Determine the constant of variation for the stated condition.
-If $y$ varies directly as the square root of $x$, and $y = 9$ when $x = 49$, find $y$ when $x = 36$.
A) $\frac { 54 } { 7 }$
B) $\frac { 324 } { 49 }$
C) $\frac { 21 } { 2 }$
D) $\frac { 49 } { 4 }$

Question

Quizplus · Accepted Answer

The constant of variation $k$ can be found using the given condition $y = k\sqrt{x}$. Substituting $y = 9$ and $x = 49$, we get $9 = k\sqrt{49}$ or $9 = 7k$, leading to $k = \frac{9}{7}$. To find $y$ when $x = 36$, substitute $x = 36$ and $k = \frac{9}{7}$ into the original equation: $y = \frac{9}{7}\sqrt{36} = \frac{9}{7} \times 6 = \frac{54}{7}$.

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

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