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March 29, 2024, 05:39:58 am

Author Topic: 3U Maths Question Thread  (Read 1230351 times)  Share 

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imnotdani

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Re: 3U Maths Question Thread
« Reply #225 on: June 20, 2016, 07:21:12 pm »
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Hey there! You sure can, the first bit is to handle the integrand:



Now we complete the integration. We'll use our double angle result to handle the cos squared, which is something you may have seen before, let me know if not!



Let me know if anything here doesn't quite make sense!!  ;D
Hey! Thanks for the quick reply, but I still don't quite get it. I understand YOUR working method, but the answers say it's pi( 3pi + 8 ) units3 :(? [or the answers could be completely wrong that works too]
« Last Edit: June 20, 2016, 07:24:49 pm by imnotdani »

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #226 on: June 20, 2016, 08:22:31 pm »
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Hey! Thanks for the quick reply, but I still don't quite get it. I understand YOUR working method, but the answers say it's pi( 3pi + 8 ) units3 :(? [or the answers could be completely wrong that works too]

Woops! I did make an error, let me redo the last section, I forgot the pi out the front for the first few terms!



It seems as though your answer might be missing the divided by 4 bit on the bottom?  I triple checked with Wolfram Alpha and this is definitely correct ;D sorry for that error!! I'm on uni exams at the moment so my heads a bit all over the shop  ;)

RuiAce

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Re: 3U Maths Question Thread
« Reply #227 on: June 20, 2016, 08:28:11 pm »
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I'm getting Jamon's second answer.

And definitely so is WolframAlpha
http://www.wolframalpha.com/input/?i=integrate+pi(cosx%2B1)%5E2+from+0+to+pi%2F2
« Last Edit: June 20, 2016, 08:31:31 pm by RuiAce »

imnotdani

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Re: 3U Maths Question Thread
« Reply #228 on: June 20, 2016, 08:37:07 pm »
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Thanks heaps to both of you ^_^

conic curve

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Re: 3U Maths Question Thread
« Reply #229 on: June 22, 2016, 09:39:45 pm »
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Is this for prelim or HSC?

RuiAce

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Re: 3U Maths Question Thread
« Reply #230 on: June 22, 2016, 10:53:46 pm »
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Is this for prelim or HSC?

As you can see, there are no prelim threads on this forum. Hence, you should assume the answer to your question is both.
« Last Edit: June 22, 2016, 10:56:06 pm by RuiAce »

birdwing341

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Re: 3U Maths Question Thread
« Reply #231 on: June 27, 2016, 04:59:39 pm »
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Having a bit of a struggle over here...

Grain is ejected from a chute at the rate of 0.1 metres cubed a minute and is forming a heap on a flat horizontal floor. The heap is in the form of a circular cone of semi-vertical angle 45 degrees. Find the rate, in metres per minute, at which the height of the cone i s increasing at the instant 3 minutes after the opening of the chute. Answer is 0.0732.

Any help would be appreciated :)

jakesilove

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Re: 3U Maths Question Thread
« Reply #232 on: June 27, 2016, 05:50:35 pm »
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Having a bit of a struggle over here...

Grain is ejected from a chute at the rate of 0.1 metres cubed a minute and is forming a heap on a flat horizontal floor. The heap is in the form of a circular cone of semi-vertical angle 45 degrees. Find the rate, in metres per minute, at which the height of the cone i s increasing at the instant 3 minutes after the opening of the chute. Answer is 0.0732.

Any help would be appreciated :)

Hey! This was a bit of an odd question, mainly because you have to figure out the height after 3 minutes yourself. I hope my working out is sufficient: let me know if I can be more explicit!



Also, it's on it's side. Sorry, not sure how to fix that!
Jake
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #233 on: June 27, 2016, 05:53:26 pm »
+1
Having a bit of a struggle over here...

Grain is ejected from a chute at the rate of 0.1 metres cubed a minute and is forming a heap on a flat horizontal floor. The heap is in the form of a circular cone of semi-vertical angle 45 degrees. Find the rate, in metres per minute, at which the height of the cone i s increasing at the instant 3 minutes after the opening of the chute. Answer is 0.0732.

Any help would be appreciated :)

Edit: Jake just beat me to a solution, but I finished it, so I'll post it anyway. Maybe it will be equally useful, we used the same method  ;)

Hey there! This is a chain rule question. These questions can be gnarly, but they all have a very similar approach.

First, let's take the question and break it down into some equations. We are told that the cone is being formed from a flow of 0.1 cubic metres per minute. That is, if we take V to be in cubic metres and t to be in minutes:



Now, we need a second formula to apply the chain rule. Remember the formula for a volume of a cone:



Now this would be great, except we don't want the radius in there. So, to remove it, we use the angle that they gave us. Draw the cone, and you'll be able to see that through some right-angled trigonometry, we can deduce:



Or, you might just be able to tell from the info they give you, both are fine! So, that volume formula becomes:



Now we apply the chain rule:



Now to find the final answer, we require the height at 3 minutes. At 3 minutes, we know the volume is 0.03, therefore:



Substituting this into the formula above will give you the answer!  ;D

RuiAce

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Re: 3U Maths Question Thread
« Reply #234 on: June 27, 2016, 05:56:43 pm »
+1
Edit: Jake just beat me to a solution, but I finished it, so I'll post it anyway. Maybe it will be equally useful, we used the same method  ;)

It was about time he got a question :P

jakesilove

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Re: 3U Maths Question Thread
« Reply #235 on: June 27, 2016, 06:00:04 pm »
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It was about time he got a question :P

Yeah was pretty happy with myself, sorry matey
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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #236 on: June 27, 2016, 06:00:47 pm »
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Yeah was pretty happy with myself, sorry matey

The race continues  ;) or we just need to actually make a system like we always say we are going to aha

birdwing341

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Re: 3U Maths Question Thread
« Reply #237 on: June 27, 2016, 06:02:46 pm »
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Many thanks, it seems like a classic case of calculator mistake for me, but that's alright :).

Yeah was pretty happy with myself, sorry matey

Glad someone could get a self-confidence boost!!

jakesilove

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Re: 3U Maths Question Thread
« Reply #238 on: June 27, 2016, 06:06:01 pm »
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Many thanks, it seems like a classic case of calculator mistake for me, but that's alright :).

Glad someone could get a self-confidence boost!!

Calculator mistakes are the worst, especially for a question like this where you've done a solid piece of Mathematics to get to the answer. Rui and Jamon are just too good at the typing-up-maths-on-the-forums-thing, it's difficult to compete.
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RuiAce

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Re: 3U Maths Question Thread
« Reply #239 on: June 27, 2016, 06:34:11 pm »
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The race continues  ;) or we just need to actually make a system like we always say we are going to aha

But I mean if I see a question unanswered for 3 hours and you guys are MIA... :P

Calculator mistakes are the worst, especially for a question like this where you've done a solid piece of Mathematics to get to the answer. Rui and Jamon are just too good at the typing-up-maths-on-the-forums-thing, it's difficult to compete.

Actually I would've written this one out just cause of the triangle haha