Determine the constant of variation for the stated condition.
-If $y$ varies directly as the cube of $x$, and $y = 5$ when $x = 2$, find $y$ when $x = 8$.
A) 320
B) 20
C) $\frac { 5 } { 4 }$
D) $\frac { 5 } { 64 }$

Question

Quizplus · Accepted Answer

The constant of variation $k$ can be found using the given condition $y = kx^3$. Substituting $y = 5$ and $x = 2$, we get $5 = k(2)^3$, leading to $k = \frac{5}{8}$. To find $y$ when $x = 8$, substitute $x = 8$ and $k = \frac{5}{8}$ into the original equation: $y = \frac{5}{8}(8)^3 = 5 \times 8^2 = 5 \times 64 = 320$.

Determine the Constant of Variation for the Stated Condition yyy Varies Directly as the Cube Of

Determine the Constant of Variation for the Stated Condition $y$ Varies Directly as the Cube Of