Question

the force y (in pounds) required to stretch a particular spring x in beyond its rest (or \equilibrium\) position is given by the equation y = 2.5x, where 0 ≤ x ≤ 40.
part 1 of 3
(a) use the equation to determine the amount of force necessary to stretch the spring 4 in from its rest position. how much force is necessary to stretch the spring twice as far?
the amount of force necessary to stretch the spring 4 in from its rest position is 10 lb.
part 2 of 3
the amount of force necessary to stretch the spring twice as far is 20 lb.
part 3 of 3
(b) if 30 lb of force is exerted on the spring, how far will the spring be stretched?
the spring will be stretched

Explanation:

Step1: Identify the formula

The formula for force is $y = 2.5x$, where $y$ is force and $x$ is the stretch distance.

Step2: Solve for $x$ when $y = 30$

We substitute $y = 30$ into the formula $y=2.5x$ and solve for $x$. So, $30 = 2.5x$. Then $x=\frac{30}{2.5}=12$.

Answer:

12