Question

A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at is deepest point. A cross-section is shown in the figure. If the pool is being filled at a rate of 0.8 ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft? (Round your answer to five decimal places.)

Answer #1

By differentiating the equation we get

now substituting the values we get

A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the
shallow end, and 9 ft deep at is deepest point. A cross-section is
shown in the figure. If the pool is being filled at a rate of 1
ft3/min, how fast is the water level rising when the
depth at the deepest point is 5 ft? (Round your answer to five
decimal places.)
______ft/min

A swimming pool is 50 ft wide and 100 ft long and its bottom is
an inclined plane, the shallow end having a depth of 4 ft and the
deep end, 7 ft. Assume the pool is full of water. (Round your
answers to the nearest whole number. Recall that the weight density
of water is 62.5 lb/ft3.)
(a) Estimate the hydrostatic force on the shallow end.
(b) Estimate the hydrostatic force on the deep end.
(c) Estimate the hydrostatic...

incorrect,8.6.23 A rectangular swimming pool is 40 ft wide by 75
ft long. The table gives depths (d) from xequals0 at the shallow
end to the diving end. Use the Trapezoidal Rule with nequals15 to
estimate the volume of the pool, VequalsIntegral from 0 to 75 40
times d left parenthesis x right parenthesis dx. x 0 5 10 15 20 25
30 35 40 45 50 55 60 65 70 75 d 4.8 7 8 8.7 9.3 9.8 10.3...

A trough is 10 ft long and its ends have the shape of isosceles
triangles that are 5 ft across at the top and have a height of 1
ft. If the trough is being filled with water at a rate of 11
ft3/min, how fast is the water level rising when the
water is 5 inches deep?

A water trough is 10 m long and has a cross-section in the shape
of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm
wide at the top, and has height 60 cm. If the trough is being
filled with water at the rate of 0.2 m3/min how fast is
the water level rising when the water is 30 cm deep?

i. A trough is 12 ft long and its ends have the shape of
isosceles triangles that are 3 ft across at the top and have a
height of 1 ft. If the trough is being filled with water at a rate
of 8 ft3/min, how fast is the water level rising when
the water is 5 inches deep?
ii. y = 5x3+2x, dx/dt = 4, find dy/dt
when x = 2

A swimming pool has the following interior measurements: 3
meters long, 2 m wide and 120 cm deep. If you find water up to 4/5
of its capacity, how many 20 cm diameter cylindrical containers 30
cm high can be filled with the pool water? Round to the nearest
integer.
a. 942
b. 191
c. 764
d. 611

A trough is 8 ft long and its ends have the shape of isosceles
triangles that are 2 ft across at the top and have a height of 1
ft. If the trough is being filled with water at a rate of 13
ft^3/min, how fast is the water level rising when the water is 6
inches deep?

a) A hemispherical tank with a radius of 18 meters is filled
from an inflow pipe at a rate of 8 cubic meters per minute. The
depth of the water in the tank is changing at a rate of about 0.001
meters per minute. What is the rate of change of the exposed
surface area of the water when the water is 9 meters deep?
b) A swimming pool is 50 m long and 20 m wide. Its depth
decreases...

A trough is 8 ft long and it's ends have the shape of
isosceles triangles that are 4 ft across at the top and have a
height of 1 ft. If the trough is being filled with water at a rate
of 13ft^3/min, how fast is that water level rising when the water
is 7 inches deep?

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