Login

Welcome, Guest. Please login or register.

March 29, 2024, 08:26:06 am

Author Topic: Mathematics Question Thread  (Read 1296911 times)  Share 

0 Members and 2 Guests are viewing this topic.

dreamdog10

  • Adventurer
  • *
  • Posts: 14
  • Respect: 0
Re: Mathematics Question Thread
« Reply #255 on: July 30, 2016, 02:55:34 pm »
0
wow okay fantastic thank you so much :)
HSC 2016: 3U english: 44, english: 88, 3U maths: 44, maths: 91 ancient history: 90, biology: 86 and VA: 95

vamshimadas

  • Fresh Poster
  • *
  • Posts: 2
  • Respect: 0
  • School: TKS
  • School Grad Year: 2017
Re: Mathematics Question Thread
« Reply #256 on: July 30, 2016, 04:58:46 pm »
0
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

jakesilove

  • HSC Lecturer
  • Honorary Moderator
  • Part of the furniture
  • *******
  • Posts: 1941
  • "Synergising your ATAR potential"
  • Respect: +196
Re: Mathematics Question Thread
« Reply #257 on: July 30, 2016, 05:03:16 pm »
+1
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.



Where A=4, B=-3, C=-5, x=0 and y=0

I think the radius turns out to be 1!

Jake
ATAR: 99.80

Mathematics Extension 2: 93
Physics: 93
Chemistry: 93
Modern History: 94
English Advanced: 95
Mathematics: 96
Mathematics Extension 1: 98

Studying a combined Advanced Science/Law degree at UNSW

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #258 on: July 30, 2016, 05:15:52 pm »
+3
The above method is endorsed in 2U however is not completely clear as to why it works, so a brief, non-rigorous (and probably not as easy to follow) explanation is provided here for the sake of reference.


On the other hand, it would be more easier to identify for a 3U student due to the circle geometry theorem "the radius is perpendicular to the tangent drawn to point of contact". The formalised proof is found here.

An alternate informal proposal (that is, however, probably much easier to understand,) is that since the tangent only meets the circle once, the distance from the tangent to the centre is forcibly the radius. Basically, the tangent meets the circumference.
« Last Edit: July 30, 2016, 05:18:01 pm by RuiAce »

jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #259 on: July 30, 2016, 08:45:57 pm »
+1
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.

(Image removed from quote.)

Where A=4, B=-3, C=-5, x=0 and y=0

I think the radius turns out to be 1!

Jake

This is definitely the correct method, since we know the centre of the circle we just need the radius, which can be obtained through this formula, and it does indeed end up as 1!

Rui's method above is a cool proof, but far beyond what is required here. At this level, intuition is absolutely fine. The perpendicular distance to a line is the shortest distance to said line. Since it is the shortest distance, a circle with a radius equal to that distance will clearly only touch the line once.

So basically, in a 2 Unit Exam, just the formula would suffice, but if you are doing 3 unit or above Rui's proof is good to understand  ;D

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: Mathematics Question Thread
« Reply #260 on: July 31, 2016, 08:19:42 am »
0
I don't know whether or not this is a 2U or 3U mahs question, so I just posted it here

if secθ-tanθ= 3/5 show sinθ=8/17

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #261 on: July 31, 2016, 09:04:45 am »
+1


conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: Mathematics Question Thread
« Reply #262 on: July 31, 2016, 09:07:35 am »
0



Why is cos theta not equal to zero at the beginning of the question?

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #263 on: July 31, 2016, 09:11:17 am »
+1
Why is cos theta not equal to zero at the beginning of the question?

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: Mathematics Question Thread
« Reply #264 on: August 01, 2016, 08:31:44 am »
0


Thanks I get it now

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

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #265 on: August 01, 2016, 08:39:53 am »
+3
Thanks I get it now

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.


« Last Edit: August 01, 2016, 08:51:12 am by RuiAce »

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: Mathematics Question Thread
« Reply #266 on: August 01, 2016, 01:10:21 pm »
0
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

RuiAce

  • ATAR Notes Lecturer
  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 8814
  • "All models are wrong, but some are useful."
  • Respect: +2575
Re: Mathematics Question Thread
« Reply #267 on: August 01, 2016, 01:21:15 pm »
0
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


jamonwindeyer

  • Honorary Moderator
  • Great Wonder of ATAR Notes
  • *******
  • Posts: 10150
  • The lurker from the north.
  • Respect: +3108
Re: Mathematics Question Thread
« Reply #268 on: August 01, 2016, 02:06:43 pm »
+1
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

And remember that you can always check yourself/give yourself some idea of where to go by just differentiating the function normally  ;D

conic curve

  • Forum Leader
  • ****
  • Posts: 714
  • Respect: +2
Re: Mathematics Question Thread
« Reply #269 on: August 01, 2016, 03:53:53 pm »
0
Could you please elaborate further for what I have attached below because I don't seem to understand that

Thanks  ;D