1. A man walks along a straight path at a speed of π ft/s. A searchlight...

1. A man walks along a straight path at a speed of π ft/s. A searchlight is located on the ground 18 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 30 ft from the searchlight? Draw a picture first to understand the problem.

2. Suppose square ABCD has straight edges of length 2, and its corners are connected by hinges. When pulling corners A and C, the square slowly deforms into a rhombus. Given that the area A of a rhombus can be expressed as A = 2a² sinθ, where θ is one of the angles of the rhombus, and a is the side length, find the rate of change of the area when one of the angles of the rhombus is π/3 rad, and it is also decreasing at a rate of π/12 rad/s.

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milcah answered 1 year ago

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