Math141_Related Rates_4.1

Math141_Related Rates_4.1 - 7. Substitute the given...

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Related Rates Example1 A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from a wall 1 ft/se, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft. from the wall? Strategy: 1. Read the problem carefully 2. Draw a diagram if possible. 3. Introduce notation. Assign symbols to all quantities that are functions of time. 4. Express the given information and the required rate in terms of derivatives. 5. Write an equation that relates the various quantities of the problem. If necessary, use the geometry of the situation to eliminate one of the variables by substitution. 6. Use the chain rule to differentiate both sides of the equation with respect to t.
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Unformatted text preview: 7. Substitute the given information into the resulting equation and solve for the unknown rate. Example 2 A water tank has the shape of an inverted circular cone with base radius 2 m. and height 4 m. If water is being pumped into the tank at a rate of 2 m^3/min, find the rate at which the water level is rising when the water level is 3m. deep. Example 3 A plane flying horizontally at an altitude of 1 mile and a speed of 500 mph passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station....
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