Question

select the correct answer
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 c?
a. $b = 25c$
b. $b = 200c$
c. $b\sqrt{c} = 50$
d. $b = 50\sqrt{c}$

Explanation:

Step1: Define direct variation form

Since \(b\) varies directly as \(\sqrt{c}\), the relationship is \(b = k\sqrt{c}\), where \(k\) is the constant of variation.

Step2: Solve for constant \(k\)

Substitute \(b=100\) and \(c=4\):
\(100 = k\sqrt{4}\)
\(100 = k\times2\)
\(k = \frac{100}{2}=50\)

Step3: Substitute \(k\) into variation equation

Replace \(k\) with 50 in \(b = k\sqrt{c}\):
\(b = 50\sqrt{c}\)

Answer:

D. \(b = 50\sqrt{c}\)