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An automobile windshield wiper 12 inches long rotates through an angle of 60°. If the rubber part of the blade covers only the last 10 inches of the wiper, find the area of the windshield cleaned by the windshield wiper.

Respuesta :

[tex]\begin{gathered} r1=12in \\ r2=10\text{ in} \\ \theta=60\text{ \degree} \\ A_s=\frac{\pi r^2\theta}{360} \\ A_{cleaned}=\frac{\pi r2^2\theta}{360}-\frac{\pi r1^2\theta}{360} \\ \text{Common factor} \\ A_{cleaned}=\frac{\pi\theta}{360}(r2^2-r1^2) \\ A_{cleaned}=\frac{\pi(60)}{360}((12in)^2^{}-(10in)^2) \\ A_{cleaned}=\frac{\pi(60)}{360}(144in^2^{}-100in^2) \\ A_{cleaned}=\frac{\pi(60)}{360}(44in^2) \\ A_{cleaned}=\frac{\pi(60)}{360}(44in^2) \\ A_{cleaned}\approx23in^2 \\ \text{The area cleaned is }23in^2 \end{gathered}[/tex]

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