Find the constant of variation for the stated condition: y is directly proportional to the square of x and inversely proportional to the cube of z , and $y = 8 \frac { 1 } { 6 }$ when x = 42 and z = 36.
A) k = 6
B) k = 7
C) k = 216
D) k = 36
E) k = 49

Question

Quizplus · Accepted Answer

We know that $y$ is directly proportional to the square of $x$ and inversely proportional to the cube of $z$. This can be written as:

$$y=k\frac{x^2}{z^3}$$

where $k$ is the constant of variation.

We can solve for $k$ using the given values:

$$8\frac{1}{6}=k\frac{42^2}{36^3}$$

Simplifying the right side:

$$8\frac{1}{6}=k\frac{14^2}{12^3}$$

$$8\frac{1}{6}=k\frac{196}{1728}$$

$$k=\frac{8\frac{1}{6}\cdot1728}{196}$$

$$k=216$$

Therefore, the constant of variation is $k=216$, making the answer choice C the correct one.

Find the Constant of Variation for the Stated Condition: Y y=816y = 8 \frac { 1 } { 6 }y=861​

Find the Constant of Variation for the Stated Condition: Y $y = 8 \frac { 1 } { 6 }$