LINKING concepts... For Individual or Group Explorations Designing a Race Track An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track. a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section. b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track. c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track. d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
LINKING concepts... For Individual or Group Explorations Designing a Race Track An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track. a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section. b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track. c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track. d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
Solution Summary: The author calculates the dimensions of xandy in the figure that will maximize the area of the rectangular center section.
An architect is designing a race track that will be 60 feel wide and have semicircular ends, as shown in the accompanying figure. The length of the track is to he one mile. measured on the inside edge of the track.
a) Find the exact dimensions for x and y in the figure that will maximize the area of the rectangular center section.
b) Round the answers to part (a) to the nearest tenth of a foot and make an accurate drawing of the track.
c) Find the exact dimensions for x and y that will maximize the total area enclosed by the track.
d) Repeat parts (a), (b), and (c) assuming that the one-mile length is measured on the outside edge of the track.
You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
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