The conical watering pail with height 0.45 m and radius 0.15 m has a grid of holes. Water flows out through the holes at a rate of kA m³/min, where k is a constant and A is the surface area of the part of the cone in contact with the water. This surface area is A = ar/h² + r² and the volume is V = ar²h. Calculate the rate at which the water level changes at h = 0.18 m, assuming that k = 0.32 m/min. 0.15 m 0.45 m

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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The conical watering pail with height 0.45 m and radius 0.15 m has a grid of holes. Water flows out through the holes at a
rate of kA m³/min, where k is a constant and A is the surface area of the part of the cone in contact with the water. This
surface area is A = ar/h² + r² and the volume is V = arh. Calculate the rate at which the water level changes at
= tr V
h = 0.18 m, assuming that k = 0.32 m/min.
0.15 m
0.45 m
h
(Give your answer to two decimal places.)
dh
m/min
dt
Transcribed Image Text:The conical watering pail with height 0.45 m and radius 0.15 m has a grid of holes. Water flows out through the holes at a rate of kA m³/min, where k is a constant and A is the surface area of the part of the cone in contact with the water. This surface area is A = ar/h² + r² and the volume is V = arh. Calculate the rate at which the water level changes at = tr V h = 0.18 m, assuming that k = 0.32 m/min. 0.15 m 0.45 m h (Give your answer to two decimal places.) dh m/min dt
Two parallel paths 28 m apart run east-west through the woods. Brooke walks east on one path at 5 km/h, while Jamail
walks west on the other path at 6 km/h. If they pass each other at time t = 0, how far apart are they 5 s later, and how fast is
the distance between them changing at that moment?
(Use decimal notation. Give your answer to three decimal places.)
distance between them:
meters
dL
m/s
dt
Transcribed Image Text:Two parallel paths 28 m apart run east-west through the woods. Brooke walks east on one path at 5 km/h, while Jamail walks west on the other path at 6 km/h. If they pass each other at time t = 0, how far apart are they 5 s later, and how fast is the distance between them changing at that moment? (Use decimal notation. Give your answer to three decimal places.) distance between them: meters dL m/s dt
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