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March 29, 2024, 10:14:24 am

Author Topic: 4U Maths Question Thread  (Read 659908 times)  Share 

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RuiAce

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Re: 4U Maths Question Thread
« Reply #1125 on: April 27, 2017, 07:59:02 pm »
+1
(Image removed from quote.)

This is an absolute monster question. I think atleast ahahaha any help is ridiculously appreciated


I don't see how that can be simplified any further and neither does Wolfram
« Last Edit: April 27, 2017, 08:12:44 pm by RuiAce »

legorgo18

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Re: 4U Maths Question Thread
« Reply #1126 on: April 27, 2017, 09:54:07 pm »
0
Hello, i need some help with the following

1) If x,y>0 show that 1/x + 1/y > or equal to 4/(x+y)
2) Using cauchy's inequality, prove that 2(a^3 + b^3 + c^3) greater than or equal to ab(a+b) + ac(a+c) + bc(b+c) greater than or equal to 6abc

Thank you :c
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RuiAce

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Re: 4U Maths Question Thread
« Reply #1127 on: April 27, 2017, 11:30:09 pm »
+1
Hello, i need some help with the following

1) If x,y>0 show that 1/x + 1/y > or equal to 4/(x+y)
2) Using cauchy's inequality, prove that 2(a^3 + b^3 + c^3) greater than or equal to ab(a+b) + ac(a+c) + bc(b+c) greater than or equal to 6abc

Thank you :c


____________________

I have no idea what they teach there because the Cauchy-Schwarz inequality isn't even in the HSC...
I do not see how this benefits students when they can't even use it in the exam.


Remarks: A lot of algebra was rushed. You may consider working through the algebra more slowly.
For the linear algebra version |a.b| ≤ ||a|| ||b||, simply treat the terms of the sequence as the components of the vectors instead.

Haven't figured out how C-S can be used for the first half yet

RuiAce

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Re: 4U Maths Question Thread
« Reply #1128 on: April 28, 2017, 03:11:07 pm »
+1
Hello, i need some help with the following

1) If x,y>0 show that 1/x + 1/y > or equal to 4/(x+y)
2) Using cauchy's inequality, prove that 2(a^3 + b^3 + c^3) greater than or equal to ab(a+b) + ac(a+c) + bc(b+c) greater than or equal to 6abc

Thank you :c

I have absolutely no clue why it's called that though - that's wrong to me.

This means I'll have to look at 2) properly later to determine what to substitute into the 3-variable AM-GM inequality.

Edit: Found a convoluted proof for part 2





« Last Edit: April 28, 2017, 03:19:57 pm by RuiAce »

beau77bro

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Re: 4U Maths Question Thread
« Reply #1129 on: April 29, 2017, 01:11:25 pm »
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I don't see how that can be simplified any further and neither does Wolfram

Omg THANKYOU tho I don't know series. The answer is this if it helps. Sorry for such a random Q and it probably would've helped a lot if I'd shown where u actually need to get to sorrryy

Maybe this will help? All g if it doesn't just stumped

RuiAce

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Re: 4U Maths Question Thread
« Reply #1130 on: April 29, 2017, 04:35:20 pm »
+1
Omg THANKYOU tho I don't know series. The answer is this if it helps. Sorry for such a random Q and it probably would've helped a lot if I'd shown where u actually need to get to sorrryy(Image removed from quote.)

Maybe this will help? All g if it doesn't just stumped




\begin{align*}&\quad \left[(1-x\cos x)-i(x\sin x)\right][(1-x\cos x)+i(x\sin x)]\\ &= (1-x\cos x)^2+(x\sin x)^2\\ &= 1-2x\cos x + x^2(\cos^2x+\sin^2x)\\ &= 1-2x\cos x + x^2\end{align*}

Cis notation is ew.


I might've made an algebra mistake because I don't quite agree with what they got for b.

Kle123

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Re: 4U Maths Question Thread
« Reply #1131 on: April 30, 2017, 10:43:53 am »
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HEY, could anyone help me out with this integration? THANK YOU. I edited the red minus in(forgot to rewrite it after erasing it). The answer is also attached.

RuiAce

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Re: 4U Maths Question Thread
« Reply #1132 on: April 30, 2017, 11:06:25 am »
+1
HEY, could anyone help me out with this integration? THANK YOU. I edited the red minus in(forgot to rewrite it after erasing it). The answer is also attached.

The method of computing your integral can be found in post #1040. In your scenario, take R = 6

Kle123

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Re: 4U Maths Question Thread
« Reply #1133 on: April 30, 2017, 01:08:47 pm »
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Sorry Rui, I dont understand how you got from the first to second step and how the integration of the first part of the 2nd step is equal to the first part of the 3rd step. Could you explain? Thanks

RuiAce

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Re: 4U Maths Question Thread
« Reply #1134 on: April 30, 2017, 01:10:48 pm »
+1
Sorry Rui, I dont understand how you got from the first to second step and how the integration of the first part of the 2nd step is equal to the first part of the 3rd step. Could you explain? Thanks



Kle123

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Re: 4U Maths Question Thread
« Reply #1135 on: April 30, 2017, 01:40:38 pm »
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Sorry. Before I meant i didn't know how to get from the first line to the second line on the right hand side. Also instead i tried differentiating it to check the integration but i got different.

RuiAce

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Re: 4U Maths Question Thread
« Reply #1136 on: April 30, 2017, 01:52:41 pm »
+1
Sorry. Before I meant i didn't know how to get from the first line to the second line on the right hand side. Also instead i tried differentiating it to check the integration but i got different.
Oh my bad, this whole time there were typos floating around.

Given the typo's I'm not too sure how my original answer came out nicely (unless it didn't).

That being said, these are 4U integration tricks that you are expected to know.
« Last Edit: April 30, 2017, 01:55:38 pm by RuiAce »

Kle123

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Re: 4U Maths Question Thread
« Reply #1137 on: April 30, 2017, 02:25:59 pm »
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That being said, these are 4U integration tricks that you are expected to know.
I see. Thanks for the help Rui!

chelseam

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Re: 4U Maths Question Thread
« Reply #1138 on: May 01, 2017, 11:45:17 pm »
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Hi! Could someone please help me with this question? The exercise is about using the substitution t=tanθ/2. Thank you :)

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RuiAce

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Re: 4U Maths Question Thread
« Reply #1139 on: May 02, 2017, 06:55:40 am »
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Hi! Could someone please help me with this question? The exercise is about using the substitution t=tanθ/2. Thank you :)
What textbook is this? That substitution is a horrible idea; u = sin(x) would be a much better substitution.