Activity E Translate the following inverse variation statements into mathematical equation Write your answer on the spac provided before each item 1. The length L of a rectangular field varies inversely as its width w. 2 The density d of air varies inversely as the volume v of water in the atmosphere.
Activity E Translate the following inverse variation statements into mathematical equation Write your answer on the spac provided before each item 1. The length L of a rectangular field varies inversely as its width w. 2 The density d of air varies inversely as the volume v of water in the atmosphere.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Activity I: Translate the following inverse variation statements into mathematical equation. Write your answer on the space
provided before each item.
1. The length L of a rectangular field varies inversely as its width w.
2 The density d of air varies inversely as the volume v of water in the atmosphere.
Important Concept: Given the table of values, if the product xy is common (equal or the same) for all ordered pairs, then it
lustrates an inverse variation
Examples Determine if the tables below express an inverse variation between the variables. If they do, find the constant of
varlation and the equation that defines the relation
6T
6.
12
2
y 30 15 106
4.
61
10
1.
y 2
k= xy
k = xy
Since the products are the
same, the table shows an
Inverse variation
• The constant of variation k
is 60
• Since the products are the
same, the table shows an
Inverse variation
• The constant of variation k
is 6.
• The equation is y =
k= (2)(30) = 60
k= (3)(2) = 6
k= (4)(15) = 60
k= (6)(1) = 6
k ( = 6
k= (12)) == 6
k= (6)(10) = 60
k (10)(6) = 60
60
• The equation is y:
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