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Difference between revisions of "1954 AHSME Problems/Problem 3"

(Created page with "== Problem 3== If <math>x</math> varies as the cube of <math>y</math>, and <math>y</math> varies as the fifth root of <math>z</math>, then <math>x</math> varies as the nth po...")
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Revision as of 13:35, 6 June 2016

Problem 3

If $x$ varies as the cube of $y$, and $y$ varies as the fifth root of $z$, then $x$ varies as the nth power of $z$, where n is:

$\textbf{(A)}\ \frac{1}{15} \qquad\textbf{(B)}\ \frac{5}{3} \qquad\textbf{(C)}\ \frac{3}{5} \qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 8$

Solution

$x=k\cdot y^3$, $y=j\cdot z^{\frac{1}{5}}\implies y^3=j^3\cdot z^{\frac{3}{5}}$, so $x=k\cdot j^3\cdot z^{\frac{3}{5}}$, $\fbox{C}$

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