The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by

A pumping station adds sand to the beach at a rate modeled by the function S, given by

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.

(a) How much sand will the tide remove from the beach during this 6-hour period? Indicate units of measure.

First plug integrate the function at with the x values fnInt(2+5sin(4pi t/25),x,0,6)

shoul get =31.816^3 yds

(b) Write an espression for Y(t), total number of cubic yards of sand on the beach at time t.

y(t)= fnInt(s(t)-fnIntR(t)) dt +2500

(c) Find the rate at which the total amount of sand on the beach is changing at time t=4.

y'(4)= { (15t/1+3t) dt - { (2+5sin(4pi t/25 dt + 2500

=

plug in 4 and integrate result=-1.908 yd/hr

(d) For

, at what time t is the amount of sand on the beach a minimum? What is the minimum value? Justify your answers.

find where the y1-y2 gives you 0 or undefined. (critical points)

at that x value plug in to the funvtion integrate and final result will give you the minimum value.