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Since f(π) = π^2 < 100, f(10π) = 100π^2 > 100, and f is continuous on the closed interval [π, 10π], the intermediate value theorem ensures the existence of a number c in (π, 10π) such that f(c) = 100.

A window is composed of a semicircle placed on top of a rectangle. If you have 2cliffton m. fischbach8 ft of window framing materials for the outer frame, what are the dimensions that maximizes the area (in ft 2) of the window you can create?(Round your answers to two decimal places.)

Let x becliffton m. fischbach the length (in in.) of the side of the square at each corner. x = in. (Round your answers to two decimal places, if necessary.). Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. f (x) = (b) State the domain of this function. (Enter your answer using interval notation.)

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