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March 29, 2024, 11:43:37 am

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164468 times)  Share 

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paulsterio

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Re: Specialist 3/4 Question Thread!
« Reply #585 on: August 12, 2012, 09:44:19 pm »
+1
To be honest, if you're going to ask a question, you should be specific.

What have you been able to do?

What are you stuck on?

What do you need help on?

It's not that I don't want to do those questions for you, it won't help you to just read solutions!

1i1ii1i

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Re: Specialist 3/4 Question Thread!
« Reply #586 on: August 12, 2012, 09:47:51 pm »
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i can't get my answers in the form that the back of the book has it

1i1ii1i

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Re: Specialist 3/4 Question Thread!
« Reply #587 on: August 12, 2012, 09:49:02 pm »
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its mainly the constructing the de and solving it, i can't do it the back of the book has weird answers

paulsterio

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Re: Specialist 3/4 Question Thread!
« Reply #588 on: August 12, 2012, 09:55:18 pm »
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What is your DE that you have written, and what is the form at the back of the book - is this for all the questions?

1i1ii1i

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Re: Specialist 3/4 Question Thread!
« Reply #589 on: August 12, 2012, 09:57:15 pm »
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Yes for all of them okay i will show you wwhat i did

1i1ii1i

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Re: Specialist 3/4 Question Thread!
« Reply #590 on: August 12, 2012, 10:03:20 pm »
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well thats really awkward....i figured the first 1 out by redoing it =.=

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Re: Specialist 3/4 Question Thread!
« Reply #591 on: August 12, 2012, 10:05:55 pm »
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its mainly the constructing the de and solving it, i can't do it the back of the book has weird answers

If you cant do it, read the examples in the textbook again and apply the formula.
If you have SAC tomorrow, you should do all of those earlier, dont just leave until the day before the SAC.

1i1ii1i

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Re: Specialist 3/4 Question Thread!
« Reply #592 on: August 12, 2012, 10:13:20 pm »
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Wow that's really messed up i figured them all out, sometimes when i come back to a question i get it so weird >.<
um i couldn't figure out how to construct a de for the water tank question i used newtons law of cooling
 and did dT/dt=k(T-20)
the answer is (100-T)/(40)

Jenny_2108

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Re: Specialist 3/4 Question Thread!
« Reply #593 on: August 13, 2012, 06:21:18 pm »
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Wow that's really messed up i figured them all out, sometimes when i come back to a question i get it so weird >.<
um i couldn't figure out how to construct a de for the water tank question i used newtons law of cooling
 and did dT/dt=k(T-20)
the answer is (100-T)/(40)

dT/dt=k(T-20)
At T=60, dT/dt=1
Sub: 1=k(60-20) => k=1/40

Remember the question asks: cooling and heating are both taking place.
dT/dt=k (100-T)= (100-T)/40 because water is boiled at 100 degrees and its cooled down over time

rife168

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Re: Specialist 3/4 Question Thread!
« Reply #594 on: August 14, 2012, 08:11:05 pm »
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Hey does anyone have some tricky 'Volumes of solids of revolution' questions? I have a SAC tomorrow that is supposed to feature the topic.
Thanks
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pi

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Re: Specialist 3/4 Question Thread!
« Reply #595 on: August 14, 2012, 08:16:43 pm »
+2
I've got a gold one.

A cissoid (where and ) is rotated about it's asymptote to form a volume of revolution. Find this volume in terms of . You don't really need a CAS until the very last part to get the answer. TYPO FIXED, SORRY! D:

:)

edit: another good exercise is finding the volume of a torus, ie. when it is rotated around the x-axis to form a solid volume of revolution, in terms of and .

Post your working/answers up here :)
« Last Edit: August 14, 2012, 09:44:01 pm by LovesPhysics »

rife168

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Re: Specialist 3/4 Question Thread!
« Reply #596 on: August 14, 2012, 09:27:59 pm »
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I've got a gold one.

A cissoid (where and ) is rotated about it's asymptote to form a volume of revolution. Find this volume in terms of . You don't really need a CAS until the very last part to get the answer.

 :)

edit: another good exercise is finding the volume of a torus, ie. when it is rotated around the x-axis to form a solid volume of revolution, in terms of and .

Post your working/answers up here :)

What's the asymptote???


Yeah I did that earlier today and got a solution for the volume in terms of the inner and outer radii of the torus.
It's a good question nonetheless, maybe someone else can try put up a solution, I already spent some time on it and verified my results so there isn't really any point in me doing it.
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pi

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Re: Specialist 3/4 Question Thread!
« Reply #597 on: August 14, 2012, 09:30:35 pm »
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haha, you're supposed to find that out! The asymptote is though in case you couldn't find a way (graph it to help though) :)


The solution to the other one is

brightsky

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Re: Specialist 3/4 Question Thread!
« Reply #598 on: August 14, 2012, 09:35:57 pm »
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for second question:
volume = pi* int^(r)_(-r) (sqrt(r^2 + x^2) + a)^2 dx - pi*int^(r)_(-r) (-sqrt(r^2 + x^2) + a)^2 dx
= pi*int^(r)_(-r) (4a sqrt(r^2+x^2)) dx
= 4*pi*a*int*(r)_(-r) sqrt(r^2 +x^2) dx
the integral we know equals to the area of a semicircle pi/2 r^2
so volume = 4*pi*a*pi/2 * r^2 = 2a*pi^2*r^2

hopefully that's right..
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pi

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Re: Specialist 3/4 Question Thread!
« Reply #599 on: August 14, 2012, 09:36:58 pm »
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Yep, all good :)