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March 29, 2024, 03:36:23 am

Author Topic: 3U Maths Question Thread  (Read 1230313 times)  Share 

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FallonXay

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Re: 3U Maths Question Thread
« Reply #795 on: October 22, 2016, 09:02:43 am »
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Hi for this question part ii, how do you solve for the constant B?

 Thanks!
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RuiAce

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Re: 3U Maths Question Thread
« Reply #796 on: October 22, 2016, 09:20:14 am »
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Hi for this question part ii, how do you solve for the constant B?

 Thanks!
One way of approaching this question is to work with negative time.

Let t=0 be when the object was found, which was at 30oC.

A = 22 because that's the ambient temperature (of the park).
Then using t=0, T=30 we can get B=8.

Then, try to work backwards in time to find when T=37.

FallonXay

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Re: 3U Maths Question Thread
« Reply #797 on: October 22, 2016, 09:30:55 am »
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One way of approaching this question is to work with negative time.

Let t=0 be when the object was found, which was at 30oC.

A = 22 because that's the ambient temperature (of the park).
Then using t=0, T=30 we can get B=8.

Then, try to work backwards in time to find when T=37.

Yeah, I got B=8, although the answers say B=15?>
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RuiAce

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Re: 3U Maths Question Thread
« Reply #798 on: October 22, 2016, 09:37:36 am »
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Yeah, I got B=8, although the answers say B=15?>
They didn't do negative time. They did positive time.

If we use positive time, initially the object's temperature is 37, not 30.

FallonXay

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Re: 3U Maths Question Thread
« Reply #799 on: October 22, 2016, 09:41:13 am »
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They didn't do negative time. They did positive time.

If we use positive time, initially the object's temperature is 37, not 30.

Ahh, I see. Cheers  :)
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FallonXay

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Re: 3U Maths Question Thread
« Reply #800 on: October 22, 2016, 11:32:34 am »
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With this question part (iii), how come you can't solve by mathematical induction? (or can you?)
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atar27

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Re: 3U Maths Question Thread
« Reply #801 on: October 22, 2016, 11:50:22 am »
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Hey, this may be a stupid question but when they tell us to simplify in a binomial question what do they mean?
I have attached a photo below:

/

RuiAce

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Re: 3U Maths Question Thread
« Reply #802 on: October 22, 2016, 12:21:46 pm »
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With this question part (iii), how come you can't solve by mathematical induction? (or can you?)

RuiAce

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Re: 3U Maths Question Thread
« Reply #803 on: October 22, 2016, 12:27:51 pm »
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Hey, this may be a stupid question but when they tell us to simplify in a binomial question what do they mean?
I have attached a photo below:

/(Image removed from quote.)



FallonXay

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Re: 3U Maths Question Thread
« Reply #804 on: October 22, 2016, 01:50:18 pm »
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Hiya, how do you do d (ii) of this question?  :P
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FallonXay

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Re: 3U Maths Question Thread
« Reply #805 on: October 22, 2016, 03:30:17 pm »
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and how would you solve Q6/10?
« Last Edit: October 22, 2016, 03:41:48 pm by FallonXay »
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jakesilove

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Re: 3U Maths Question Thread
« Reply #806 on: October 22, 2016, 03:43:07 pm »
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Hiya, how do you do d (ii) of this question?  :P

Hey! For Newton's method, we need to set up an equation such that 0.3 is a zero. Recall that Newton's method is a way of finding x-intercepts! Therefore, we create the equation



You can then use Newton's method in the regular way, starting from t=20s! Let me know if you want an actual worked answer for this
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FallonXay

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Re: 3U Maths Question Thread
« Reply #807 on: October 22, 2016, 03:47:57 pm »
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Hey! For Newton's method, we need to set up an equation such that 0.3 is a zero. Recall that Newton's method is a way of finding x-intercepts! Therefore, we create the equation



You can then use Newton's method in the regular way, starting from t=20s! Let me know if you want an actual worked answer for this

How does that equation make 0.3 a zero/root?
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jakesilove

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Re: 3U Maths Question Thread
« Reply #808 on: October 22, 2016, 03:48:50 pm »
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and how would you solve Q6/10?

For 6, you can go straight to your reference sheet. Instead of a theta, you have 2x, so just let 2x equal the general solution for arcsin(a) (again, this is on your formula sheet). Divide through by two, and you're done!

10 is an interesting one. I can't really think of a better method than guess and check to be honest. Nah, scratch that. We can see clearly that x=3 is a solution to our given equation. However, x=3 is NOT a solution to a) or b), and if it were we would be dividing by zero. So, c) and d) are left. Unfortunately, x=3 is a solution to both of them, so that's not very helpful. x=2 is also a solution to our given equation, but NOT for d), leaving us with c) as the answer :)

Jake
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jakesilove

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Re: 3U Maths Question Thread
« Reply #809 on: October 22, 2016, 03:50:51 pm »
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How does that equation make 0.3 a zero/root?

We want to find where C(t)=0.3, right? Like, for what value of t will C(t)=0.3. If I SHIFT the graph down 0.3, then what used to be 0.3 is now going to be zero. Thus, it will be an x-intercept. But, just logically, if I want C(t) to equal 0.3, then in that case C(t)-0.3=0.3-0.3=0. Does that make sense? Definitely a difficult concept, but once you've seen it once you'll be able to answer any similar question :)
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