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If 0.0030<x-√30<0.0031, which of the following options is the approxim

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If 0.0030<x-√30<0.0031, which of the following options is the approxim  [#permalink]

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New post 23 Feb 2017, 19:38
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If \(0.0030<x-\sqrt{30}<0.0031\), which of the following options is the approximation of  \(\frac{1}{\sqrt{30}}-\frac{1}{x}\)?

A. 0.001     
B. 0.002     
C. 0.0001     
D. 0.0002     
E. 0.0003

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Re: If 0.0030<x-√30<0.0031, which of the following options is the approxim  [#permalink]

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New post 24 Feb 2017, 01:46
3
AustinKL wrote:
If \(0.0030<x-\sqrt{30}<0.0031\), which of the following options is the approximation of  \(\frac{1}{\sqrt{30}}-\frac{1}{x}\)?

A. 0.001     
B. 0.002     
C. 0.0001     
D. 0.0002     
E. 0.0003


Hi

\(0.0030<x-\sqrt{30}<0.0031\)

\(\sqrt{30} + 0.0030 < x < \sqrt{30} + 0.0031\)

\(\frac{1}{\sqrt{30}}-\frac{1}{x}\) = \((x - \sqrt{30}) / x * \sqrt{30}\)

\(min = \frac{0.003}{(\sqrt{30} + 0.003)*\sqrt{30}} = \frac{0.003}{30 + 0.003*\sqrt{30}} ≈ \frac{0.003}{30} = \frac{3*0.001}{3*10} = 0.0001\)

\(max = \frac{0.0031}{(\sqrt{30} + 0.0031)*\sqrt{30}} = \frac{0.0031}{30 + 0.0031*\sqrt{30}} ≈ \frac{0.0031}{30} = \frac{0.003}{30} + \frac{0.0001}{30} ≈ \frac{0.003}{30} = 0.0001\)
.

Answer C.
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If 0.0030<x-√30<0.0031, which of the following options is the approxim  [#permalink]

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New post 30 Sep 2018, 12:09
1
hazelnut wrote:
If \(0.0030<x-\sqrt{30}<0.0031\), which of the following options is the approximation of  \(\frac{1}{\sqrt{30}}-\frac{1}{x}\)?

A. 0.001     
B. 0.002     
C. 0.0001     
D. 0.0002     
E. 0.0003


here is my approach

The \(\sqrt{30}\) is about 5.4

Hence x is between \(0.0030<x-5.4<0.0031\) add 5.4 to both sides so difference between maximum and minimum value is 0.0001

so I clicked on C :) :lol:
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If 0.0030<x-√30<0.0031, which of the following options is the approxim &nbs [#permalink] 30 Sep 2018, 12:09
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