Find the dimensions x (horizontal side) and y (vertical side) of the rectangle inscribed in a circle of radius r that maximizes the quantity 4xy^2. r (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the answers in terms of the radius, r.) x = y =
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So, using the Pythagorean theorem, we have x^2 + y^2 = (2r)^2 = 4r^2. We want to maximize the quantity 4xy. We can express y in terms of x using the equation above: y = sqrt(4r^2 - x^2). Substitute y into the quantity we want to maximize: 4xy = 4x*sqrt(4r^2 - Show more…
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