Filling a reservoir A reservoir with a capacity of 2500 m 3 is filled with a single inflow pipe. The reservoir is empty when the inflow pipe is opened at t = 0. Letting Q( t ) be the amount of water in the reservoir at time t , the flow rate of water into the reservoir (in m 3 /hr) oscillates on a 24-hr cycle (see figure) and is given by Q ′ ( t ) = 20 ( 1 + cos π t 12 ) . a. How much water flows into the reservoir in the first 2 hr? b. Find the function that gives the amount of water in the reservoir over the interval [0. t], where t ≥ 0. c. When is the reservoir full?
Filling a reservoir A reservoir with a capacity of 2500 m 3 is filled with a single inflow pipe. The reservoir is empty when the inflow pipe is opened at t = 0. Letting Q( t ) be the amount of water in the reservoir at time t , the flow rate of water into the reservoir (in m 3 /hr) oscillates on a 24-hr cycle (see figure) and is given by Q ′ ( t ) = 20 ( 1 + cos π t 12 ) . a. How much water flows into the reservoir in the first 2 hr? b. Find the function that gives the amount of water in the reservoir over the interval [0. t], where t ≥ 0. c. When is the reservoir full?
Filling a reservoir A reservoir with a capacity of 2500 m3 is filled with a single inflow pipe. The reservoir is empty when the inflow pipe is opened at t = 0. Letting Q(t) be the amount of water in the reservoir at time t, the flow rate of water into the reservoir (in m3/hr) oscillates on a 24-hr cycle (see figure) and is given by
Q
′
(
t
)
=
20
(
1
+
cos
π
t
12
)
.
a. How much water flows into the reservoir in the first 2 hr?
b. Find the function that gives the amount of water in the reservoir over the interval [0. t], where t ≥ 0.
xy²
Find
-dA, R = [0,3] × [−4,4]
x²+1
Round your answer to four decimal places.
Find the values of p for which the series is convergent.
P-?- ✓
00
Σ nº (1 + n10)p
n = 1
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SUBMIT ANSWER
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SESSCALCET2 8.3.513.XP.
Consider the following series.
00
Σ
n = 1
1
6
n°
(a) Use the sum of the first 10 terms to estimate the sum of the given series. (Round the answer to six decimal places.)
$10 =
(b) Improve this estimate using the following inequalities with n = 10. (Round your answers to six decimal places.)
Sn +
+ Los
f(x) dx ≤s ≤ S₁ +
Jn + 1
+ Lo
f(x) dx
≤s ≤
(c) Using the Remainder Estimate for the Integral Test, find a value of n that will ensure that the error in the approximation s≈s is less than 0.0000001.
On > 11
n> -18
On > 18
On > 0
On > 6
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University Calculus: Early Transcendentals (4th Edition)
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