Question
Asked Oct 23, 2019
A trough is 12 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 15 ft3/min, how fast is the water level rising when the water is 9
inches deep?
X ft/min
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A trough is 12 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 15 ft3/min, how fast is the water level rising when the water is 9 inches deep? X ft/min

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check_circleExpert Solution
Step 1

Let the volume of the water in the trough at time be V. The rate of change of V is,

dV
- 15 ft3 /min
dt
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dV - 15 ft3 /min dt

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Step 2

Let h be the depth of water in the trough, which is equal to the height of the triangle which the water makes at the end of the trough.

Step 3

The following equation can be formed which...

V= (base area oftrough) (ht. of trough)
- base ht(12)
2
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V= (base area oftrough) (ht. of trough) - base ht(12) 2

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Tagged in

Math

Calculus