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March 29, 2024, 08:34:16 am

Author Topic: Mathematics Question Thread  (Read 1296913 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #1230 on: February 21, 2017, 12:31:55 pm »
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please help
This is Extension 2 mathematics. Complex numbers are only a part of Extension 2 - I have no clue why it should appear here in 2U.

jakesilove

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Re: Mathematics Question Thread
« Reply #1231 on: February 21, 2017, 12:33:40 pm »
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please help

So the answer is the last option :)
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smile123

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Re: Mathematics Question Thread
« Reply #1232 on: February 21, 2017, 12:44:13 pm »
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thanks  :)

kylesara

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Re: Mathematics Question Thread
« Reply #1233 on: February 21, 2017, 02:13:07 pm »
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Hi could i please have help with this hw question.
"Show that the volume of a sphere is given by the formula V= 4/3 pi.r^3 by rotating the semicircle y= (r^2-x^2)^1/2 about the x axis.
Thanks

laurenf58

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Re: Mathematics Question Thread
« Reply #1234 on: February 21, 2017, 02:16:32 pm »
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How do you find the primitive function of (-x+1)/3 ???

Thanks!
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jamonwindeyer

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Re: Mathematics Question Thread
« Reply #1235 on: February 21, 2017, 02:46:52 pm »
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How do you find the primitive function of (-x+1)/3 ???

Thanks!

Hey Lauren! You can consider it term by term:



Remember, to find the primitive, we add one to the power, then divide by the new power:



Don't forget the constant! ;D there are other ways of course but I think this is the simplest ;D

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #1236 on: February 21, 2017, 02:52:58 pm »
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Hi could i please have help with this hw question.
"Show that the volume of a sphere is given by the formula V= 4/3 pi.r^3 by rotating the semicircle y= (r^2-x^2)^1/2 about the x axis.
Thanks

Sure! So that is a typical semicircle, radius \(r\), sitting above the \(x\) axis. Therefore, it crosses the \(x\) axis at \(-r\) and \(r\): Those are the bounds of our integral!

If you know the volume formula and how it works, this should be reasonably clear on its own, but definitely let me know if it isn't ;D the only thing to note, besides the fact that we use the function squared as usual, is that we are integrating with respect to \(x\) ONLY - We treat \(r\) as a constant! :)



We also could have used symmetry to simplify the integral, by evaluating this instead:



You would get the same answer :) let me know if any of those steps needs clarifying!

teapancakes08

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Re: Mathematics Question Thread
« Reply #1237 on: February 21, 2017, 04:55:33 pm »
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Hey! Assuming they mean that little triangular looking region enclosed by the parabolas and the x-axis, just take the volume in two halves! One from 0 to 1 for \(y=x^2\), then the other for 1 to 2 for \(y=(x-2)^2\) ;D

Oh and never apologise for asking a question! Seriously all good, we are happy to help ;D

I got the answer ;D

Thank you for helping ^^
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smile123

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Re: Mathematics Question Thread
« Reply #1238 on: February 21, 2017, 09:07:18 pm »
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please help

Mathew587

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Re: Mathematics Question Thread
« Reply #1239 on: February 21, 2017, 11:20:18 pm »
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the range is pretty much: 0<theta<360
let o = theta

sin o = -1
      o = -90        sin's positive in 1,2 quadrants
cos o = 0
       o = 90        cos's positive in 1,4 quadrants
therefore 1st quadrant is constant
therefore o = 90 degrees = 180/2 = pi/2

:)
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RuiAce

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Re: Mathematics Question Thread
« Reply #1240 on: February 21, 2017, 11:21:13 pm »
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Alternatively, sketch a simple graph and just read off it

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #1241 on: February 22, 2017, 12:06:43 am »
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I got the answer ;D

Thank you for helping ^^

Woo! Nice work pancakes! ;D

Shadowxo

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Re: Mathematics Question Thread
« Reply #1242 on: February 22, 2017, 12:12:56 am »
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please help

Disclaimer: I don't know the HSC content or what you know from 2U
As Rui said, I'd sketch a graph and use that. With a circle, you can find sin and cos by the angle. Sketch a unit circle. Let theta = ø
y=sinø, x=cosø, y=-1 and x=0 so you know the angle is 270º. Convert this into radians and you get 3π/2.
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kylesara

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Re: Mathematics Question Thread
« Reply #1243 on: February 22, 2017, 04:20:53 pm »
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Hi, could you please help me with finding the intercepts for these 2 graphs. I know how to find the area by integrating, its just this bit that is confusing me.
Calculate area of the region bounded by x-axis and curves y= x^1/2 and y=6-x.
Thanks

Hplovers

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Re: Mathematics Question Thread
« Reply #1244 on: February 22, 2017, 08:22:25 pm »
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Thankyou so so much for all your help on this! :)