The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by
R(T)= 2+5sin(4piT/25)
A pumping station adds sand to the beach at a rate modeled by the function S, 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 0 to 6. At time t=6, 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.
b. write an expression for Y(t), the total number of cubic yards of sand on the beach at time t.
c. find the rate at which the total amount of sand on the beach is changing at time t=4.
d. for time 0 to 6, at what time t is the amount of sand on the beach minimum? what is the minimum value? Justify your answers.
i know this is very long..but i have been working on it for a while and i just can't seem to get it %26gt;.%26lt; any help at all is very much appreciated..thank you so much in advance!
Math help please????
a) Find integral of R(T) from 0 to 6.
b) Find integral of R(T) + S(T) from 0 to t. Use the initial condition to find the value of the constant of integration.
c) Just put t = 4 into R(T) + S(T)
d) Minimum will occur when net rate of change is zero, so solve the equation R(T) + S(T) = 0
This part won't be at all easy. I think that you will have to use approximate methods.
