Question

the value of m varies inversely as the square of n. when n = 3, m = 6. what is the positive value of n when m = 13.5?
a. 0.8
b. 9
c. 2
d. 4

Explanation:

Step1: Define inverse variation formula

If \( m \) varies inversely as the square of \( n \), the formula is \( m=\frac{k}{n^{2}} \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

Given \( n = 3 \) and \( m = 6 \), substitute into the formula:
\( 6=\frac{k}{3^{2}} \)
\( 6=\frac{k}{9} \)
Multiply both sides by 9: \( k = 6\times9=54 \).

Step3: Find \( n \) when \( m = 13.5 \)

Now the formula is \( m=\frac{54}{n^{2}} \). Substitute \( m = 13.5 \):
\( 13.5=\frac{54}{n^{2}} \)
Multiply both sides by \( n^{2} \): \( 13.5n^{2}=54 \)
Divide both sides by 13.5: \( n^{2}=\frac{54}{13.5}=4 \)
Take the positive square root: \( n=\sqrt{4}=2 \).

Answer:

C. 2