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A bucket that weighs 3.4 pounds and a rope of negligible weight are used to draw water from a well that is 76 feet deep. The bucket is filled with 36 pounds of water and is pulled up at a rate of 2.8 feet per second, but water leaks out of a hole in the bucket at a rate of 0.3 pounds per second. Find the work done pulling the bucket to the top of the well. Your answer must include the correct units. (You may enter lbf or lb*ft for ft-lb.)
Assume that a watermelon dropped from a tall building falls y=16t^2 in t sec. Find the watermelon's average speed during the first 3 sec of fall and the speed at the instant t=3sec.
Let T be an exponential random variable with parameter λ.let X be a discrete random variable defined as X=k if k
Use the euclidean algorithm to find the greatest common divisor of 981 and 1234.
Use the limit comparison test to determine if this series converges or diverges.
How many distinct isosceles triangles with sides of integral legnth have a perimeter of 40cm?
Find a number in the interval [1/2, 3/2] such that the sum of thee number and its reciprocal is as large as possible.
A merchant has coffee worth $20 a pound that she wishes to mix with 50 pounds of coffee worth $80 a pound to get a mixture that can be sold for $30 a pound. How many pounds of the $20 coffee should be used.
Please show work step by step. Find the derivatives of.
Use the method of undetermined coecients to fi nd the general solution of
A baseball diamond is a square with side 90ft. A batter hits the ball and runs towards first base with a speed of 29 ft/s.
Plot the value of each strategy over time for a single interaction of the simulation. What is the total value of each strategy after six years? Do either of the strategies reach the target?
Assume that the field is algebraically closed and has zero characteristic, G is finite and representations are finite-dimensional.
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