Question

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 linearly along the length from 3 m to 1 m. It is initially empty and is filled at a rate of 1 mcubed/min. How fast is the water level rising 160 min after the filling begins? How long will it take to fill the pool?

Answer #1

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 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.)

Consider a hemispherical tank with a radius of 3 meters that is
resting upright on its curved side. Using 9.8 m/s^2 for the
acceleration due to gravity and 1,000 kg/m^3 as the density of
water, Set up the integral for the work required to pump the water
out of the tank if:
(a) the tank is full of water and it is being pumped out of a
1-meter long vertical spout at the top of the tank.
(b) the tank...

A cylindrical tank with a large diameter is filled with water to
a depth D = 0.405 m. A hole of cross-sectional area A = 5.62 cm^2
in the bottom of the tank allows water to drain out. (a) What is
the rate at which water flows out, in cubic meters per second? (b)
At what distance below the bottom of the tank is the
cross-sectional area of the stream equal to one-half the area of
the hole?

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 large diameter closed top tank is filled with a depth of 3
meters of a fluid (density 1200 kg/m3). A small pipe leading from
the bottom of the tank must carry the fluid some height above the
fluid level in the tank. a) If a pressure of 2.5 Atmospheres is
maintained in the space above the fill line in the tank how high
above the fill line can the pipe carry the fluid and still provide
an exit speed...

A shallow reservoir has a one-square-kilometer water surface and
an average water depth of 2 meters. Initially it is filled with
fresh water, but at time t=0 water contaminated with a liquid
pollutant begins flowing into the reservoir at the rate of 200
cubic meters per month. The well-mixed water in the reservoir flows
out at the same rate. Your first task is to find the amount x(t) of
pollutant (in millions of liters) in the reservoir after t months....

A shallow reservoir has a one-square-kilometer water surface
and an average water depth of 4 meters. Initially it is filled with
fresh water, but at time t=0
water contaminated with a liquid pollutant begins flowing into the
reservoir at the rate of 500 thousand cubic meters per month. The
well-mixed water in the reservoir flows out at the same rate. Your
first task is to find the amount x(t) of pollutant (in millions
of liters) in the reservoir after t...

A farmer wants to pump water from a river to a very big open
storage tank nearby using a 55-m long, 16-cm diameter plastic pipe
with 5 threaded 90° regular bends, 5 threaded 45° regular bends,
and one fully open gate valve. The water velocity near the river
surface is 2.7 m/s and the pipe's inlet is placed in the
river normal to the direction of water flow to take advantage of
this water speed. The elevation difference between the...

Activity 2: Applications of
the Derivatives
To make a phrase/words, solve the 18 application of derivatives
below. Then replace each numbered blank with the letter
corresponding to the answer for that problem. Show all
solutions on the answers given below.
"__ __ __ __ __ __ __ __ __
, __ __ __ __
__ __ __ __ __
."
1-2. A certain calculus student hit Mr. Pleacher in the head
with a snowball. If the snowball is melting...

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