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a windshield wiper sweeps out a circular sector with radius r inches, and arc length = 1.4 times the radius.Write a SIMPLIFIED EXPRESSION in the box below that represents the area, in square inches, of the sector the wiper sweeps out.

a windshield wiper sweeps out a circular sector with radius r inches, and arc length-example-1
User Gadoma
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1 Answer

10 votes
10 votes

The central angle θ in radians is given by


\begin{gathered} \theta=\frac{arc\text{ length}}{radius} \\ \text{ Therefore,} \\ \theta=(1.4r)/(r)=1.4 \end{gathered}

Area A of a sector with a radius r and a central angle θ in radians is given by:


A=(1)/(2)r^2\theta

Hence, the area A is:


\begin{gathered} A=(1)/(2)r^2(1.4) \\ A=0.7r^2 \end{gathered}

Therefore, the required simplified expression for the area is

A = 0.7r²

User Arvid Heise
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