Question

the width, y, of a rectangle with a fixed area varies inversely with its length, x. the width is 3 inches when the length is 14 inches. find the width when the length is 30 inches. multiple - choice 1 point 0.71 inches 4.48 inches 6.43 inches 1.4 inches

Explanation:

Step1: Write the inverse - variation formula

For inverse variation, $xy = k$ (where $k$ is the constant of variation). Given $x = 14$ inches and $y = 3$ inches, we find $k$.
$k=xy=14\times3 = 42$

Step2: Find the new width

We know $k = 42$ and the new length $x = 30$ inches. Using $xy = k$, we solve for $y$.
$y=\frac{k}{x}=\frac{42}{30}=1.4$ inches

Answer:

1.4 inches