks in advance :)
____________________________
(http://i1164.photobucket.com/albums/q566/Rui_Tong/Screen%20Shot%202016-10-10%20at%201.29.11%20PM_zpsnz6vxwit.png)
I want to let you have a go at (iii) first. Use a graph similar to the graph in (ii). Come back with whatever progress you have.
Hi, I'm can some please complete this question for me.
find the stationary points on the curve y=(x-4)(x+2)^2 and hence sketch the curve
TYVM i understand. i just didn't know you had to expand the equation of the graph :-[
I was wondering how do we simply imaginary numbers? We just started doing them but im already confused.
I was wondering if i could get help understanding how to graph cubics and tan graphs please
Wait is this any maths course or just 2 Unit cause I swear I have seen nothing like that before.It's not in 2U.
It's not in 2U.
Hey Liiz:
HEY Im jake (obviously not haha). Im a year 12 student who completed my 2u HSC mathematics course in year 11 and lm just happy to help out here. Now, this type of question is amongst one of the most difficult ones in geometrical applications of calculus, and unfortunately in HSC exams there WILL be harder ones. But don't worry, once you have practised enough, you will begin to seize some tricks to approach these questions.
Before I begin answering your question, just a few generally tips to help you answer questions like these where only one number value is provided:
BEFORE YOU DO ANYTHING, DRAW A DIAGRAM WITH LABELS
1. Highlight all USEFUL INFORMATIONS (in this case, highlight rectangular box, square base, no top, 500cm^3 and least area)
2. Appoint two variables to the unknown sides (in this case, I named the side length of the square base as x, and the height of the rectangular box as L)
3. There will be at least one number quantity in every one of these questions in 2u mathematics, so the first equation you should construct, using your name variables to construct an equation that uses the numbers provided by the question
4. Draw out the relationship between the two variables through this equation that you have constructed
5. Construct another equation using your variables and the subject that is asked for in the question (In this case, for example, we constructed an Area equation which directly relates to what we are asked to find)
6. Substitute in the equivalent expression of a variable (In this case, for example, L = 500/x^2, so we substitute any L we see with 500/x^2) to reduce the total number of values down to one, so that we can construct an equation entire out of only one variable, which then allows us to perform differentiation
7. Clean up the equation after the substitution to make life easier
8. Differentiate the equation
9. Let this derivative = 0 to find any stationary points (In an Exam, YOU MUST STATE "LET dy/dx = 0 TO FIND ANY STATIONARY POINTS, OTHERWISE MARKS MAYBE DEDUCTED!!!)
10. Solve the derivative equation and find a value for your variable which will be your stationary point
11. Test both sides to show that a local minimum/maximum occurs at your stationary points
12. Substitute your minimum value back into the area equation (or maximum value if the question asks for maximum area) to find the minimum area (or the maximum area if you substitute in the maximum value)
So here is my solution:
(http://i.imgur.com/t6wtIk1.jpg)
Hope you find my solutions clear and useful! If you are confused with anything, dont hesitate to ask!!! :D
Best Regards
Jacky He
Hey,
Could someone please explain to me how solve the following?
7sin3x=2x-1
Thank you in advance! ;D
Hey! I feel like this would be really obvious but I'm struggling with a few questions like find the gradient of the tangent to the curve: y= square root of x at (4,2) and find the gradient of the normal to the curve y=x^{2} + 5 at (-2,9)
___________
Rui I swear that the normal is the exact same method as tangent but you swap it to the reciprocal? Like in my method above^^*Negative reciprocal
*Negative reciprocal
But yeah nothing I said really contradicts the main idea you posed
No I just meant the second part because I thought you were alluding that the answer was -1. Had no idea what you were trying to sayI never said that. I said that two lines that are perpendicular have their gradients multiply to -1.
I never said that. I said that two lines that are perpendicular have their gradients multiply to -1.
Your answers should be close to WolframAlpha's exact answers
i need help with this question ty
sketch y=√x+5 for −4≤x≤4 and find its max and min values. btw, the square root is over x+5, not just x
This question. This was a 1998 2 unit paper and I know I didn't get taught what the hell a table of possible outcomes is. Was this part of the older syllabus or something? Cause nowadays they just ask us to do probability trees.It means to draw a table listing out every single outcome.
I'm stuck on part b) of the question, but this includes the whole thing: A farmer wants to make a rectangular paddock with an area of 4000m^2. However, fencing costs are high and she wants the paddock to have a minimum perimeter. a) Show that the perimeter is given by the equation P = 2x + 8000/x b) Find the dimensions of the rectangle that will give the minimum perimeter, correct to 1 decimal place.
(Sorry new to this - don't know how to reply to one comment on its own...)Can you please show me your working out? There's guides to how you can upload images onto this forum if you don't want to type it.
In reference to my differentiation and nation of SP question, I tried testing points on either side but it doesn't match up to the answers or what the actual graph looks like.
Could you solve it and let me see if my answers match. The 2 SP I got were (5, 20) and (-5,-20). I thought the first was the minimum and the second a maximum.
Thanks in advance.
Can you please show me your working out? There's guides to how you can upload images onto this forum if you don't want to type it.
Or you can upload through the ATARnotes app.
Ok, so my differentiation is in my working.Its 2x+50/x right?
I used the table in the picture to figure out if it was the maximum or minimum. For (5,20), because it is negative before and positive after, I thought that would make it a minimum but the answers have maximum. Turns out my diagram isn't right according to geogebra so ignore that btw.
I haven't learnt using second derivatives, but am keen to learn it if helps me understand the question.
Thanks again
Hey Rui!
Need help for the whole question please!
(http://i63.tinypic.com/260d1xl.png)
Hi, can someone please help me with the 2015 q.16 c. Looked at the working out and cant understand it :/
Thank youuu :)
What are the steps to graphing this sine curve?
Hi, thanks for the help but how did u get 2R/3
I have to differentiate: 3x/√3x-4+√3x-4
I end up getting (9√2)/8 but the answer is (3√2)8
I'm so close yet so far... help!
Oh I'm so sorry, I meant to add that f'(x) = 2
Oh I'm so sorry, I meant to add that f'(x) = 2Doesn't mean anything because that has no (real) solutions.
Doesn't mean anything because that has no (real) solutions.
Are you sure you haven't differentiated already and were trying to say that what you gave us WAS the derivative?
Nup, that still produces a complex solutionI have no clue either then. We need the actual question.
I have no clue either then. We need the actual question.
Here you go :)
Sorry if I stuffed up the question
I understand how to get f'(x) but don't know how to get f''(x) which will let me finish the question as I can sub in 2 then.
Sorry, your post came up with random symbols thrown into it making it very difficult to read...If you're in an app, go into web view. LaTeX does not get produced on the app; you need a proper web browser.
Sorry for being so naggy, but where did the 2 go at the end of the first differentiation?Fixed, my bad on the accident there
Fixed, my bad on the accident there
How do you do these questions?
How many solutions of the equation (sin x – 1)(tan x + 2) = 0 lie between 0 and 2π ?
How do you do these questions?
How many solutions of the equation (sin x – 1)(tan x + 2) = 0 lie between 0 and 2π ?
Hey! For that equation to hold true, either
or
Looking to the first equation,
Looking to the second equation
So those should be our three solutions!
Sorry man the answers says 2. Its multiple choice question 7 for the 2014 paper. Also could you explain to me how you quickly worked out the fractions for the solutions like:
Anyway, I explained his mistake.
Hello, can you please help me with HSC 2007 question 7a(i)... Its a little confusing....In the future, please provide a link to the paper.
Sorry I quoted and said the wrong thing... I meant the answers for the second part. When I put those values into my calc it does not equal exactly zero, and is there a way to figuring it out fast?2.03 and 5.18 are obviously rounded.
2.03 and 5.18 are obviously rounded.
Yes but can you please tell me how you get that answer quickly... you dont just randomly test those points in your calculator.. there must be some method to getting those values.
Thanks,
Bobby
In the future, please provide a link to the paper.
help plz A rectangle is cut from a circular disc of radius 6 cm. Find the area of the largest rectangle that can be produced(http://i1164.photobucket.com/albums/q566/Rui_Tong/Capture_zpsffwxytg1.png)
hi, i always get stuck when it comes to drawing the derivative function of a graph, has anyone got any tips to draw these?Be more specific please? If you're given the function, say, f(x)=x^{3}+3x^{2} then all you have to do is differentiate it and then continue.
Be more specific please? If you're given the function, say, f(x)=x^{3}+3x^{2} then all you have to do is differentiate it and then continue.
Do you mean drawing the graph of the derivative, given the graph of the original thing?
I need help with this question pleaseDraw a diagram and show us your working out thus far, like how I used a diagram for your earlier question. You cannot simply do those questions without a diagram.
A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard, correct to 2 decimal places.
sorry for the confusion!
like with (iii) i could get it all except from t1 to t3
Depending on whether a function is concave up or down, how does Simpsons rule over/underestimate the exact area?Recall that Simpson's rule uses a parabolic arc to estimate the area.
Recall that Simpson's rule uses a parabolic arc to estimate the area.I see, thanks
Given any three points, sketch a parabola through them. Look at whether the area under the parabola is greater than, or less than the original area.
Note that the concavity of the function itself isn't enough for Simpson's rule. For the trapezoidal rule it is all that's needed because you're estimating with just trapeziums (and hence you draw straight lines). For Simpson's rule, you need to physically consider what the parabola through the three points looks like to make a conclusion. An example of where this was needed was in the 2013 HSC.
For question 15c, could someone explain to me how to do it both graphically and algebraically. Isn't that if I equate the two expressions, square them and solve for their discriminant to = 0, i should get a value for m? (I tried and its not working, just curious as to why).The graphical method was done in post #454
Thanks.
Hey:) Just need a hand with this question from the 2012 paper. I've tried looking at the solutions but they just arent making sense to me. Thanks!
Thanks so much, your explanation really helped:)
HelpThe question says to show us part a) so please link part a) next time.
This is from question 10 of the 1995 paper and am having trouble with the working of the question. I got part I out but i am lost from there. any help would be largely appreciated...
Thanks
Emily :-\
Hello, I'm not sure if this question has been answered before and I know it's been talked about in one of the ATARNotes Maths lectures but are we still allowed to use abbreviations in the reasonings (e.g. isosceles Δ abbreviated to isos.Δ / supplementary to supp.)? A friend of mine said that this year, we wouldn't be allowed to use them and I'm just a little confused.I haven't heard anything about this (maybe the two other mods will input further).
Hey guys,
Just a question, regarding rounding.
I know that you shouldn't round any numbers until the last part of the question. But when it says round to 4dp for example, do you continue to use the whole decimal or just 4 decimal places?
E.g. rates of change when finding k - continue to use the whole thing or whatever decimal places they initially say
Just needing some help with part ii of this question from the 2011 HSC.
I've done part i, the answer is (n+1)^{1/2} - n^{1/2}.
Hey! Cool question, check out my solution below and let me know if I can clarify anything!Thanks so much! :)
(http://i.imgur.com/94nRCvj.png)
Jake
Annotation by Rui: In case his first line wasn't clear, Jake rationalised the denominator
Hello, I'm not sure if this question has been answered before and I know it's been talked about in one of the ATARNotes Maths lectures but are we still allowed to use abbreviations in the reasonings (e.g. isosceles Δ abbreviated to isos.Δ / supplementary to supp.)? A friend of mine said that this year, we wouldn't be allowed to use them and I'm just a little confused.
Sorry cajama I missed this! Why does your friend say specifically this year? What do they think has changed? That's the curious bit to me :)
In general, you want to make your work as readable for the marker as is humanly possible. I am reasonably sure that abbreviations are fine, and that they would pay you for those that you've provided, but I was always hesitant to use them. Not because they wouldn't recognise them and not pay you for it intentionally, but more along Rui's line of thinking. It's about clarity and formality of proof, and basically, I wanted to take no chances that what I'd written had been misinterpreted.
My thinking is this. The BOSTES sample solutions don't use those abbreviations, so if you want to be 100% sure that you are okay, then take the 1 second to write the full word. Of course, symbols like Δ and // are universal and definitely acceptable :)
I've seen questions like this before but they've given a time constraint. How do I do 12?
Are you an Extension student Oliver? Because I think this has strayed into that territory of difficulty :P
So we have this expression for cost in terms of speed, per hour:
$$c=150+\frac{v^2}{80}$$
What we want is the total cost for a 500km trip. To find how long THIS takes, we use our speed formula:
$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\v=\frac{500}{t}\\\therefore t=\frac{500}{v}$$
So our trip takes that many hours. To find our total cost, we multiply the cost per hour by the amount of hours taken that we just found.
$$C_\text{Total}=ct=\frac{500}{v}\left(50+\frac{v^2}{80}\right)$$
And now we're back to familiar territory, differentiate and find your minima! Does that help? :)
No 2u, this was in the textbook :)
I get 63km/h as a minimum - textbook answer says 110km/h.
What am I doing wrong?
Oh I mean like, it's strayed into that level of difficulty, definitely 2U content. I mean like, don't stress that it's hard for you, because it is a hard question, aha ;D
Snap a picture of your working? I'll see if I can spot ;D
Does anyone know how to answer the attached question (all parts please). Im super confused :(Part (iii) was already addressed in post #533
Hello, can you please explain the last question... I always get confused on those types... Thanks :)Can we please have a link to the paper or the answers to all the previous parts? For a question like this that might be relevant.
Can we please have a link to the paper or the answers to all the previous parts? For a question like this that might be relevant.
Hello,
with this question, why does the minimum of D occur at the same time as the minimum of D^2?
Also, why do you use the negative root in the volume question?
And, how do you solve c part ii (Using the graph... find the values of m... one solution) :D
Thanks!
Hello,
with this question, why does the minimum of D occur at the same time as the minimum of D^2?
Also, why do you use the negative root in the volume question?
And, how do you solve c part ii (Using the graph... find the values of m... one solution) :D
Thanks!
Hey can you please help me with this question. It's from the 2013 hsc paper. I did part (i) but I don't understand how to do part (ii)Already done in post #454
Why do we specifically need to use the left branch though? Sorry - I still don't understand :P
Already done in post #454
I checked it and I'm still confused why would we use 2 for the gradient thing?
Can you help me with part (iv) and (v) please
Hi, could someone provide me a solution for the second derivative in i).
Thanks
Hey! So we've gotSweet, thanks for the solution.
To find the first derivative, we can just apply the chain rule to the second part
To find the second derivative, we can just apply the chain rule again.
As t is always positive, (1+t) will always be positive, and so (1+t)^(-3) will always be positive. Therefore, -2*positive will always be negative, as required.
Can someone help me with this question, please?
hey! could someone please explain how you would do this question :-)Im on a phone right now so I can't link but part i is already done.
I'm a bit stuck on this question right now. Could someone please explain how to do Q4g and Q4h?The answer is the question itself. It's called a trick question; it is already answered for you
I'm a bit stuck on this question right now. Could someone please explain how to do Q4g and Q4h?
Remember thatI nearly walked into that.
So,
I'll let you try h)
I nearly walked into that.
Jake, that index was already positive
I know it looks positive, but I assumed the picture was just bad quality. Surely they wouldn't give an already-positive indice in numerous questions, as the image appears.Yeah it makes sense because there was a "space" there. Oh well.
Yeah it makes sense because there was a "space" there. Oh well.
just did last years paper and scored 100% ;DYes. Whilst it's extremely hard, it is possible to score 100.
Can you score 100 for a subject? or is the maximum hsc mark 99? (just like the max atar is 99.95 not 100)
just did last years paper and scored 100% ;D
Can you score 100 for a subject? or is the maximum hsc mark 99? (just like the max atar is 99.95 not 100)
In case anyone is curious, the reason for this is because an ATAR of 100 means you beat 100% of students in the state. Including yourself ;)
That's a fair point but in that case why stop at 99.95? why not go to 99.99?
Policy reasons; an ATAR is one a tool to limit university intake on a supply/demand basis. There's really no point scaling people about 99.95, since only like 40 people in the state get that mark anyway!
Hiya all!This was answered somewhere in the last two pages (on my phone right now so can't link)
I'm having some trouble understanding how to go about doing part v of this question. ???
Thanks for the help btw!
This was answered somewhere in the last two pages (on my phone right now so can't link)
(http://uploads.tapatalk-cdn.com/20161018/ae3ca657354ac4d4ef18ca34ea27cb96.jpg)
I have a couple of questions! For the first one, I've done part I) but I'm having trouble with the transformation to reach the answer in part ii) and a bit lost after that. In the second question I got all but part three. The answers mentioned 'favourable outcomes' which seems quite simple but I'm not familiar, could someone enlighten me? Thank you! (http://uploads.tapatalk-cdn.com/20161018/5809966f3ef60c285d37eff0bfca1a82.jpg)(http://uploads.tapatalk-cdn.com/20161018/cb463a433b62ebdeb078691f6b64554e.jpg)
2007, Q10: having trouble understanding the answer.
(https://i.gyazo.com/801fbb3e27932847d4000021a9557c6d.png)
Thanks :P
How do we solve these sort of questions??
How do we solve these sort of questions??Covered in post #464 or alternatively just use what Jamon said
thank you both! Also, another question.
how many solutions of the equation (sinx -1)(tanx +2) = 0 lie between 0 & 2pi
How do we solve these sort of questions?
Hey :)
I was wondering if some one can help with this question part (iii)
soz for barging in but can you explain why tanx= -2 has two solutions? im confused about that
Would someone please be able to help me with this question? :) Just with the last part, (iv).
2014 Q7: How many solutions of the equation (sin x – 1)(tan x + 2) = 0 lie between 0 and 2π ?
The answers say 2, but shouldn't it be 3???
Hiya. How do you do b) part (ii) of this question?
Thanks. :)
With this question, how come the little 'triangle' section under the semi circle is shaded? Doesn't the region of the semicircle stop at the x axis?
Thankyou!
Hey, can someone please show how to do this question?
Thanks in advance!
Makes sense, but then why is the range for semicircles always stated between 0 and some number (i.e in this case stated as between 0<=y<=3 instead of just y<=3?)
Hi everyone,
I have attached a pic below (sorry for sloppy drawing). Let point D be the midpoint of hypotenuse BC. If in HSC you say CD=AD=AB (Midpoint of hypotenuse is equidistant from vertices of triangle ABC). Is the part in the brackets a valid proof or would you have to prove AD= CD or AD= DB another way.
Thanks
Hi everyone,Definitely not. The midpoint on a hypotenuse theorem is not assumed and you need to prove it from what you're given
I have attached a pic below (sorry for sloppy drawing). Let point D be the midpoint of hypotenuse BC. If in HSC you say CD=AD=AB (Midpoint of hypotenuse is equidistant from vertices of triangle ABC). Is the part in the brackets a valid proof or would you have to prove AD= CD or AD= DB another way.
Thanks
Hi! Can somebody help me with this please.Addressed in post #620
Saw that but was wondering how is there 2 solutions??? I understand sinx-1=0 but how do you solve the tan one. How do you know it has two solutions?
Hey guys, i was wondering if anyone could help give me iron out some stuff: e.gRecall that the parabola x^2=4ay has directrix y=-a and focus (0,a)
locus and parabola for y^2=4ax, is the directrix y=-a and the focus (x+ or - a, y). For some reason i cant grasp the y^2 side despite knowing how the x^2 side works
This may be hard to explain but how would i graph velocity graphs ? I can work out the intercepts and roots, but i get stumped when wondering how to draw them and i dont necessarily have a question on hand
The sum and product of roots and the variations outside of alpha + beta, alpha beta, there is one of them which i cant exactly remember ( which i know isnt helpful in trying to get help for) but its a more 'complex' one that requires a bit more algebraic manipulation
Thanks
This example isnt the best example because i know how to graph this one, essentially the motion questions where i have to graph the velocity as part of it, also for part V for questions like that when would i know i would have to integrate or i can use t = 0;x=2 , t=1;x=4 etcStill not sure what the problem is. If you're given the equation then like you said, you basically know how to draw it.
Thanks again !
For the equation (y-k)^2= 4a(x-h)^2Recall that for the parabola (x-h)^2 = 4a(y-k)
Would the focus be (k + a, h) and the directix y= k -a
So for the y^2 side would it essentially be the x value shifting up and down for the focus and the directix would be the x value minus the focal lenght?
Thanks
This is a question from the 2005 paper that no one in my class has figured out yet so just looking for a bit of help to conquer this mess.Already done in post #466
Thanks,
Emily :-\
@SimplyNikhil ( not sure how to tag your post )
But to find the area it would be top curve - bottom curve
ln2x-lnx
By index laws that would become ln2
Since ln2 is a constant you can integrate it to xln2 and you just simply sub in b and a to solve
Hope i answered your question
???This is partly wrong. Please wait for a correction. This question is actually much harder than what it looks like.
@BPunjabiYou are a fucking Beast, probs to you man!!
How i solve these ( which may not be correct, Rui may correct me after if im wrong)
Equation is Sin(2x+pi/3)
To find the where it crosses the x axis
let 2x+pi/3=0
2x = -pi/3
x = -pi/6
Therefore when we inspect A,B,C,D
A and B are eliminated
And between C and D , D is -pi/6
Again, not sure if this is the best way to do it but that is how ive always done it and it has worked for me
@BPunjabi
How i solve these ( which may not be correct, Rui may correct me after if im wrong)
Equation is Sin(2x+pi/3)
To find the where it crosses the x axis
let 2x+pi/3=0
2x = -pi/3
x = -pi/6
Therefore when we inspect A,B,C,D
A and B are eliminated
And between C and D , D is -pi/6
Again, not sure if this is the best way to do it but that is how ive always done it and it has worked for me
@SimplyNikhil ( not sure how to tag your post )
But to find the area it would be top curve - bottom curve
ln2x-lnx
By index laws that would become ln2
Since ln2 is a constant you can integrate it to xln2 and you just simply sub in b and a to solve
Hope i answered your question
Good method Deng! I'd personally suggest a more intuitive approach based on rules that you can find here, once you get the hang of doing it this way, purely for speed! ;D
At Rui for the area under the curve integral question
Would this not give the correct working
...
I'm not sure if the method you provided gave same answer because i dont understand it
Jamon please double check
At Rui for the area under the curve integral questionAh. I missed the logarithm law.
Would this not give the correct working
Area = integrate between e and 1 for ln2x-ln2
= ln 2 + ln x - ln x
= ln2 ( constant there is no x, therefore integratable )
Therefore, it becomes xln2 between e and 1
eln2 - ln2
= ln2 ( e - 1 )
I'm not sure if the method you provided gave same answer because i dont understand it
So Jamon, we are basically looking at (Bx+C)
Hey guys, i was wondering on how i would identify the second derivative for this qDo not picture the second derivative in your head. Use definitions.
The first derivative would be f'(a) < 0 since the gradient is negative
I just cant picture in my head what the second derivate would look like ( some reason i picture a horizontal line since f(x) looks like a parabola to me
anyone know how to do this?
(https://cdn.pbrd.co/images/h2KkrmZyj.png)
For this question, if i did the maths right, the x value where it is increasing is 2/3 and 2, but how would i know if its 2/3<x<2 or if its split
I've been told to draw a parabola but i dont particularly understand this method and just want more clarification
Thanks
Edit: Woops, dictation error
The denominator of a function cannot be zero, so:
But also we can't square root a negative number:
Put these together to obtain \(x>-3\) ;D
Thanks Jamon but the answer says a?That's what he got. He said in the last line that hence the answer is x > -3
Hey I'm stuck on this question:
For what values of k will the equation 2x^2 + 8kx - (1-k) = 0
have roots that differ by 2?
My first thought was to use the formula
α+β=-b/a
and αβ=c/a
I tried to replace 'β' with (α-2) but I'm not sure if I'm doing the right thing, I can't seem to get the answer
That should give the answer. Please show us your working if something happened from here onwards
Would you also need to do a case where beta = alpha + 2? As the question only asks for 'differs'? Like I dunno if you'd get different answers, but I suppose you would. Conceptually, it shouldn't make a difference, but since I think it would change the answer...Those cases should all be addressed at once though... If we do beta = alpha + 2 we just get beta = -2k+1 and alpha = -2k-1
Those cases should all be addressed at once though... If we do beta = alpha + 2 we just get beta = -2k+1 and alpha = -2k-1
(http://uploads.tapatalk-cdn.com/20161020/f16fe5c9672d37242bfd4693afcab75d.jpg)
Hey guys can someone help me with part iii) and iv)..
Thanks in adv !!
Hey:) I'm sure this is fairly simple but i cant remember how to do it:
A rectangle is cut from a circular disc of radius 6cm. Find the area of the largest rectangle that can be produced
Thanks in advance:)
Hey:) I'm sure this is fairly simple but i cant remember how to do it:Done in post #538
A rectangle is cut from a circular disc of radius 6cm. Find the area of the largest rectangle that can be produced
Thanks in advance:)
Hey guys, just a question from the 2005 HSC mathematics exam. I don't really understand this question, so i'd appreciate it if someone could explain how to do each part. Cheers :PDone in post #466
Done in post #538Done in post #466
How the hell do you remember these? ;D(http://i1164.photobucket.com/albums/q566/Rui_Tong/Capture_zpsfzvianbw.png)
Hello, can you please help me with the last question. I cannot understand properly... Thanks
Hey! Cool question, check out my solution below and let me know if I can clarify anything!
(http://i.imgur.com/94nRCvj.png)
Jake
Annotation by Rui: In case his first line wasn't clear, Jake rationalised the denominator
Annotation by Jake of Annotation by Rui: Cheers buddy
Thank You so muchh! Much more easier to understand :D
Quick question... Why does root 2 go infront and root 1 becomes negative?
Can you please help me with the last question
Hi everyone,Refer to post #522
I was just wondering if anyone could help me with this question: 10b from the 1995 10b (i, ii, iii, iv).
Thanks for your help :)
Hi everyone,
I was just wondering if anyone could help me with this question: 10b from the 1995 10b (i, ii, iii, iv).
Thanks for your help :)
Hey! So we can say that Alex's salary grows like this
If they save a third of their funds, then they will save
etc. Now, we want this value to equal $87,500. You can use the sum of an arithmetic sequence (a formula you should definitely know!) to simplify the terms in brackets. Then, set that equal to 87,500 and solve for n! Let me know if you need a worked solution for this.
Jake
Okay understandable! But what do we do with the 1/3? Thats where I am confused, how do we place it into formula?
Hi again,Both ∆ABC and ∆ACD are isosceles.
I was just wondering if any could help as I am unsure of how to complete question 10a, iv of the 2010 paper. I have attached a copy of the question and my working for the other parts :) Thankyou
Both ∆ABC and ∆ACD are isosceles.How do you do part iv? Thankyou :)
This implies that we can use base angles on isosceles triangles twice.
< ACD = < ABC (= common < A)
Hi again,
I was just wondering if any could help as I am unsure of how to complete question 10a, iv of the 2010 paper. I have attached a copy of the question and my working for the other parts :) Thankyou
Help please
Hey, I came across this question and realised that I have absolutely no idea what simple interest is. Could someone explain to me the last part of this question, the parts before are fine just the last part. The answers used some PRT/100 = I formula, which i have never used lol.
Cheers :P
Hey, I came across this question and realised that I have absolutely no idea what simple interest is. Could someone explain to me the last part of this question, the parts before are fine just the last part. The answers used some PRT/100 = I formula, which i have never used lol.
Cheers :P
Hey! So, we need to set up a geometric series. We can easily see that
So, which of the terms fit into this pattern? It's clearly looking at the 10th and 11th term (as that will get us a power of 10 and 11 for x).
Okay, not helpful
So, the answer is C
Alright! Thank You!
Btw for limiting some the absolute ratio should be less than 1 right? Because I saw a question where they used ratio more than one ???
Alright! Thank You!
Btw for limiting some the absolute ratio should be less than 1 right? Because I saw a question where they used ratio more than one ???
This would imply that you can have a complex series with a limiting sum? Interesting....
Hey guys! :D
I just have a quick question about an easy question but I always get confused...
Solve 3 tan(x) + 1= 0 for 0° ≤ x ≤ 360°
Are the answers: 150 and 210???
Thank you! :D
This would imply that you can have a complex series with a limiting sum? Interesting....What are you trying to pull here Jake lol I don't get it
Oh, yeah sorry I meant the root of 3 :)
What are you trying to pull here Jake lol I don't get it
To illustrate the r and R, for a rate of 6% p.a.
R = 6
r = 0.06
_____________
That being said: To do that question, just deduct off the original principal and plug it into the formula. I = PrT = PRT/100 is assumed knowledge from Year 10.
I suck at this part of series :PRefer to post #631
Help on last q
Can you do the solution? I think I was taught a different way...I don't have all the answers to the previous parts
Hi, just wondering if someone would be able to explain to me how to do part ii) of this question?
Thank you!
Hi, just wondering if someone would be able to explain to me how to do part ii) of this question?
Thank you!
This is just something that you need to be comfortable using
The maximum value of velocity will clearly occur when cos(theta)=-1, thus
Thanks, that helps:) Definitely wasn't thinking that one through properly!
Thanks, that helps:) Definitely wasn't thinking that one through properly!
Btw, there is an easy method typically known by 3u or 4u students, maximum velocity occurs when the acceleration is zero; if you just differentiat velocity then make it equal to zero to find t then just sub back into velocity you get max velocity. May seem a bit more confusing or may make you go like "oh yeahhhh I see" but it can sometimes make life easier especially if you get ugly equations.That works in general. 2U are taught this.
Pretty damn sure that is a rumour, they can't just take out the integral section without telling the students.
Wait I just realized something, did you do ur 2u hsc in year 10?Yes
The whole reference sheet is in the exam right? Coz ive been hearing rumours that theyre taking out integrals part... Just confirming that the rumour is a rumour lol
Pretty damn sure that is a rumour, they can't just take out the integral section without telling the students.
Yea! I guess people are making up stuff, I mean HSC is already stressful, y give more surprises lolOnly 2 or 3 of the standard integrals are not on the reference sheet. Every other standard integral has been transferred
Heyy! How do we know the procedure to solve this?
The answer is different, its 91/216
Sorry if this has been answered previously but could someone help me out with this question please?
The answers can be found here - http://www.pasthsc.com.au//HSC_Mathematics_files/Maths2U07WorkedSolutions.pdf - on page eight however I don't understand part (i).
For the first part, I got tan(x) =√3, yet I then used this to say that x = π/3, and that the intercepts occur at π/3 and 2π/3. I don't understand why the 2π/3 isn't right and why it's 4π/3 instead??
Sorry if this has been answered previously but could someone help me out with this question please?You're looking at the wrong quadrants.
The answers can be found here - http://www.pasthsc.com.au//HSC_Mathematics_files/Maths2U07WorkedSolutions.pdf - on page eight however I don't understand part (i).
For the first part, I got tan(x) =√3, yet I then used this to say that x = π/3, and that the intercepts occur at π/3 and 2π/3. I don't understand why the 2π/3 isn't right and why it's 4π/3 instead??
Okay! But y do we cube it?They give you the probabilities for 1 week.
Does anyone have prelim formula sheet?What's a prelim formula sheet? You're going to be given that same reference sheet as you have been tomorrow
For iii), I'm unsure as to why AP = AC (according to the answer, its because of part II).AP is not equal to AC. AP/AC = 1/2 according to (ii)
(https://i.gyazo.com/22dd1130d3f0673db48ce6351b24fa1d.png)
Also, any tips on drawing a displacement graph from a velocity graph or acceleration and vice versa? (without knowing the function itself) :P
AP is not equal to AC. AP/AC = 1/2 according to (ii)
Here are the answers from BOSTE 2009 HSC exam.That's CP. Not AC.
(https://i.gyazo.com/f78e5a0f152aba594d4c4502e6e9cf27.png)
For iii), I'm unsure as to why AP = AC (according to the answer, its because of part II).
(https://i.gyazo.com/22dd1130d3f0673db48ce6351b24fa1d.png)
Also, any tips on drawing a displacement graph from a velocity graph or acceleration and vice versa? (without knowing the function itself) :P
Hi there!Addressed in post #464
I don't understand how to do these questions:
1) the answer is 4.5. I don't even know how to approach this...
2) the answer is 2. Wouldn't it be 3? Sin gives us one solution and tan gives us the 2nd?
Thank you so much in advance!
Addressed in post #464
Addressed in post #620
Help please last part
Good Morning :)
For a question like (iii) we have to differentiate, so can be times the power 'k' with the whole number? In this case k= 0.0347 (4dp) but the whole number is 0.03465735903
Can we times it with the whole number? because the answer multplies it with only 4dp....
Morning! You would be paid for either, but as a rule of thumb, if you find a rounded value in an earlier part of the question, carry it through the rest of the questions! It is cleaner and still yields the required level of accuracy ;D
hi
with this time payment question, I don't understand why the expression for A1 ends up as Px1.04^7+5000 instead of Px1.04^8 +5000. Is there a general rule for working out the time period in time repayment questions where they don't just state over a period of n years but rather say between this year and that year etc because to me it seems the answer varies between different questions and I don't know why.
Thanks :))
How do we know when to use a discriminant and which one to use (>, <, =)
hi
with this time payment question, I don't understand why the expression for A1 ends up as Px1.04^7+5000 instead of Px1.04^8 +5000. Is there a general rule for working out the time period in time repayment questions where they don't just state over a period of n years but rather say between this year and that year etc because to me it seems the answer varies between different questions and I don't know why.
Thanks :))
Its too late now just wing it ;D.
But here:
1. if triangle is <0, roots are real, rational and equal
2. If triangle is =0 roots are unreal and unrational
3. If triangle is >0 roots are unreal, irrational and unequal
Its too late now, dont worry just wing it!
If the discriminate is less than 0 there is no real roots...
= 0 is 1 real root
> 0 is 2 real, unequal roots
> and equal to means real roots
How do we know when to use a discriminant and which one to use (>, <, =)Note that f'(x) ≥ 0 means monotonic increasing
Note that f'(x) ≥ 0 means monotonic increasing
f'(x) ≤ 0 means monotonic decreasing
f'(x) = 0 for stationary points
f'(x) > 0 means strictly increasing
f'(x) < 0 means strictly decreasing
When they don't say monotonic, assume strictly
Hi, my answers say that d.) is correct but how did they get to this point?
Hi, my answers say that d.) is correct but how did they get to this point?
so on top of this for clarity you will have to differentiate f(x) and make the discriminate less than 0 (as it will have no roots)In theory, if we were to fully complete the question
I would do the calculation the normal way (just add them all together) and then see which answer matches your answers via calculationTakes far too long. That's what you do after you've finished the paper and it's time to check your answers, not during.
Takes far too long. That's what you do after you've finished the paper and it's time to check your answers, not during.
There are 13 terms to add up in the sum.
Eh, when in doubt go back to basics; the techniques are obviously more effective. But if you have a choice between spending 1 minute getting an answer you are 50% confident with, and 3 minutes getting an answer you KNOW is correct, then why not (assuming you know you've got the time). Plus, doing the calculator work for this with 13 terms isn't actually that bad :PEven at the fastest typing speed on the calculator that still takes me a full 45 seconds to get through all the options whereas I could've evaluated it in 15-25 :P
Even at the fastest typing speed on the calculator that still takes me a full 45 seconds to get through all the options whereas I could've evaluated it in 15-25 :P
They say to check your answers for reasons - get an answer on the paper first, and then calm the paranoia down when you find time to.
Of course, if you have a stress attack though then yeah that's when you should just go back to basics or you'll be overly paranoid
Yep valid point Rui but since it was a simple calculation thats just where my mind went :)At least it's 100% not penalisable
hey guys! i was just wondering if someone could please quickly run through locus? i don't think i understand it and i just noticed it in the syllabus 😳 please and thankyouu!!Find the section on locus
You know those velocity graphs or acceleration graphs and it says describe the motion of the particle at t=whatever? Can someone give me a run down on how to do that please!Well if you need to describe the motion based off what you have.
Hey anyone know how to find the asymptotes for tan graphs? For normal tanx graph asymptote is at pi/2 and 3pi/2 but what if it was tan(1/2 x) or tan (2x) how to find new asymptote.. thanks
How do we know how to solve the last 2 questions
Guys have confidence, we will smash it!
Hi,
I saw a post above that "monotonic increasing" is when f'(x) greater than or equal to zero.
Can someone please 100% confirm this, i always thought when it said "monotonic increasing" it meant f'(x) was just larger than 0 and not equal to it.
Thanks!!!
Hi,Ditto to Jamon.
I saw a post above that "monotonic increasing" is when f'(x) greater than or equal to zero.
Can someone please 100% confirm this, i always thought when it said "monotonic increasing" it meant f'(x) was just larger than 0 and not equal to it.
Thanks!!!
Hi again,The discriminant is positive OR zero when ALL you care about is real roots.
What kind of question would want you to make the discriminant greater and equal to zero?
Hey! For the second part, you need to think about the cases. Pat can win on the first turn (probability same as i) ), or Pat can win on the second turn. If he wins on the second turn, it will be (1-P(win on first turn))*P(win). Then, we add up these two cases!
You need to create some sort of 'series' which you can add up in a sum-to-infinity type equation for the last part. Can you see how?
Its still confusing...
Hi, I have a couple of questions:
1. If the question doesn't specify do we leave answer in exact form or decimal and would we get marked down for either?
2. If we answer a question and you could take out a common factor - should you do that or not - some past paper answers do it and some don't and would we get marked down either way?
3. What are acceptable abbreviations for proving geometrical questions?
4. do we leave our answer in improper fraction or mixed numeral - if not specified in question?
5. If not specified in question how many decimals should you round to?
Thank You!
Hi, I have a couple of questions:
1. If the question doesn't specify do we leave answer in exact form or decimal and would we get marked down for either?
2. If we answer a question and you could take out a common factor - should you do that or not - some past paper answers do it and some don't and would we get marked down either way?
3. What are acceptable abbreviations for proving geometrical questions?
4. do we leave our answer in improper fraction or mixed numeral - if not specified in question?
5. If not specified in question how many decimals should you round to?
Thank You!
Hey!
Just wondering, would changing our calculators to radians by default change our calculations for other answers that don't need radians? I always have mine in degrees and change it to radians whenever i need it ???
Thanks!
Some chaos occurs with mixed numerals. Don't smack me Jamon but I need to emphasise your point on this one :P preferably improper fractions please.
Good luck to everyone who is sitting the exam today ;D (although I'm probably the one that's going to need it ;) )Have faith, don't imply that about yourself
Hey guys,I recommend rounding so that your units are consistent, but I think unless they explicitly say how many years and months it isn't that much of a concern to use a decimal answer.
Just a question with rates of change.
If t equals something like 152.65 months, what is your final answer if it says when does P = x, occur. Do we leave it as a decimal? Or round to a month?
Hey guys, this is more just a rule that i'm asking, but I remember that when there are parallel lines and two transversal intersect them, the ration between the two transversals are equal or something? Could someone just rephrase that properly or enlighten me on whether that is the correct rule?You can call it "Ratio of intercepts on transversals of parallel lines" when you write out the ratio relevant. Or just "intercepts on transversals of parallel lines"
Cheers, ALSO GOOD LUCK PEEPS and a MASSIVE shoutout to all the moderators and members that make revising for 2U that much easier. :P
is using the @ symbol ok?
is using the @ symbol ok?That just stands for "at". It's not too much of a hassle to write two letters lol
In what sense? But probably not a good idea
Well if you need to describe the motion based off what you have.
Suppose you have the graph of the displacement.
Velocity is the first derivative of the displacement
Therefore if the graph is increasing, velocity is positive
If graph is decreasing, velocity is negative
If graph is at a stationary point, particle is at rest
Acceleration is the second derivative of the displacement
Therefore if the graph is concave up, acceleration is positive
If the graph is concave down, acceleration is positive
If we are at a point of inflexion, acceleration is constant (possibly 0 but we don't know).
And say we were given the graph of the velocity.
Velocity is the first derivative
Hence v > 0 means particle is travelling away from the origin (+'ve direction, to the right, however you memorised it)
v < 0 means particle is travelling in the other direction from the origin (-'ve direction, to the left etc.)
And those are just some examples. If you know what the derivatives actually MEAN then this is more intuitive than trying to rote learn a few dot points.
are both these formulas right for surface area of a cone?
If velocity is positive, does that mean its going in thd positive direction?
Also if acceleration is positive, does that mean it is speeding up and if accelerstion is negative, its slowing down?
also, how do i know it has changed direction if it gives me a displacement, velocity or acceleration graph
If velocity is positive, does that mean its going in thd positive direction?
Also if acceleration is positive, does that mean it is speeding up and if accelerstion is negative, its slowing down?
also, how do i know it has changed direction if it gives me a displacement, velocity or acceleration graph
Yep they are both correct!
Please help!!
Good Luck Guys!! We will need it. See you in an hour.
Yep, that's pretty much right. However, if the velocity is negative, and the acceleration is negative, the particle is actually speeding up in the negative direction!
It changes direction if the displacement starts to decrease (ie. go back towards the origin) or the velocity changes sign (ie. goes from positive to negative).
So if velocity is negative but acceleration is positive, the particle is going in the negative direction but slowing down?
Yes. If velocity and acceleration are opposite in direction, the particle would be decelerating in the direction of the velocity (although, I'd wait for someone else to second that)The displacement is equivalent to the area under the velocity curve: (8×4)/2=16. In the question, it states that at t=0, x=2. Therefore, the maximum displacement at t=4 would be x=2+16=18 :)
Also, I don't get how to do this Q
Hi. Sorry to ask silly questions, but I'm having trouble doing these questions. We just started these topic and I'm so confused. I just can't keep up with my teacher, he's just too fast. I hope you can help me. :'(
...
I hope you can explain these questions to me. I really want to improve my maths. Thankyou. :)
Hey Yogi! Welcome to the forums! Definitely don't be sorry for wanting to improve, good on you for working hard! ;D
Before we give you a hand with these, I'll get you to read this guide which covers some of the theory that you are confused with. Have a read, and see if it helps you understand the questions you've posted (it's brief, but it might help a tad). Otherwise, pick the question there that is confusing you the most and post it back, and we'll give you a hand! Best to start with the most confusing and then see if it helps you answer the others ;D
Hi could i get help with these questions?
You have been given the displacement equation and are being asked to find the velocity which means you have to differentiate your equations before you substitute
Thank you for the help
I was also wondering if i could get help with q15 and 16c-e
Hi Jake or anyone who wants to answer,
I am a 2017 Year 12 Student. This year I did accelerated 2U Mathematics and just 3 and a bit hours ago I did my HSC mathematics. It was ok- but I am certain I was way off 100%, which would probably mean I'll redo it next year. With that in mind, along with my experience of doing past HSC papers, I realised that It was pretty easy for me to get 70% to 80% in a Mathematics Paper since so much of that style of question I had seen before. I found it much trickier getting that last 15-20% since it involves far more application of skills and technique than the earlier questions.
I know this is a problem partially due to the fact I kinda rushed the course in one year, but with respect to the next year, I just wanted to know if you have any advice on how I could fine tune maths skills to the level I could actually do those harder questions...or even just have the confident mindset. Whether it's more past papers, or maybe going back to basic text book work, I just want to know how I should approach the next year keeping in mind the fact that I have bascially completed "course work" already.
Thanks,
Samuel
Hello,Addressed in post #505
Can someone please help me with Q16c ii from the 2015 paper. Thankyou
there are no answers >:( >:( for the practice test i didNot sure what cos^x is meant to mean there. If it was a typo for cos(x) then there are many ways of simplifying that and we cannot say for certain which is "the correct answer". Presumably sin^2x-sin^2x cos^2x which might make some sense.
q6. Novy leaves her base camp, O and walks in the direction 150°T until she reaches point A on the bank of the river.
Unable to cross the river, she follows it on a bearing of 030°T and stops at point C. The bearing and distance of C from O are 120°T
and 4km respectively
ii)show that angle OAC=60°
I proved it by drawing the diagram which is the first part of the diagram
figured out a few angles
proof
(co-interior angle sum is 180 on parallel lines)
Q5. A person on top of a building 49m in height wishes to find the height of an adjacent building.
If the angle of depression of the adjacent building is 47° 21' from where the person is standing and the
buildings are a distance of 12 m apart.
ii) Calculate the height of the adjacent building (2 dp)
my answer=35.97m
simplify
i) sin^2x - sin^2x cos^x
Thank you!! :)
thanks ruiAce(http://i1164.photobucket.com/albums/q566/Rui_Tong/Capture_zps0bvz0oxt.png)
I've attached it here
How would I integrate x^-3 / 3
hi i've got a question.
the area bounded by the curve y=x^2 and y=x+2 is rotated about the x axis. find the exact volume of the solid formed
Hey, I have a series of question I need help with; please and thank you.
1. Find the discriminant of the quadratic equation:
A) -x^{2} - 3x = 0
B) x^{2} + 4 = 0
2. Find any values of b for which 2x^{2} + x + b + 1 = 0
Again, thanks!!! :D
Oh yep thanks;
I forgot the last bit of the question.
Find any values of b for which 2x^{2} + x + b + 1 = 0 has real roots.
Cool! For real roots we require our discriminant to be greater than or equal to zero!Well damn I didn't type fast enough
Would be great if you could help me out with 4 (ii) please :)
Thankyou!
Thankyou so so much!
Probably should be able to answer this, but the second term is throwing me off:
4. Simplify:
(h) 1 - sin^2 (180-x)
If it was just 1-sin^2x it would be cos^2x, but...
If someone could help clarify that would be great, thanks ^^
Hey!!! I have two new questions that I need help with. :-\ I think I know how to do them but I just need some reassurance; please and thank you!!!
1. Express x^{2} - 4x + 5 in the form Ax (x+2) + B (x +1) + C + 4
2. Show that x^{2} + 2x + 9 can be written in the form a (x-2)(x+3) + b (x-2) + c where a=1, b=1, and c=17
Can you please try explaining that another way? It didn't make sense at all to me. Thank you!!! :D
Can you please try explaining that another way? It didn't make sense at all to me. Thank you!!! :D
Hey again!
Can we tell I suck at maths yet?
Thanks for the help!
Find values of A, B, and C if x^{2} + x - 2 = A (x-2)^{2} + Bx + C
need help solving this trig identity
need help solving this trig identityRegarding the website you used, that was a trigonometric equation; not proving an identity. So if you chose the next option on that list on the left you would've gotten the computerised solution(http://i.imgur.com/OrdUL13.png)
i cant find it in exact value form :(
thanks in advance :)
question on series
The sum of the first 5 terms of an arithmetic series is 35 and the sum of the next 5 terms is 160
find the first term and the common difference
I know that nobody really cares, but I just felt the need to share this exponential growth question which could've gotten 4-6 marks in the HSC... as opposed to in ACTL ;D
(http://i.imgur.com/jS1KfIa.png)
Any thoughts Jamon? :P
Ruiace thanks for your replyT_{6}, T_{7}, T_{8}, T_{9}, T_{10}
but im having trouble grasping the second part of your answer.
would u mind elaborating on s=5/2 [2(a+5d) +4d]
why is it +4d when the formula is sn=n/2 [2a+(n-1)d]
i dont understand :P
thanks Ruiace got it !Excellent :)
When proving that:
(sin^2x tanx) + (cos^2x cotx) + 2sinxcox = tanx + cotx
Assuming that factorised it correctly (tbh, I sort of bludged it through brute force...), is it allowed to skip to:
(sin^2x + cos^2x)(tanx +cotx)
Or do you have to show the whole working out from A to B?
I was taught that (and pretty sure that for the HSC):
"Prove that" questions: you can start off with LHS or RHS. You could even work on both sides and show that they are equal, although it's not recommended if not necessary.
"Show that" questions: you can only start off with LHS.
... however this seems to go against RuiAce's guide Verbs and Maths.
When proving that:
(sin^2x tanx) + (cos^2x cotx) + 2sinxcox = tanx + cotx
Assuming that factorised it correctly (tbh, I sort of bludged it through brute force...), is it allowed to skip to:
(sin^2x + cos^2x)(tanx +cotx)
Or do you have to show the whole working out from A to B?
I was taught that (and pretty sure that for the HSC):
"Prove that" questions: you can start off with LHS or RHS. You could even work on both sides and show that they are equal, although it's not recommended if not necessary.
"Show that" questions: you can only start off with LHS.
... however this seems to go against RuiAce's guide Verbs and Maths.
The sum of 12 terms of an arithmetic series is 186 and the 20th term is 83 find the sum of 40 term....I triedIs that supposed to mean the sum of the first 12 and the first 40 terms?
Is that supposed to mean the sum of the first 12 and the first 40 terms?thats the issue i had RuiAce so i just assumed it was the first 12
thats the issue i had RuiAce so i just assumed it was the first 12Well doing a check with WolframAlpha this gives you
Well doing a check with WolframAlpha this gives you
a=-12
d=5
Which gives S_{40} = 3420
Is that meant to be the answer? (Where confusion arises supplying the answer helps.)
Lucia currently earns $25,000
her wage increases by 5% each year.
Find
a) her wage after 6 years
b) her total earnings (before tax)
in 6 years
Lucia currently earns $25,000
her wage increases by 5% each year.
Find
a) her wage after 6 years
b) her total earnings (before tax)
in 6 years
I'll take a stab at what it means! This is a geometric series question, where \(a=25000\) and ](r=1.05\) (the 5% interest rate).Yeah the question was just irritating with its wording. Upsetting when you're studying business at uni haha
The wage after 6 years is just the 6th term (assuming the question means the sixth, like, the wage during the sixth year, which is why my answer differs from Rui's). The question makes a bit more sense this way.
Then the total earned is just the sum of the first six terms:
This topic is just about knowing your formula and knowing the numbers to sub :) hope this helps!
thanks Ruiace! it popped up in a series exercise?
also i think the answers are wrong
the common ratio of a geometric series is 4 and the sum of
the first 5 terms is 3069 find the first term
I'll take a stab at what it means! This is a geometric series question, where \(a=25000\) and ](r=1.05\) (the 5% interest rate).
The wage after 6 years is just the 6th term (assuming the question means the sixth, like, the wage during the sixth year, which is why my answer differs from Rui's). The question makes a bit more sense this way.
Then the total earned is just the sum of the first six terms:
This topic is just about knowing your formula and knowing the numbers to sub :) hope this helps!
question why did you use the arithmetic series formula?Haha lol I thought something was weird but I didn't pick up on it. I think he made a mistake there.
a
Haha lol I thought something was weird but I didn't pick up on it. I think he made a mistake there.
phew thats why there was a discrepancy between both your answers ;D
should i write notes for my maths testBack when there was no "reference sheet" I found it acceptable for some people to write a formula sheet or formula book. Things in there were meant to be really basic and serve no more purpose than be a refresher, and their only advantage was that they're going to be easier to use than textbooks.
i know y'all did 3 or 4 unit and are maths geniuses
and jamon and jake advice against it
and i know the emphasis of solving problems over
writing notes but i personally find that writing notes
helps me to remember all aspects of the topic.
tips?
should i write notes for my maths test
i know y'all did 3 or 4 unit and are maths geniuses
and jamon and jake advice against it
and i know the emphasis of solving problems over
writing notes but i personally find that writing notes
helps me to remember all aspects of the topic.
tips?
note i am not a maths genius i take 2u and get around 80s
(my teacher keeps on saying my results have fluctuated and
i have 'potential' ;D let's hope so)
oh and when i mean writing notes i mean like transcribing
everytime after i have a maths lesson
A loan of $6000 over 5 years at 15% p.a. interest, charged monthly, is paid back in 5 annual instalments.
(a) What is the amount of each instalment?
Answer is $1835.68.
I tried the question and got $1712.87, any help is appreciated. Thanks in advance!
A loan of $6000 over 5 years at 15% p.a. interest, charged monthly, is paid back in 5 annual instalments.
(a) What is the amount of each instalment?
Answer is $1835.68.
I tried the question and got $1712.87, any help is appreciated. Thanks in advance!
Hey James! So two steps here; find the total amount owed, and then divide that into the 5 repayments :) I'd be happy to lend a hand, but we need to know whether this is simple interest or compound interest? Indeed, perhaps you used the wrong one in your working? Or did the question not say? :)When you're an actuary and just chuck it into the present value formula before doing the question 8)
If you let me know whether its simple or compound I'd be happy to show you the working for it! ;D
Edit: Yeah actually, sorry, these are always compound. That said, reckon you could snap a pic of your working and pop it as an attachment?Since you are close I reckon you might have just made a small mistake, I'll try and spot it for you! :)
Need to check for this question:
25. The sum of the first six terms of an arithmetic sequence is -12 and the sum of it's first fourteen term is 196. Find (a) in the sum of n terms, (b) the smallest value of n if the sum is to exceed 250.
I got the part a fine by using the formula Sn = (n/2)[2a + (n-1)d] and simultaneous equations, but the answer I got was 2n^2 - 12n....and the answer at the back is 2n^2 - 14n.
In part b I'm having trouble following. I tried using quadradics but with either one I end up getting surds (which is probably the point since 250 isn't a factor that fits nicely with either of them). And I don't think it possible to do logs because there are three terms...
If anyone could help that would be much appreciated, thanks ^^
Need to check for this question:
25. The sum of the first six terms of an arithmetic sequence is -12 and the sum of it's first fourteen term is 196. Find (a) in the sum of n terms, (b) the smallest value of n if the sum is to exceed 250.
I got the part a fine by using the formula Sn = (n/2)[2a + (n-1)d] and simultaneous equations, but the answer I got was 2n^2 - 12n....and the answer at the back is 2n^2 - 14n.
In part b I'm having trouble following. I tried using quadradics but with either one I end up getting surds (which is probably the point since 250 isn't a factor that fits nicely with either of them). And I don't think it possible to do logs because there are three terms...
If anyone could help that would be much appreciated, thanks ^^
Hey! Just setting n=6, you'll see that the only equation that gets out the required value of -12 is the one at the back of the book. Potentially you messed up some algebra somewhere? Check it over, and if you still need help, post it here and I'll take a look!
As for the second part, you're 100% on the right track. Set your equation equal to 250, and find the surd value. Using the equation at the back of the book, n will equal -8.215 and 15.215. Now, obviously n can't be zero, so we take the positive value 15.215. Let's think about what that means for a second; if n=15, the answer will be LESS than 250. If n=16, the answer will be MORE than 250. So, 16 is out answer, because that's what the question wants!
Let me know if that all makes sense.
Jake
(1/27)^(3n+1)=sqrt{3}/81
This is a prelim question which i couldnt manage to do
Using indices, not log, thanks
Wondering about this question:
20. Show that the sum of the first n odd natural numbers is a perfect square.
The method I've tried is similar to that of induction, letting the sum equal to n^2 and solving it by plugging in terms, where n = the number of terms in current series and the difference being two...if that makes any sense (as in 1 = 1^2, 1 + 3 = 2^2....etc.). Is there a way to neatly show this without confusing yourself (and, by extension, probably the marker)? Or is there a better way to express this proof in general?
Hi everyone
I got this question. And it is nothing like the usual ones I have done before. It is probably really easy, but I found it a little tricky.
Thanks,
Samuel
Hello, please and thank you for your help!
Alpha & beta are roots of the quadratic equation x^{2} - 6x + 3 = 0.
Find alpha x beta^{2} + alpha^{2} x beta
so i got n=19Snipping tool (automatically in Windows 7 and above) works miracles for captures; saves you having to use PrtScn to get a full screenshot
i couldn't get it any bigger becos the limit for file size
A gp has 1st term 12
the terms of the sequence are all different and the sum of the 1st 2 two terms is equal to twice the third term
Find the 1st 3 terms of the sequence
So I interpreted this as
a=12
S2=2T3
So how do I know which formula to use for Sn becos I don't know what r is ? Or do I test them into both formulas
Having trouble visualising this:
31. The track of a gramophone record is in the shape of a spiral curve and may be considered as a number of concentric circles of inner and outer radius 5.25cm and 10.5cm respectively. The record rotates at 33 1/3 rev/min and takes 18 minutes to play. Find the length of the track.
I'm presuming you have to use Sn = (n/2)(a+l) as it's possible to find both values by using C = 2πr (if I'm doing this correctly...), but the other values throw me off. Do I use d = st to help solve the question, or is there a entirely different way of solving it? The question also suggests to take π = 22/7, although I'm not sure what to do with it...any suggestions? Thanks to anyone who can help ^^
Weird question! Here's how I interpret it; if it takes 18 minutes to play, and the speed is 33 1/3 rev/min, then the number of revolutions will be (33.3333)*(18)=600 revolutions. So, we have 600 circles with radius' between 5.25cm and 10.5cm. That means that the radius will increase by (10.5-5.25)/600= 0.0525cm with each subsequent circle. This is a seriously weird question.
Our first circumference is 2π(5.25), then 2π(5.325) etc. etc. Clearly, this is increasing by 2*0.0525π with each circle, so that is going to be our value for d! We have n, a, l and d, so we can sum up the equation :)
Let me know if that all made sense!
It seriously does...
My working out kind of looked like this:
full rev = speed*time
C = 2πr
a = 2π*5.25
l = 2π10.5
d (total revolutions) = speed*time
hence n = vt
n = 100/3 x 18
n = 600
...and then I pretty much plug in everything into Sn = (n/2) (a+l) and then BOOM. Answer. (Which is 296.88m for 2.d.p or 297m if you round it up to the nearest whole.)
To be honest the first thing that came to mind was physics, haha...
But yeah, it makes a lot more sense now - thanks so much for the clarifications ;D