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March 28, 2024, 11:05:46 pm

Author Topic: 3U Maths Question Thread  (Read 1230228 times)  Share 

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anotherworld2b

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Re: 3U Maths Question Thread
« Reply #615 on: August 22, 2016, 10:49:38 pm »
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I got 5^2 -3^2? But the answer is -2?
I also tried this question but im not sure to do next

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #616 on: August 22, 2016, 11:12:57 pm »
+1
I got 5^2 -3^2? But the answer is -2?
I also tried this question but im not sure to do next

Take a look at the quick map of how I do it, maybe you'll spot your mistake?



That second question is broken, as Rui pointed out above (and something I should have noticed given I did complex analysis last semester), a negative base to a fractional exponent is well beyond your scope ;D




RuiAce

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Re: 3U Maths Question Thread
« Reply #617 on: August 23, 2016, 08:02:19 am »
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@anotherworld2b

Just to clear things up - Your textbook is full of typos. I think the answers they provide can be reached if all those TYPOs were amended.

anotherworld2b

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Re: 3U Maths Question Thread
« Reply #618 on: August 23, 2016, 09:15:45 am »
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I had a feeling some of the answers were wrong but I wasn't completely sure
Thank you RuiAce, jamonwindeyer and jakesilove for your help :)
@anotherworld2b

Just to clear things up - Your textbook is full of typos. I think the answers they provide can be reached if all those TYPOs were amended.

FallonXay

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Re: 3U Maths Question Thread
« Reply #619 on: August 25, 2016, 04:12:58 pm »
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Hi, I'm having trouble with part b of this question. I've tried finding the cartesian equation of each projectile and equating them, but I keep getting a weird answer. (the textbook answer is x=11.5m and y=8.2m). I'm not sure what I'm doing wrong, help would be appreciated! Thanks!  :)
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RuiAce

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Re: 3U Maths Question Thread
« Reply #620 on: August 25, 2016, 05:13:39 pm »
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Hi, I'm having trouble with part b of this question. I've tried finding the cartesian equation of each projectile and equating them, but I keep getting a weird answer. (the textbook answer is x=11.5m and y=8.2m). I'm not sure what I'm doing wrong, help would be appreciated! Thanks!  :)
Note: Part a) looked fine.

When I simulated the relevant Cartesian equations of motion on GeoGebra, I found the diagram that they provided was highly deceptive. Unless my equation was wrong, particle B literally soars right over particle A.

When I plugged the values for the answer in, I found that particle A travels through the given coordinates, but not particle B.

These are the equations I had for particle B. Tell me what you think.

FallonXay

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Re: 3U Maths Question Thread
« Reply #621 on: August 25, 2016, 06:24:36 pm »
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Note: Part a) looked fine.

When I simulated the relevant Cartesian equations of motion on GeoGebra, I found the diagram that they provided was highly deceptive. Unless my equation was wrong, particle B literally soars right over particle A.

When I plugged the values for the answer in, I found that particle A travels through the given coordinates, but not particle B.

These are the equations I had for particle B. Tell me what you think.


Yeah, I had similar equations but since the velocity is in the opposite direction [relative to the other projectile], acceleration is -10, velocity is -10 - 20sin(45) and therefore displacement is -5t^2 - 20 sin(45) t. (Just a sign difference).
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RuiAce

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Re: 3U Maths Question Thread
« Reply #622 on: August 25, 2016, 06:32:35 pm »
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Yeah, I had similar equations but since the velocity is in the opposite direction [relative to the other projectile], acceleration is -10, velocity is -10 - 20sin(45) and therefore displacement is -5t^2 - 20 sin(45) t. (Just a sign difference).
The direction of the velocity is flipped for the horizontal component but not the vertical.

If when t=0, y'=-20sin(45), then we'd be implying that the projectile was being fired into the ground, not upwards.

FallonXay

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Re: 3U Maths Question Thread
« Reply #623 on: August 25, 2016, 06:47:48 pm »
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The direction of the velocity is flipped for the horizontal component but not the vertical.

If when t=0, y'=-20sin(45), then we'd be implying that the projectile was being fired into the ground, not upwards.

ohhh right, my bad
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RuiAce

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Re: 3U Maths Question Thread
« Reply #624 on: August 25, 2016, 07:09:02 pm »
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Bear in mind maths in focus is full of mistakes. I might be wrong but I'm pretty sure I didn't do anything stupid here (if anyone would like to check, please do).

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #625 on: August 25, 2016, 10:48:43 pm »
+2
Bear in mind maths in focus is full of mistakes. I might be wrong but I'm pretty sure I didn't do anything stupid here (if anyone would like to check, please do).

Cast my eye, see no mistakes ;D

Mei2016

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Re: 3U Maths Question Thread
« Reply #626 on: August 27, 2016, 11:49:15 pm »
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Hi,

I've only just recently started doing some binomial questions. In a textbook, I got through 8.1 fine, but got stuck on a few 8.2 questions. (The first two questions are from a textbook). Also, I found that I could do some of the past paper questions on binomial theorem, but the last two pics are 2 questions which I didn't how to approach.

Thanks.

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #627 on: August 28, 2016, 07:42:07 am »
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Hi,

I've only just recently started doing some binomial questions. In a textbook, I got through 8.1 fine, but got stuck on a few 8.2 questions. (The first two questions are from a textbook). Also, I found that I could do some of the past paper questions on binomial theorem, but the last two pics are 2 questions which I didn't how to approach.

Thanks.

Hey there! I'll give you a bit of a hand! ;D I'm a tad short on time so I'll leave your first question, it has a bit of messy algebra, if no-one has jumped in by this evening I'll come back!

Quite a few of your other questions are very similar, and just require equating coefficients for binomial identities. Let me use the 1996 question as an example. For the result we need to prove, the RHS is the coefficient of x^4 on the right hand side of the result we are given (did you spot this?) ;D So, let's see what the coefficient of x^4 is on the LHS:



Notice that we need pairs of term that give a total power of x^4, yielding:



I think you see where I'm heading, it gives the LHS of the result, and we are done! ;D

Many questions require this method of thinking, it is what is required in your second textbook question.

Oops, gotta go (train), however, for your 1992 question:

i) x=-1 might work ;)
ii) Hmmm, I wonder what integrating the given expression might do...

Spencerr

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Re: 3U Maths Question Thread
« Reply #628 on: August 28, 2016, 01:38:03 pm »
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For the last one ii) the binomial identity, i've tried integrating, factoring out the x then subbing in x equals -1 and it gives you the lhs but not the rhs :/
Will work on this further

But wait! After integrating and subbing in x=0 you get the entire lhs equals to 0 and the rhs equalling 1/n +1

Summing the two would give the final identity. I think I might have broken a maths law haha could someone check?
« Last Edit: August 28, 2016, 01:41:42 pm by Spencerr »
1st in HSC Eco 2016

RuiAce

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3U Maths Question Thread
« Reply #629 on: August 28, 2016, 01:48:43 pm »
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For the last one ii) the binomial identity, i've tried integrating, factoring out the x then subbing in x equals -1 and it gives you the lhs but not the rhs :/
Will work on this further

But wait! After integrating and subbing in x=0 you get the entire lhs equals to 0 and the rhs equalling 1/n +1

Summing the two would give the final identity. I think I might have broken a maths law haha could someone check?


Not too sure how your method broke. I need to test it out.

Edit it works so not sure what you meant
« Last Edit: August 28, 2016, 01:56:00 pm by RuiAce »