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hw10-10

hw10-10 - Math 170-010 Homework 10/10 Fall 2011 Goals Work...

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Math 170-010 Homework 10/10 Fall 2011 Goals: Work Type I problems in which some or all functions are implicit. Be able to recognize what role a letter plays in a given problem. Sometimes it’s a constant; sometimes it’s an input variable; sometimes it’s an unknown or implicit function. Warm Up: 1. Suppose that x 2 + y 2 = 100. Find dy dx at the location x = 5, y = - 5 3. 2. Suppose that x 2 + y 2 = 100. In this problem: y measures the height of an object in feet x measures the position of a second object in feet. t is time in seconds. dx dt = - 2 ft/s. Find dy dt when x = 5 3 feet and y = 5 feet. Exercises: 1. Suppose that x 2 = y 3 . In this problem y is measured in feet and is a function of time, t . x is measured in feet and is a function of time, t . t is measured in seconds. Find dy dt when x = 8 feet, y = 4, and dx dt = - 3 ft/s. 2. Suppose that x 2 + y 2 = 169. In this problem x and y measure the positions of two moving objects, both measured in miles.

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