A trough is 16 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 14 ft3/min, how fast is the water level rising when the water is 6 inches deep? Step 1 Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 7T
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Step 3
We must find dh/dt. We have
14 = dv
48h
dh
dt
dt
48h
Step 4
In feet, we know that
h =
ft.
Submit Skip_(you cannot come back)
Transcribed Image Text:Step 3 We must find dh/dt. We have 14 = dv 48h dh dt dt 48h Step 4 In feet, we know that h = ft. Submit Skip_(you cannot come back)
A trough is 16 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 14 ft3/min, how fast is
the water level rising when the water is 6 inches deep?
Step 1
Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h.
3
h
Step 2
The volume of the water is as follows.
V =
16
8 (3h)(h)
24h
24h?
Transcribed Image Text:A trough is 16 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 14 ft3/min, how fast is the water level rising when the water is 6 inches deep? Step 1 Let h be the water's height and b be the distance across the top of the water. Using the diagram below, find the relation between b and h. 3 h Step 2 The volume of the water is as follows. V = 16 8 (3h)(h) 24h 24h?
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