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Difficulty:
15%
(low)
Question Stats:
78% (01:06) correct
22%
(01:19)
wrong
based on 77
sessions
History
Date
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If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
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Official Solution:
If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
Cross-multiply: \(\sqrt{x} = 4x\)
Square both sides of the equation to eliminate the square root: \(x = 16x^2\)
Given that \(x\) is a positive number, we can safely divide both sides by \(x\): \(1 = 16x\). This gives us \(x = \frac{1}{16}\).
Answer: B
_________________
If \(x\) is a positive number and \(\frac{1}{2}*\sqrt{x} = 2x\), what is the value of \(x\)?
A. \(0\)
B. \(\frac{1}{16}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)
E. \(1\)
Cross-multiply: \(\sqrt{x} = 4x\)
Square both sides of the equation to eliminate the square root: \(x = 16x^2\)
Given that \(x\) is a positive number, we can safely divide both sides by \(x\): \(1 = 16x\). This gives us \(x = \frac{1}{16}\).
Answer: B
_________________
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General Discussion
I got B 1/16
I eliminated 1 and 0 (zero, I think would be undefined, 1 would be itself)
I plugged in answers (fast for me), so no help on a formula.
I eliminated 1 and 0 (zero, I think would be undefined, 1 would be itself)
I plugged in answers (fast for me), so no help on a formula.
sqrt(x)/2 = 2x --> sqrt(x) = 4x
Answer is 1/16
Answer is 1/16
1/2sqrt(x) = 2x
sqrt(x) = 4x
x = 16x^2
x(16x-1) = 0
x = 0, x = 1/16
Since question says x is positive, then x = 1/16
sqrt(x) = 4x
x = 16x^2
x(16x-1) = 0
x = 0, x = 1/16
Since question says x is positive, then x = 1/16
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