An inverted conical water tank with a height of 8 ft and a radius of 4 ft is drained through a hole in the vertex at a rate of 3 ft³/s (see figure). What is the rate of change of the water depth when the water depth is 5 ft? (Hint. Use similar triangles.) 4 ft R Outflow 3 ft /s 8 ft Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. (Type an exact answer, using as needed.) Differentiate both sides of the equation with respect to t. dV dt dh dt When the water depth is 5 ft, the rate of change of the water depth is about (Round to the nearest hundredth as needed.)
An inverted conical water tank with a height of 8 ft and a radius of 4 ft is drained through a hole in the vertex at a rate of 3 ft³/s (see figure). What is the rate of change of the water depth when the water depth is 5 ft? (Hint. Use similar triangles.) 4 ft R Outflow 3 ft /s 8 ft Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. (Type an exact answer, using as needed.) Differentiate both sides of the equation with respect to t. dV dt dh dt When the water depth is 5 ft, the rate of change of the water depth is about (Round to the nearest hundredth as needed.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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An inverted conical water tank with a height of 8 ft and a radius of 4 ft is drained through a hole in the
vertex at a rate of 3 ft³/s (see figure). What is the rate of change of the water depth when the water
depth is 5 ft? (Hint: Use similar triangles.)
4 ft
R
Outflow 3 ft /s
H
8 ft
Q Search
D
&
A
r
acer
Let V be the volume of water in the tank and let h be the depth of the water. Write an equation
that relates V and h.
(Type an exact answer, using as needed.)
Differentiate both sides of the equation with respect to t.
dV
dt
dh
dt
When the water depth is 5 ft, the rate of change of the water depth is about
(Round to the nearest hundredth as needed.)
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