Question

the distance that a spring will stretch varies directly as the force applied to the spring. a force of 70 pounds is needed to stretch a spring 7 inches. what force is required to stretch the spring 18 inches? a -pound force is required to stretch the spring 18 inches.

Explanation:

Step1: Find the constant of proportionality

Since the distance \(d\) varies directly as the force \(F\), the equation is \(d = kF\). Given \(F = 70\) pounds and \(d=7\) inches. Substitute into the equation: \(7=k\times70\). Solve for \(k\): \(k=\frac{7}{70}=\frac{1}{10}\).

Step2: Find the force for \(d = 18\) inches

Now use the equation \(d = kF\) with \(k=\frac{1}{10}\) and \(d = 18\). So \(18=\frac{1}{10}F\). Multiply both sides by \(10\) to solve for \(F\): \(F=18\times10 = 180\).

Answer:

\(180\)