sin(z) Complete the following to write an expression for f(x) where f'(x) = and f(2) = 4. I f(x) = g(t) dt + h(x), where g(t) = h(x) = a = Find the general solution to each differential equation below (all integrating constants should be written as 'C'). What is the solution satisfying y(1) = 2? a) dy = x + 2x General Solution: y Solution satisfying y(1) 2: y= b) = 2 cos x General Solution: y = Solution satisfying y(1) = 2: y = c) = 4, where x>0 dy General Solution: y Solution satisfying y(1) = 2: y = A car going 76 mph stops in 155 feet. Find the acceleration (assuming it is constant). Acceleration: a = miles per square hours A stone thrown upward from the top of a 300 foot cliff at 136 ft/sec eventually falls to the beach below. Note: the acceleration due to gravity is a constant -32 ft/sec. It may help to try and find a formula for the height as a function of t. a) How long does the stone take to reach its maximum height? Time to maximum height: seconds b) What is the maximum height reached by the stone? Maximum height:| feet c) How long does it take for the stone to hit the beach? Time to hit the beach: seconds d) What is the velocity of the stone on impact? Velocity on impact: ft/sec A revenue R(p) is obtained by a farmer from selling grain at price p dollars per unit. The marginal revenue is given by R'(p) = 25 - 2p. a) Find R(p). (Assume revenue is zero when price is zero.) R(p)= b) For what prices does the revenue increase as the price increases? For what prices does the revenue decrease as price increases? Revenue increases as price increases: Revenue decreases as price increases: c) At what price does the farmer obtain the most revenue? Price for most revenue: dollars Ice is forming on a pond at a rate given by dy =kt, dt where y is the thickness of the ice in centimeters at time t measured in hours since the ice started forming, and k is a positive constant. Find y as a function of t. y = A cat, walking along the window ledge of a New York apartment, knocks off a flower pot, which falls to the street 310 feet below. How fast is the flower pot traveling when it hits the street? (Give your answer in ft/s and in mi/hr, given that the acceleration due to gravity is 32 ft/s and 1 ft/s = 15/22 mi/hr.) Speed when hitting the ground: ft/s Speed when hitting the ground: mph