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March 29, 2024, 03:39:06 pm

Author Topic: 3U Maths Question Thread  (Read 1230518 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #465 on: August 05, 2016, 10:36:55 pm »
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #466 on: August 05, 2016, 11:54:13 pm »
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what about something like this?

This one was a little tricky actually, but again, let's use some intuition (you'd want something a little more rigorous in an exam).

The particle starts going to the right at 4ms^-1. The acceleration is negative after x=1, and this will eventually turn it around. When it returns to x=1 it is travelling backwards:



The acceleration is zero at this point, and although between x=0 and x=1 it will be positive acceleration, it won't be enough to turn it back around, the thing is going to zoom off to negative infinity. This can also be gleamed from the fact that the expression for velocity only has a single root at about x=2.5, the point where it turned around initially. Besides that, it ain't stopping, so it does return to the origin and then zooms off to negative infinity ;)


massive

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Re: 3U Maths Question Thread
« Reply #467 on: August 06, 2016, 11:45:54 am »
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Thanks Jamon!

Guys for the question attached, in part iii, I know that we have to differentiate the eqn of part ii, but do you differentiate with respect to theta or respect to alpha? 

RuiAce

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Re: 3U Maths Question Thread
« Reply #468 on: August 06, 2016, 12:26:54 pm »
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Thanks Jamon!

Guys for the question attached, in part iii, I know that we have to differentiate the eqn of part ii, but do you differentiate with respect to theta or respect to alpha?




conic curve

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Re: 3U Maths Question Thread
« Reply #469 on: August 06, 2016, 06:07:55 pm »
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In how many ways can five writers and five artists be arranged in a circle so that the writers are separated?
In how many ways can this be done if two particular artists must not sit next to a particular writer?

It's from the Fitzpatrick book. I got the first part by doing 1 * 4! * 5! = 2880 but I can't do the second part. I was thinking 2880 - the number of arrangements with 2 artists sitting next to the write but I can't figure it out. Any help appreciated.

anotherworld2b

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Re: 3U Maths Question Thread
« Reply #470 on: August 07, 2016, 01:56:25 am »
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Hi i was wondering if i could get help with these two questions

RuiAce

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Re: 3U Maths Question Thread
« Reply #471 on: August 07, 2016, 07:43:43 am »
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Hi i was wondering if i could get help with these two questions



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conic curve

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Re: 3U Maths Question Thread
« Reply #472 on: August 07, 2016, 08:56:42 am »
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If you factorised the whole thing by 6 that should be 18 there not 1/2.

Anyway, regardless of if you factorise the 6 out, put the negative back in there and complete the square.


Just curious but why specifically take out 1/squareroot of 18

RuiAce

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Re: 3U Maths Question Thread
« Reply #473 on: August 07, 2016, 09:04:46 am »
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Just curious but why specifically take out 1/squareroot of 18
To use the standard form of the integral, the coefficient on t must be 1.

Otherwise we'd probably need integration by substitution.

conic curve

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Re: 3U Maths Question Thread
« Reply #474 on: August 07, 2016, 09:08:12 am »
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What am I supposed to do after?

RuiAce

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Re: 3U Maths Question Thread
« Reply #475 on: August 07, 2016, 09:10:57 am »
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conic curve

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Re: 3U Maths Question Thread
« Reply #476 on: August 07, 2016, 09:15:10 am »
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I don't get the bit where you went to tan? (from how the integral was converted into tan)

RuiAce

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Re: 3U Maths Question Thread
« Reply #477 on: August 07, 2016, 09:16:28 am »
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I don't get the bit where you went to tan? (from how the integral was converted into tan)

conic curve

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Re: 3U Maths Question Thread
« Reply #478 on: August 07, 2016, 09:33:12 am »
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What did I do wrong here?

RuiAce

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Re: 3U Maths Question Thread
« Reply #479 on: August 07, 2016, 09:38:21 am »
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What did I do wrong here?
Two mistakes in the last line.

1. You dropped off the 1/16
2. The x went missing inside the inverse tangent