Question

1. Suppose that you are standing on the ground, under the flight path of an airplane....

1. Suppose that you are standing on the ground, under the flight path of an airplane. The airplane is flying at an altitude of 10 km. Using a radar device, you are able to detect that the plane is currently 26 km away from you, and that its distance to you is currently shrinking at a rate of 840 kilometers per hour. What is the current speed of the airplane?

Hint: use the Pythagorean theorem to express a relationship between the plane’s distance to you and the unlabeled side of the triangle.

2. Which point on the graph y = √ x is closest to the point (7, 0)?

3. A cone is constrained to have a volume of 100 cubic feet. Find the height and radius that minimize the surface area of the cone. Hint: the surface area of a cone is given by the formula: S = πr2 + πrs Where s is the ”slant”, given by: s 2 = r 2 + h 2 And h is the height.

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