Question

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.

Answer 1