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Given the formula T , If t is doubled and r is doubled and r is

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Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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New post 18 Apr 2019, 15:18
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Given the formula T = \(2\pi\)\(\sqrt{\frac{r^3}{GX}}\), If T is doubled and r is doubled, by what factor does X change?

A)\(\frac{1}{4}\)
B)\(\frac{1}{2}\)
C)1
D)2
E)4

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Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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New post Updated on: 19 Apr 2019, 04:54
we have to make LHS = RHS
if T and r are doubled, \((2T)^1\) become \(2T\), while \((2r)^\frac{3}{2}\) become \(2\sqrt{2}*r^\frac{3}{2}\) :

2*T = \(2\pi\)\(\sqrt{\frac{r^3}{GX}}\)*\(2\sqrt{2}\)
T = \(2\pi\)\(\sqrt{\frac{r^3}{GX}}\)*\(\sqrt{2}\)

so to equalize the \(\sqrt{2}\) in the RHS,
the RHS should be divided by \(\sqrt{2}\)
so \(\sqrt{X}\) become \(\sqrt{2X}\), or X become 2X ---> D
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Originally posted by Mahmoudfawzy83 on 19 Apr 2019, 00:05.
Last edited by Mahmoudfawzy83 on 19 Apr 2019, 04:54, edited 1 time in total.
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Re: Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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New post 19 Apr 2019, 03:57
Mahmoudfawzy83 wrote:
we have to make LHS = RHS
if T and r are doubled, \((2T)^1\) become \(2T\), while \((2r)^\frac{3}{2}\) become \(2\sqrt{2}*r^\frac{3}{2}\) :

2*T = \(2\pi\)\(\sqrt{\frac{r^3}{GX}}\)*\(2\sqrt{2}\)
T = \(2\pi\)\(\sqrt{\frac{r^3}{GX}}\)*\(\sqrt{2}\)

so to equalize the \(\sqrt{2}\) in the RHS,
the RHS should be divided by \(\sqrt{2}\)
or \(\sqrt{X}\) = \(\sqrt{2}\), so X = 2 ---> D




can you make this more clear.. i couldnt understand it !
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Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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New post 19 Apr 2019, 07:56
Hi, payalpathak
I will explain it step-wise

First, we can simplify the equality to:
T = k*\(\sqrt{\frac{r^3}{X}}\)

Second, separate the variable we want to examine in the LHS, while other variables in the RHS.
\(X = k^2*\frac{r^3}{T^2}\)

third, apply the changes (T become 2T, and r become 2r) to see how X will change:
\(k^2*\frac{(2r)^3}{(2T)^2}\) = \(k^2*\frac{8r^3}{4T^2}\) = \(2*(k^2*\frac{r^3}{T^2})\) \(= 2X\)

so when T and r are doubled, X will become 2X (doubled also)
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Given the formula T , If t is doubled and r is doubled and r is   [#permalink] 19 Apr 2019, 07:56
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