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If the function Q is defined by the formula \(Q = \frac{5w}{4x(z^2)}\), by what factor will Q be multiplied if w is quadrupled, x is doubled, and z is tripled?
A. 1/9
B. 2/9
C. 4/9
D. 3/9
E. 2/27
A. 1/9
B. 2/9
C. 4/9
D. 3/9
E. 2/27
21 Apr 2012, 00:10
Kudos
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If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what factor will Q be multiplied if w is quadrupled, x is doubled, and z is tripled?
A. 1/9
B. 2/9
C. 4/9
D. 3/9
E. 2/27
Given: \(Q=\frac{5w}{4x*z^2}\).
Now, quadruple \(w\), so make it \(4w\); double \(x\) so make it \(2x\); triple \(z\) and substitute these values instead of \(x\), \(y\), and \(z\) in the original equation:
\(\frac{5(4w)}{4(2x)*(3z)^2}=\frac{4*5w}{4*2x*9*z^2}=\frac{4*5w}{18*(4x*z^2)}=\frac{4}{18}*\frac{5w}{4x*z^2}=\frac{2}{9}*\frac{5w}{4x*z^2}\). Thus Q is multiplied by \(\frac{2}{9}\).
Answer: B.
Else plug-in values for \(x\), \(y\), and \(z\). Let \(x=y=z=1\) --> \(Q=\frac{5w}{4x*z^2}=\frac{5}{4}\).
\(4w=4\), \(2x=2\) and \(3z=3\) --> \(\frac{5*4}{4*2*3^2}=\frac{4}{18}*\frac{5}{4}=\frac{2}{9}*\frac{5}{4}\). Thus Q is multiplied by \(\frac{2}{9}\).
Answer: B.
Hope it's clear.
A. 1/9
B. 2/9
C. 4/9
D. 3/9
E. 2/27
Given: \(Q=\frac{5w}{4x*z^2}\).
Now, quadruple \(w\), so make it \(4w\); double \(x\) so make it \(2x\); triple \(z\) and substitute these values instead of \(x\), \(y\), and \(z\) in the original equation:
\(\frac{5(4w)}{4(2x)*(3z)^2}=\frac{4*5w}{4*2x*9*z^2}=\frac{4*5w}{18*(4x*z^2)}=\frac{4}{18}*\frac{5w}{4x*z^2}=\frac{2}{9}*\frac{5w}{4x*z^2}\). Thus Q is multiplied by \(\frac{2}{9}\).
Answer: B.
Else plug-in values for \(x\), \(y\), and \(z\). Let \(x=y=z=1\) --> \(Q=\frac{5w}{4x*z^2}=\frac{5}{4}\).
\(4w=4\), \(2x=2\) and \(3z=3\) --> \(\frac{5*4}{4*2*3^2}=\frac{4}{18}*\frac{5}{4}=\frac{2}{9}*\frac{5}{4}\). Thus Q is multiplied by \(\frac{2}{9}\).
Answer: B.
Hope it's clear.
General Discussion
04 Jun 2011, 19:09
Kudos
Bookmarks
IN the expression Q=5w/4xz^2, substitute the values as mentioned :
So new expression is -> 5 * (4w)/(4 * (2x) * (3z)^2)
= 5 * w/(2x * 9 * z^2)
= (2/9) * 5w/4xz^2
= 2/9 * Q
So Q will be multiplied by the factor 2/9.
So new expression is -> 5 * (4w)/(4 * (2x) * (3z)^2)
= 5 * w/(2x * 9 * z^2)
= (2/9) * 5w/4xz^2
= 2/9 * Q
So Q will be multiplied by the factor 2/9.
