Question

the variable a varies directly as $sqrt{b}$. if a = 8 when b = 324, what is a when b = 49? round your answer to two decimal places if necessary.

Explanation:

Step1: Find the constant of variation.

Since $a$ varies directly as $\sqrt{b}$, the equation is $a = k\sqrt{b}$. When $a = 8$ and $b = 324$, first find $\sqrt{b}=\sqrt{324}=18$. Then substitute into the equation: $8=k\times18$, so $k=\frac{8}{18}=\frac{4}{9}$.

Step2: Find $a$ when $b = 49$.

First, find $\sqrt{b}=\sqrt{49} = 7$. Then use the equation $a=k\sqrt{b}$ with $k = \frac{4}{9}$ and $\sqrt{b}=7$. So $a=\frac{4}{9}\times7=\frac{28}{9}\approx3.11$.

Answer:

$3.11$