a) To find out how much sand will be removed, you must find the interval of the function from 0 to 6; which is about, 31.816 cubic yards.
b) Y(t)= S(t)-R(t)+2500
S(t) is the sand being added subtracted by R(t) which is the sand being taken away + the initial sand the beach originally had, (2500).
c) To find out the rate of sand being taken out at time 4, we have to plug it into Y(t), which is -1.909 cubic yards/an hour.
d) Graph both S(t) and R(t) into the graphing calculator and find the point where they intersect. The point would be, (5.1178, 4.6943), so 5.1178 is the minimum, and the output at that time would be 4.6943, since we are trying to find out how much sand we have at that time, we add 2500 (initial amount of sand)+4.6943=2504.694.
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For part b, you are supposed to take the integral from 0 to t, since you want the sand, not the rate. so for c, you plug it into Y ' (t), which actually is S(t)-R(t), since taking the derivative of the antiderivative (integral) gives you just S(t)-R(t). (remember the fundamental theorem of calculus part 1! And dont forget to explain your part d! (Justify your answer)! (:
ReplyDeleteexplain me more,...,
ReplyDeletei agree, a little more work please?
ReplyDeletelol
i know you understand it, but i personally didnt and had to look in the book alot.
for c you have to plug in the numbers into nderiv not y(t)
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