/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 70 A car's rear windshield wiper ro... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 70

A car's rear windshield wiper rotates \(125^{\circ} .\) The total length of the wiper mechanism is 25 inches and wipes the windshield over a distance of 14 inches. Find the area covered by the wiper.

Short Answer

Expert verified
The area covered by the windshield wiper is approximately \(213.830 square inches\).

Step by step solution

01

Identify Information

Identify the information given in the problem: the wiper's angle of rotation is \(125^{\circ}\), the total length of the wiper is 25 inches, and the length that actually wipes the windshield is 14 inches. This implies that the total length doesn't impact the area cleaned; just the 14 inches that comes in contact with the windshield.
02

Convert Degrees to Radians

Since the formula for calculating the area of a sector of a circle requires the angle to be in radians, the given angle in degrees needs to be converted to radians. Use the formula \(\(radians\) = \(\(degrees\) * \(\pi\)/180\). Hence, \(125^{\circ}\) is equal to \(125 * \(\pi\)/180 = 2.18166 radians\).
03

Calculate the area

The area swept by the wiper (which we'll assume acts like a sector of a circle) can be found with the formula: \(Area = 0.5 * r^2 * theta = 0.5 * (14)^2 * 2.18166 = 213.830 square inches\)

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