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Asked Dec 2, 2019
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A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r.

A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r.
(smaller value)
(larger value)
(x, y
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A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r. (smaller value) (larger value) (x, y

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Expert Answer

Step 1

Given:

Assume that the center of the semicircle be (0,0).

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(х ул

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Step 2

Concept used:

The equation of the semicircle is given:

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y r* =x° .. Area of rectangle inscribed in a semicircle is, A 2xy

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Step 3

Substitute the value of ‘y’ in Area...

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A(x) 2xy A (x) 2x-r-x differentiate with respectto'x': d A(x)(2x) ( (2x) by produet rule] +(vr° -x : by product rule] dx 1 (-2x)+r-x2 A'(x)= 2x- 2/r-x -2x2 +2/r -x° A'(x)

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Tagged in

Math

Calculus

Derivative