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what is the least integer value of x?
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22 Nov 2016, 16:46
22 Nov 2016, 16:46
Expert Reply
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Question Stats:
71% (00:56) correct
28% (01:00) wrong based on 21 sessions
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If \(\frac{2}{x^3}< 0.02\)what is the least integer value of x?
A. No such least value exists.
B. 101
C. 100
D. 5
E. 4
A. No such least value exists.
B. 101
C. 100
D. 5
E. 4
Drill 4
Question: 11
Page: 295
Question: 11
Page: 295
Re: what is the least integer value of x?
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22 Nov 2016, 16:48
22 Nov 2016, 16:48
Expert Reply
Explanation
First, rewrite 0.02 as a fraction, \(\frac{2}{100}\). For \(\frac{2}{3^x}\) to be less than \(\frac{2}{100}\) \(3^x\) must be greater than 100.
Plugging In the Answers is the easiest way to get this right. Choice (E) is \(3^4\) = 81 and the fraction is greater than 0.02; eliminate it.
Choice (D) is \(3^5\) = 243 and this makes the fraction inequality would be true if the denominator of less than 0.02. Therefore, the least value for x is 5. Be sure to answer what is asked. The \(\frac{2}{3^x}\) were 101, which is choice (B); however, the question is asking for the least value of x, not of 3x, so the correct answer is choice D.
The correct option is D.
First, rewrite 0.02 as a fraction, \(\frac{2}{100}\). For \(\frac{2}{3^x}\) to be less than \(\frac{2}{100}\) \(3^x\) must be greater than 100.
Plugging In the Answers is the easiest way to get this right. Choice (E) is \(3^4\) = 81 and the fraction is greater than 0.02; eliminate it.
Choice (D) is \(3^5\) = 243 and this makes the fraction inequality would be true if the denominator of less than 0.02. Therefore, the least value for x is 5. Be sure to answer what is asked. The \(\frac{2}{3^x}\) were 101, which is choice (B); however, the question is asking for the least value of x, not of 3x, so the correct answer is choice D.
The correct option is D.
Re: what is the least integer value of x?
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06 Oct 2018, 02:10
06 Oct 2018, 02:10
3^X OR X^3 ? I am confused
