Question

hw 11.1_inverse variation
score: 12/14 answered: 12/14
question 9
the force f (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length l (in inches) of the handle.
a force of 50 pounds is needed when the handle is 8 inches long. if a person needs 20 pounds of force to loosen the bolt, estimate the length of the wrench handle.
round answer to two decimal places if necessary.
inches
question help: video

Explanation:

Step1: Define inverse variation formula

Inverse variation is modeled as $F = \frac{k}{L}$, where $k$ is the constant of variation.

Step2: Solve for constant $k$

Substitute $F=50$, $L=8$:
$50 = \frac{k}{8}$
$k = 50 \times 8 = 400$

Step3: Find length for $F=20$

Use $k=400$, $F=20$ in $F = \frac{k}{L}$:
$20 = \frac{400}{L}$
$L = \frac{400}{20}$

Answer:

20 inches