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anotherworld2b

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Re: Mathematics Question Thread
« Reply #1740 on: April 25, 2017, 08:24:37 pm »
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Thank you for your help :)
I was hoping to get some help with these questions please

mcheema

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Re: Mathematics Question Thread
« Reply #1741 on: April 25, 2017, 09:06:42 pm »
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Hey! I've attached my working below - Pretty sure there is a more efficient way to find \(BF\), but this method only uses pythagoras and basic ideas of similarity ;D

Working



Thanks really appreciate your help.  I realised what my mistake was

RuiAce

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Re: Mathematics Question Thread
« Reply #1742 on: April 25, 2017, 09:32:24 pm »
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Thank you for your help :)
I was hoping to get some help with these questions please
Warning to everyone else: This is NOT HSC content.




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« Last Edit: April 25, 2017, 09:37:34 pm by RuiAce »

laurenf58

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Re: Mathematics Question Thread
« Reply #1743 on: April 26, 2017, 05:31:26 pm »
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Can I have some help with this question please?
2017 HSC || Legal. Business. Studies of Religion 2. English Advanced. Mathematics.

RuiAce

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Re: Mathematics Question Thread
« Reply #1744 on: April 26, 2017, 05:33:51 pm »
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Can I have some help with this question please?

« Last Edit: April 26, 2017, 05:39:32 pm by RuiAce »

anotherworld2b

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Re: Mathematics Question Thread
« Reply #1745 on: April 26, 2017, 07:59:14 pm »
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thank you for your help :D
Warning to everyone else: This is NOT HSC content.




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JuliaPascale123

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Re: Mathematics Question Thread
« Reply #1746 on: April 26, 2017, 08:39:40 pm »
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Hey Julia! Welcome to the forums!
...

could you please label this as in which questions you are answering (a,b,c,d,e..)! I am getting so confused :D
« Last Edit: April 26, 2017, 08:56:07 pm by jamonwindeyer »

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #1747 on: April 26, 2017, 08:55:35 pm »
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could you please label this as in which questions you are answering (a,b,c,d,e..)! I am getting so confused :D

I'll copy paste the response with headings :)

Hey Julia! Welcome to the forums!

Question A
The first part is pretty straight forward, and I'm not sure how to construct a table on the forum. Basically, the quantity will decrease over time by 25% every 40 minutes. If t is minutes, and Q is in mg,







etc.

Question B

Now, we want to find an equation for Q. We know that what we're looking for here is some sort of exponential function. Once you've done these questions a number of times, you'll know that the form of the answer must be



Now, we know that the initial quantity is 300mg. So




We also know that the quantity has dropped to 225mg after 40 minutes. So,





So, the equation for the quantity of the medicine is



Question D (C Skipped)
Next, we want to find the time it takes for the quantity of medicine to half. I won't bother guessing and checking, let's just find the actual answer.





Remember that this is in minutes. So, dividing by 60, we get t=9.04 hours.

Question E
Part e starts to get tricky. We could use an arbitrary time t=a. However, it's exactly the same thing to start at an arbitrary quantity, A. That is because, at time t=a, there will be some quantity A of medicine in the system. Then, we would look for when A halves!



is our new formula. t is still arbitrary, but so is A. Now, we need to show that, regardless of A, the halving time of this equation is a constant (ie. the time we proved in part d).

Our halving time will occur when the quantity is 0.5A (half of the initial, arbitrary amount). So,




But this is exactly the same equation as above, with the same solution! So, the halving time is a constant for any arbitrary starting point.

Question F
The next part is just a standard sketch of an exponential function. If you're not sure what it will look like, plot some points, or use an online graphing tool.

Question G
For the last part, we solve for




Which equals 50.99 hours. We should definitely round up, for the safety of the patient, giving us 51 hours.

JuliaPascale123

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Re: Mathematics Question Thread
« Reply #1748 on: April 27, 2017, 11:06:30 am »
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I'll copy paste the response with headings :)

Hey Julia! Welcome to the forums!

Question A
The first part is pretty straight forward, and I'm not sure how to construct a table on the forum. Basically, the quantity will decrease over time by 25% every 40 minutes. If t is minutes, and Q is in mg,







etc.

Question B

Now, we want to find an equation for Q. We know that what we're looking for here is some sort of exponential function. Once you've done these questions a number of times, you'll know that the form of the answer must be



Now, we know that the initial quantity is 300mg. So




We also know that the quantity has dropped to 225mg after 40 minutes. So,





So, the equation for the quantity of the medicine is



Question D (C Skipped)
Next, we want to find the time it takes for the quantity of medicine to half. I won't bother guessing and checking, let's just find the actual answer.





Remember that this is in minutes. So, dividing by 60, we get t=9.04 hours.

Question E
Part e starts to get tricky. We could use an arbitrary time t=a. However, it's exactly the same thing to start at an arbitrary quantity, A. That is because, at time t=a, there will be some quantity A of medicine in the system. Then, we would look for when A halves!



is our new formula. t is still arbitrary, but so is A. Now, we need to show that, regardless of A, the halving time of this equation is a constant (ie. the time we proved in part d).

Our halving time will occur when the quantity is 0.5A (half of the initial, arbitrary amount). So,




But this is exactly the same equation as above, with the same solution! So, the halving time is a constant for any arbitrary starting point.

Question F
The next part is just a standard sketch of an exponential function. If you're not sure what it will look like, plot some points, or use an online graphing tool.

Question G
For the last part, we solve for




Which equals 50.99 hours. We should definitely round up, for the safety of the patient, giving us 51 hours.

Thanks Jamon you f*&king Legend! You guys are awesome and amazing.

BTW for c) the answer would be -0.00128 right?

JuliaPascale123

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Re: Mathematics Question Thread
« Reply #1749 on: April 27, 2017, 11:26:39 am »
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RuiAce

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« Last Edit: April 27, 2017, 12:24:24 pm by RuiAce »

michaelalt

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Re: Mathematics Question Thread
« Reply #1751 on: April 27, 2017, 01:40:52 pm »
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Can someone please explain to me how to do q. 13? I don't quite understand. Thank you!

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #1752 on: April 27, 2017, 01:47:47 pm »
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Can someone please explain to me how to do q. 13? I don't quite understand. Thank you!

Hey Michael! These trig equations are applications of the angles of any magnitude system, you should have done this back when you first did trig equations in degrees (unless you've started in radians!) ;D

Let me show you the process with the first one:



So we first think, okay, what puts \(\cos{x}=\frac{1}{2}\)? Well if you check out your reference sheet and do some right angled trig, the answer to that is \(x=60\text{ degrees}=\frac{\pi}{3}\)

Now we need answers for \(0\le x\le2\pi\) - We need the All Stations to Central (ASTC) stuff. When is cosine positive? In the first quadrant, and the fourth quadrant. So the answers are:



Does that help at all? This is something that requires a lot of pre-knowledge, not sure what you know and what you don't ;D

michaelalt

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Re: Mathematics Question Thread
« Reply #1753 on: April 27, 2017, 01:54:51 pm »
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Hey Michael! These trig equations are applications of the angles of any magnitude system, you should have done this back when you first did trig equations in degrees (unless you've started in radians!) ;D

Let me show you the process with the first one:



So we first think, okay, what puts \(\cos{x}=\frac{1}{2}\)? Well if you check out your reference sheet and do some right angled trig, the answer to that is \(x=60\text{ degrees}=\frac{\pi}{3}\)

Now we need answers for \(0\le x\le2\pi\) - We need the All Stations to Central (ASTC) stuff. When is cosine positive? In the first quadrant, and the fourth quadrant. So the answers are:



Does that help at all? This is something that requires a lot of pre-knowledge, not sure what you know and what you don't ;D

Hi Jamon! Yes that helps. We have done the trig stuff, and we're currently doing the radians unit. I got up to the step where you found pie/3, however, didn't know how to find the other 5pie/3 value. Also, i got confused on b. Are you able to do it for me? Thank you so much for your swift response!

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #1754 on: April 27, 2017, 01:59:14 pm »
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Hi Jamon! Yes that helps. We have done the trig stuff, and we're currently doing the radians unit. I got up to the step where you found pie/3, however, didn't know how to find the other 5pie/3 value. Also, i got confused on b. Are you able to do it for me? Thank you so much for your swift response!

Cool! No dramas ;D



So again, we consider the acute angle that would give us a value of \(\frac{1}{\sqrt{2}}\) (always ignore the negative). This is 45 degrees, or \(x=\frac{\pi}{4}\). This forms the 'base angle' that we use in our angles of any magnitude calculations.

So now, we think - Where is sine negative? By the ASTC diagram, we can see it is in the third and fourth quadrants! So the answers are: