Hey guys, I was doing some practice free response questions for my upcoming AP Calc AB test but was somehwhat unsure of this one.(adsbygoogle = window.adsbygoogle || []).push({});

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Sand is removed from the beach at a certain rate by this function

R(t)= 2+5SIN(4t(pi)/25)

Sand is pumped into the beach with this equation

S(t)=15t/1+3t

Both functions are in cubic yards per hour and the interval of t is from [0,6].

A t=0, there is 2500 cubic feet of sand

a) how much sand will be removed in the 6hr period?

Here I took the integral of R(t) from 0 to 6 which came out to be 31.816 subic yards

b) write an expression for Y(t), the total number of sand on the beat at time t

I came up with Y(t)=2500-(intregal of R(T)+s(t)) from 0 to6

c) find the rate of change of sand at t=4

this was taking the derivative of the equation in part b which came to be about -1.91 cubic yd/hr

d) for [0,6], at what time t is the amount of sand on the beach minimum? what is that value? justify answer

This one I am having trouble with but I graphed the dervative and found x=3 to be when the graph was at its lowest point, although I'm not sure if that is correct.

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Any help is appreciated/assistance is greatly appreciated.

Hope you guys have a good day .

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# Homework Help: Need assistance with Derivative/Intregal Problem

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