automobiles suppose the arm of a windshield wiper is 16 in. long, with a blade 12 in. long. if the wiper moves through an angle of 90, how much of the windshield is cleaned in one pass of the wiper ?

1/4 of a complete circle, so

π/2 (16^2 - 12^2) in^2

that's assuming that the blade extends to the end of the wiper arm.

how do you now what automobiles suppose?

To determine how much of the windshield is cleaned in one pass of the wiper, we need to find the distance covered by the blade as it moves through an angle of 90 degrees.

Given:
Length of the arm = 16 in.
Length of the blade = 12 in.
Angle of movement = 90 degrees

The total distance covered by the blade can be calculated using the formula:

Distance = 2π * Radius * (Angle / 360)

In this case, the radius of the circular motion is equal to the length of the arm. So, substituting the given values, we have:

Distance = 2π * 16 in. * (90 degrees / 360 degrees)

Next, let's convert the angle from degrees to radians. We know that 2π radians is equivalent to 360 degrees. Therefore, 1 degree is equal to 2π/360 radians. Substituting this conversion factor, we get:

Distance = (2π / 360) * 16 in. * 90 degrees

Simplifying further:

Distance = (π / 180) * 16 in. * 90

Distance = π * 16 in.

Finally, we can calculate the distance covered by the blade:

Distance = approximately 50.27 in.

Therefore, in one pass of the wiper, approximately 50.27 inches of the windshield will be cleaned.