Question

A water trough is 9 feet long, and its cross section is an
equilateral triangle with sides 4 feet long. Water is pumped into
the trough at a rate of 2 cubic feet per second. How fast is the
water level rising when the depth of the water is 1/2 foot?

( *Hint*: First, what is the height h of an equilateral
triangle of side length s? Next, what is the area of an equilateral
triangle in terms of the side length s? Then write the area in
terms of h. The volume of the water in the trough at time t is the
product of the cross-sectional area with water and the length of
the trough. )

a) What is the height h of an equilateral triangle of side length
s?

h = __

b) The water level is rising at a rate of __

Answer #1

A trough is 2 feet long and 1 foot high. The vertical
cross-section of the trough parallel to an end is shaped like the
graph of y=x4 from x=−1 to x=1. The trough is full of
water. Find the amount of work in foot-pounds required to empty the
trough by pumping the water over the top. Note: In this problem,
use 62 pounds per cubic foot as the weight of water.
A trough is 3 feet long and 1 foot...

A tank of water is 15 feet long and has a cross section in the
shape of an equilateral triangle with sides 2 feet long (point of
the triangle points directly down). The tank is filled with water
to a depth of 9 inches. Determine the amount of work needed to pump
all of the water to the top of the tank. Assume that the density of
water is 62 lb/ft3.

A trough is 4 feet long and 11 foot high. The vertical
cross-section of the trough parallel to an end is shaped like the
graph of y=x^8 from x=−1 to x=1. The trough is full of water. Find
the amount of work required to empty the trough by pumping the
water over the top. Note: The weight of water is 62 pounds per
cubic foot. Your answer must include the correct units.

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?

(1 point) A trough is 6 feet long and 1 foot high. The vertical
cross-section of the trough parallel to an end is shaped like the
graph of ?=?6y=x6 from ?=−1x=−1 to ?=1x=1 . The trough is full of
water. Find the amount of work in foot-pounds required to empty the
trough by pumping the water over the top. Note: The weight of water
is 6262 pounds per cubic foot.

1. A trough in the shape of a box holds water, with base
dimensions 10 feet long by 4 feet wide. The water level starts 7
feet high in this box, and there is a circular hole in the bottom
of the box with radius 2 inches. Assume that time, t, represents
seconds from when it was filled to exactly 7 feet high, and let y
represent the current height of the water in the trough.
a. What is the...

A trough is 9 meters long, 2 meters wide, and 3 meters deep.
The vertical cross-section of the trough parallel to an end is
shaped like an isoceles triangle (with height 3 meters, and base,
on top, of length 2 meters). The trough is full of water (density
1000
kg
m
3
1000
kg
m
3
). Find the amount of work in joules required to empty the
trough by pumping the water over the top. (Note: Use
g
=...

A trough is 10 meters long, 3 meters wide, and 4 meters deep.
The vertical cross-section of the trough parallel to an end is
shaped like an isosceles triangle (with height 4 meters, and base,
on top, of length 3 meters). The trough is full of water (density
1000kg/m^3). Find the amount of work in joules required to empty
the trough by pumping the water over the top. (Note: Use g=9.8ms^2
as the acceleration due to gravity.)

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
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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?

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