a. Air is being pumped into a spherical ball in such a way that the volume increases at a rate of 10 cm /sec. How fast is the radius of the ball increasing when the diameter is 20 cm?
a. Air is being pumped into a spherical ball in such a way that the volume increases at a rate of 10 cm /sec. How fast is the radius of the ball increasing when the diameter is 20 cm?
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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Transcribed Image Text:a. Air is being pumped into a spherical ball in such a way that the volume increases at a rate
of 10 cm'/sec. How fast is the radius of the ball increasing when the diameter is 20 cm?
b. A burn on a person's skin is of the form ofa circular region. It was found out that the
1
cm/sec. Determine the rate of decrease in
20
burn increases in diameter at a rate of-
area at the instance when the diameter is measured at 1.5 cm.
c. A man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towards a lamp post
that is 15 ft high. How fast is the tip of his shadow moving when he is 30 ft from the
post?
d. A particular metal plate increases in radius when heated in a microwave oven. It was
found out that the rate of increase in the radius of the plate is 0.005 mm/min. At what
rate is the plate's area increasing when the radius of the plate is 300 mm.
Transcribed Image Text:The quantity of the demand per month of a certain accessory is related to the price (in
500
,where x is
pesos) per accessory as modeled by the demand function P(x)=-
0.01x +1
the number of accessories and 0Sxs 50. How many accessories must be sold in order
for the manufacturer to realize a maximum revenue R given by R(x) = x• P(x)?
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