Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe. For the data shown, v x is the velocity of the fluid (in cm/sec) and x represents the distance (in cm) from the center of the pipe toward the edge. a. The pipe is 30 m long (3000 cm). Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place. b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place. c. Use regression to find a quadratic function to model the data. d. Use the model from part (c) to predict the velocity of the fluid at a distance 5.5 cm from the center of the pipe. Round tot decimal place.
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe. For the data shown, v x is the velocity of the fluid (in cm/sec) and x represents the distance (in cm) from the center of the pipe toward the edge. a. The pipe is 30 m long (3000 cm). Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place. b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place. c. Use regression to find a quadratic function to model the data. d. Use the model from part (c) to predict the velocity of the fluid at a distance 5.5 cm from the center of the pipe. Round tot decimal place.
Solution Summary: The author calculates the time taken by the fluid to run the length of the pipe through the center using the tabular data.
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe. For the data shown,
v
x
is the velocity of the fluid (in cm/sec) and x represents the distance (in cm) from the center of the pipe toward the edge.
a. The pipe is 30 m long (3000 cm). Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place.
b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place.
c. Use regression to find a quadratic function to model the data.
d. Use the model from part (c) to predict the velocity of the fluid at a distance
5.5
cm from the center of the pipe. Round tot decimal place.
T
1
7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
≤
and the curve y
y =
about the line
x =
=플
2
80
F3
a
FEB
9
2
7
0
MacBook Air
3
2
stv
DG
Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x.
h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1
-
-
-
f(x) = ☐
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