Problem 761

Find an equation of variation where y varies inversely as the square of x, and where y = 0.35 when x = 0.1.

Solution:-

Since y = varies inversely as the square of x, use the form

y = $\frac{k}{x^{2}}$ .

To find the variation constant, substitute 0.1 for x and 0.35 for y.

y = $\frac{k}{x^{2}}$ .

0.35 = y = $\frac{k}{(0.1)^{2}}$ .

Simplify the exponential expression.

.035 = $\frac{k}{0.01}$

Solve for k.

0.0035 = k

The variation constant is 0.0035.

The equation of variation is y = $\frac{0.0035}{x^{2}}$ .