1. An architect is designing a special window for a museum. It consists of a rectangle of base r and height h where a se

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1 An Architect Is Designing A Special Window For A Museum It Consists Of A Rectangle Of Base R And Height H Where A Se 1 (242.54 KiB) Viewed 28 times

1. An architect is designing a special window for a museum. It consists of a rectangle of base r and height h where a semi-circle is then removed from the top. A particular building material means the total contour of this exotically shaped window needs to be fixed at 600 cm. The architect wants to maximise the area, S, of the window so as to maximise light coming into the room. (a) First, the architect considers the shape where the semi-circle spans the full width of the rectangle. (i) Give an initial set of equations that represent this problem as one equation for the area in terms of x and h along with four boundary conditions. One of the conditions of this problem is that the area has to be greater or equal to zero. Use only exact values. (ii) The four boundary conditions from part (a)(i) may be condensed to two in terms of r and h only. Give this condensed set. Then, present the problem again as the equation for the area (in terms of x and h) along with two boundary conditions in terms of x and h only). Use only exact values.