Question

The variable b varies directly as the square root of c. If b = 100 when c = 4, which equation can be used to find other combinations of b and ca. b=25cb. b√c=50c. b=200cd. b=50√c

Answer 1

Solution

Step 1:

$\begin{gathered} b\text{ }\propto\text{ }\sqrt{c} \\ b\text{ = k}\sqrt{c} \end{gathered}$

Step 2:

Use the value b = 100 and c = 4 to find the value of k.

$\begin{gathered} Substitute\text{ b = 100 and c = 4} \\ 100\text{ = k}\sqrt{4} \\ 100\text{ = 2k} \\ \text{k = }\frac{100}{2} \\ \text{k = 50} \end{gathered}$

Step 3

$b\text{ = 50}\sqrt{c}$

Final answer

The equation that can be used to find other combinations of b and c is

$\text{b = 50}\sqrt{c}$

Option D