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11 Nov 2019
Let f and g be the functions given by f(x) = 1/4 + sin(pi x) and g(x) = 4-x, Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let s be the shaded region in the first quadrant enclosed by the graphs of f and g, as shown in the figure above, Find the area of R, Find the area of S, Find the volume of the solid generated when S is revolved about the horizontal line y =-1. The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by R(t)=2 + 5sin(4 pi t/25) A pumping station adds sand to the beach at a rate modeled by the function 5, given by S(t) = 15t/1 = 3t. Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for , At time t = 0, the beach contains 2500 cubic yards of sand. How much sand will the tide remove from the beach during this 6'hour period? Indicate units of measure. Write an expression for Y(t), the total number of cubic yards of sand on the beach at time t. Find the rate at which the total amount of sand on the beach is changing at time t = 4, For , at what time t is the amount of sand on the bench a minimum? What is the minimum ? Justify your answers,
Let f and g be the functions given by f(x) = 1/4 + sin(pi x) and g(x) = 4-x, Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let s be the shaded region in the first quadrant enclosed by the graphs of f and g, as shown in the figure above, Find the area of R, Find the area of S, Find the volume of the solid generated when S is revolved about the horizontal line y =-1. The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by R(t)=2 + 5sin(4 pi t/25) A pumping station adds sand to the beach at a rate modeled by the function 5, given by S(t) = 15t/1 = 3t. Both R(t) and S(t) have units of cubic yards per hour and t is measured in hours for , At time t = 0, the beach contains 2500 cubic yards of sand. How much sand will the tide remove from the beach during this 6'hour period? Indicate units of measure. Write an expression for Y(t), the total number of cubic yards of sand on the beach at time t. Find the rate at which the total amount of sand on the beach is changing at time t = 4, For , at what time t is the amount of sand on the bench a minimum? What is the minimum ? Justify your answers,