Question

A water trough is 9 feet long, and its cross section is an equilateral triangle with...

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 __

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A trough is 2 feet long and 1 foot high. The vertical cross-section of the trough...
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...
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...
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...
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?
A water trough is 6 m long and has a cross-section in the shape of an...
A water trough is 6 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 80 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 20 cm deep? __________m/min
(1 point) A trough is 6 feet long and 1 foot high. The vertical cross-section of...
(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...
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...
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...
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...
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?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT