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4 Part A Learning Goal: To understand and use inverse proportion. Two quantities are said to be inversely proportional to each other if one quantity is proportional to the inverse of the other. Mathematically, if y is inversely proportional tox, this means that y Here A is a proportionality constant. This relationship is sometimes written as y x 1/x. SCALING •If you double x, you halve y Consider the case when the constant A = 4. Plot the graph of y = 4/x. ++ 血 No elements selected 4.0 • If you triple x, y is reduced by a factor of 3. • If you halve x, y doubles. • If you reduce by a factor of 3, y becomes 3 times as large. RATIOS For any two values of x-say, 1 and 2-we have 91 = and y2 A 22 Dividing the y1 equation by the y2 equation, we find 31 A/x1 A 22 32 A/x2 21 A = - = 12 21 That is, the ratio of y-values is the inverse of the ratio of the corresponding values of x. LIMITS • As gets very large, y approaches zero. . As a approaches zero, y gets very large. ม పా 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 1.0 2.0 3.0 4.0 5.0 H Press ENTER to select this element. Press ESC to return to the main menu. Press CTRL+Q to quit the application. Submit Request Answer Part B Complete previous part(s) ? 48°F Light rain 3

4 Part A Learning Goal: To understand and use inverse proportion. Two quantities are said to be inversely proportional to each other if one quantity is proportional to the inverse of the other. Mathematically, if y is inversely proportional tox, this means that y Here A is a proportionality constant. This relationship is sometimes written as y x 1/x. SCALING •If you double x, you halve y Consider the case when the constant A = 4. Plot the graph of y = 4/x. ++ 血 No elements selected 4.0 • If you triple x, y is reduced by a factor of 3. • If you halve x, y doubles. • If you reduce by a factor of 3, y becomes 3 times as large. RATIOS For any two values of x-say, 1 and 2-we have 91 = and y2 A 22 Dividing the y1 equation by the y2 equation, we find 31 A/x1 A 22 32 A/x2 21 A = - = 12 21 That is, the ratio of y-values is the inverse of the ratio of the corresponding values of x. LIMITS • As gets very large, y approaches zero. . As a approaches zero, y gets very large. ม పా 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 1.0 2.0 3.0 4.0 5.0 H Press ENTER to select this element. Press ESC to return to the main menu. Press CTRL+Q to quit the application. Submit Request Answer Part B Complete previous part(s) ? 48°F Light rain 3

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
Problem 21PQ
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4 Part A Learning Goal: To understand and use inverse proportion. Two quantities are said to be inversely proportional to each other if one quantity is proportional to the inverse of the other. Mathematically, if y is inversely proportional tox, this means that y Here A is a proportionality constant. This relationship is sometimes written as y x 1/x. SCALING •If you double x, you halve y Consider the case when the constant A = 4. Plot the graph of y = 4/x. ++ 血 No elements selected 4.0 • If you triple x, y is reduced by a factor of 3. • If you halve x, y doubles. • If you reduce by a factor of 3, y becomes 3 times as large. RATIOS For any two values of x-say, 1 and 2-we have 91 = and y2 A 22 Dividing the y1 equation by the y2 equation, we find 31 A/x1 A 22 32 A/x2 21 A = - = 12 21 That is, the ratio of y-values is the inverse of the ratio of the corresponding values of x. LIMITS • As gets very large, y approaches zero. . As a approaches zero, y gets very large. ม పా 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 1.0 2.0 3.0 4.0 5.0 H Press ENTER to select this element. Press ESC to return to the main menu. Press CTRL+Q to quit the application. Submit Request Answer Part B Complete previous part(s) ? 48°F Light rain 3
Transcribed Image Text:4 Part A Learning Goal: To understand and use inverse proportion. Two quantities are said to be inversely proportional to each other if one quantity is proportional to the inverse of the other. Mathematically, if y is inversely proportional tox, this means that y Here A is a proportionality constant. This relationship is sometimes written as y x 1/x. SCALING •If you double x, you halve y Consider the case when the constant A = 4. Plot the graph of y = 4/x. ++ 血 No elements selected 4.0 • If you triple x, y is reduced by a factor of 3. • If you halve x, y doubles. • If you reduce by a factor of 3, y becomes 3 times as large. RATIOS For any two values of x-say, 1 and 2-we have 91 = and y2 A 22 Dividing the y1 equation by the y2 equation, we find 31 A/x1 A 22 32 A/x2 21 A = - = 12 21 That is, the ratio of y-values is the inverse of the ratio of the corresponding values of x. LIMITS • As gets very large, y approaches zero. . As a approaches zero, y gets very large. ม పా 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 1.0 2.0 3.0 4.0 5.0 H Press ENTER to select this element. Press ESC to return to the main menu. Press CTRL+Q to quit the application. Submit Request Answer Part B Complete previous part(s) ? 48°F Light rain 3
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