Steps to Solve Related Rate Problems

Steps to Solve Related Rate Problems - What is the vertical...

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Steps to Solve Related Rate Problems – Section 3.9 1. Draw a picture. 2. Identify all given quantities and the quantities to be determined. Remember, the rate of change is the derivative with respect to time. 3. Write an equation relating the variables. You will probably need to use known formulas. 4. Differentiate both sides of your equation with respect to time ( t ). You will use the chain rule and implicit differentiation. Make sure you do not plug in any values for variables that are changing before you take the derivative. 5. After you have taken the derivative substitute all known values for the variables and their rates of change. 6. Solve the equation for the desired quantity. Example A rocket that is launched vertically is tracked by a radar station located on the ground 3 mi from the launch site.
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Unformatted text preview: What is the vertical speed of the rocket at the instant that its distance from the radar station is 5 mi and this distance is increasing at the rate of 5000 mi/h? Example Sand is being emptied from a hopper at the rate of 10 ft 3 /s. The sand forms a conical pile whose height is always twice its radius. At what rate is the radius of the pile increasing when its height is 5 ft? Example A circular oil slick of uniform thickness is caused by a spill of 1 m 3 of oil. The thickness of the oil slick is decreasing at the rate of 0.1 cm/h. At what rate is the radius of the slick increasing when the radius is 8 m?...
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Steps to Solve Related Rate Problems - What is the vertical...

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