P16 - F exerted by a body of mass m on a body of mass M has...

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Project 16 MAC 2233 1. Suppose the daily supply x of a certain product in an open-air market is related to the unit price p (in dollars) by the equation 100 p 2 + 10 xp = x 2 + 500 . Calculate dx dp implicitly. What rate of change does it represent? Find all the points on the graph of the equation having p -coordinate 3 . Evaluate dx dp at any point that makes sense in the current context. Now suppose the price of the product is rising by 50 cents per day when the price is $ 3 . Calculate the rate at which the daily supply is changing per day. Suppose the daily demand for the product is given by the relationship 10 p 2 + 3 x 2 = 1290 . Calculate the rate at which the daily demand is changing at the instant described above. What about the change in revenue? 2. Newton’s Law of Gravitation states that the force
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Unformatted text preview: F exerted by a body of mass m on a body of mass M has magnitude: F = GMm r 2 where G is the gravitational constant and r is the distance between the centers of the bodies. Suppose a rocket is launched from earth so that when it is 100 kilometers above the surface, it has speed . 5 km/sec. Assume the radius of the earth is 6 , 300 km and that the mass m of the rocket is a constant 500 kg at that instant. At what rate is the force changing at that instant? (Leave constants G,M in your answer.) Now suppose that the mass m of the rocket is decreasing by 1 . 5 kg/sec as the rocket consumes fuel. What is the new result? (Use quotient rule with m and r leave constants G,M in your answer.)...
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