Solve the variation problems in Exercises 68–73. 68. A company's profit varies directly as the number of products it sells. The company makes a profit of $1175 on the sale of 25 products. What is the company's profit when it sells 105 products? 69. The distance that a body falls from rest varies directly as the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds? 70. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet? 71. The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker? 72. The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how long would it take 5 workers to assemble 40 computers? 73. The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the volume of a pyramid with a height of 20 feet and a base with an area of 120 square feet.
Solve the variation problems in Exercises 68–73. 68. A company's profit varies directly as the number of products it sells. The company makes a profit of $1175 on the sale of 25 products. What is the company's profit when it sells 105 products? 69. The distance that a body falls from rest varies directly as the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds? 70. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet? 71. The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker? 72. The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how long would it take 5 workers to assemble 40 computers? 73. The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 15 feet and a base with an area of 35 square feet has a volume of 175 cubic feet. Find the volume of a pyramid with a height of 20 feet and a base with an area of 120 square feet.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 3P
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Transcribed Image Text:Solve the variation problems in Exercises 68–73.
68. A company's profit varies directly as the number of products
it sells. The company makes a profit of $1175 on the sale
of 25 products. What is the company's profit when it sells
105 products?
69. The distance that a body falls from rest varies directly as
the square of the time of the fall. If skydivers fall 144 feet in
3 seconds, how far will they fall in 10 seconds?
70. The pitch of a musical tone varies inversely as its wavelength.
A tone has a pitch of 660 vibrations per second and a
wavelength of 1.6 feet. What is the pitch of a tone that has a
wavelength of 2.4 feet?
71. The loudness of a stereo speaker, measured in decibels, varies
inversely as the square of your distance from the speaker.
When you are 8 feet from the speaker, the loudness is
28 decibels. What is the loudness when you are 4 feet from the
speaker?
72. The time required to assemble computers varies directly as the
number of computers assembled and inversely as the number
of workers. If 30 computers can be assembled by 6 workers
in 10 hours, how long would it take 5 workers to assemble
40 computers?
73. The volume of a pyramid varies jointly as its height and the
area of its base. A pyramid with a height of 15 feet and a base
with an area of 35 square feet has a volume of 175 cubic feet.
Find the volume of a pyramid with a height of 20 feet and a
base with an area of 120 square feet.
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