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ricekrispie
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Homework Statement
(a) Use a midpoint Riemann sum with 4 subdivisions of equal length to approximate [tex]\int_0^{24} R(t) dt[/tex]. Using correct units, explain the meaning of your answer in terms of water flow.
(b) Is there some time t, 0 < t < 24, such that R´(t) = 0? Justify your answer.
(c) The rate of water flow R(t) can be approximated by Q(t) = (1/79)(768 + 23t - t^2).
Use Q(t) to approximate the average rate of water flow during the 24-hour time period. Indicate units of measure.
P.S.: THIS IS AN AP PROBLEM :(
P.S.2: SORRY, I DON´T HAVE A CLUE OF WHERE TO START
t (hours) | R(t) (gallons per hour)
0 9,6
3 10,4
6 10,8
9 11,2
12 11,4
15 11,3
18 10,7
21 10,2
24 9,6
The rate at which water flows out of a pipe, in gallons per hour, is given by a differentiable function R of time t. The table above shows the rate as measured every 3 hrs for a 24-hour period.0 9,6
3 10,4
6 10,8
9 11,2
12 11,4
15 11,3
18 10,7
21 10,2
24 9,6
(a) Use a midpoint Riemann sum with 4 subdivisions of equal length to approximate [tex]\int_0^{24} R(t) dt[/tex]. Using correct units, explain the meaning of your answer in terms of water flow.
(b) Is there some time t, 0 < t < 24, such that R´(t) = 0? Justify your answer.
(c) The rate of water flow R(t) can be approximated by Q(t) = (1/79)(768 + 23t - t^2).
Use Q(t) to approximate the average rate of water flow during the 24-hour time period. Indicate units of measure.
P.S.: THIS IS AN AP PROBLEM :(
P.S.2: SORRY, I DON´T HAVE A CLUE OF WHERE TO START
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