Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of 10 m 2 is filled to a depth of 25 m with water. At t = 0 s. a drain in the bottom of the tank with an area of 1 m 2 is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time t ≥ 0 is d ( t ) = ( 5 − 0.22 t ) 2 . a. Check that d (0) = 25. as specified b. At what time is the tank empty? c. What is an appropriate domain for d ?
Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of 10 m 2 is filled to a depth of 25 m with water. At t = 0 s. a drain in the bottom of the tank with an area of 1 m 2 is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time t ≥ 0 is d ( t ) = ( 5 − 0.22 t ) 2 . a. Check that d (0) = 25. as specified b. At what time is the tank empty? c. What is an appropriate domain for d ?
Solution Summary: The author explains how the depth of the water at t = 0 is true.
Draining a tank (Torricelli’s law) A cylindrical tank with a cross-sectional area of 10 m2 is filled to a depth of 25 m with water. At t = 0 s. a drain in the bottom of the tank with an area of 1 m2 is opened, allowing water to flow out of the tank. The depth of water in the tank (in meters) at time
t
≥
0
is
d
(
t
)
=
(
5
−
0.22
t
)
2
.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 1 Solutions
Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)
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