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Class Note for MATH 1310 with Professor Constante at UH

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This 10 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 51 views.

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Date Created: 02/06/15
Math 1310 Chapter 3 Section 33 Variation B Constante Direct Variation Direct Variation P is directly proportional to Q is expressed by the equation P kQ where k is a nonzero constant We also say that P is proportional to Q or P varies directly as Q The constant k is called the constant of proportionality An example of direct variation Sales tax t is a function of the amount of an item purchased p 80 we can say that t varies directly with p If the sales tax is 825 then we can write t 00825p Inverse Variation Inverse Variation P is inversely proportional to Q is expressed by the equation P E where k is a nonzero constant We also say that Q P varies inversely as Q The constant k is called the constant of proportionality An example of inverse variation The time T it takes for a person to make a 40 mile trip by car to a certain destination is a function of the rate R of the car So we can say that T varies inversely as R If a trip taken is 40 miles long then we can write T Z R Joint Variation Joint Variation P is jointly proportional to Q and R is expressed by the equation P kQR where k is a nonzero constant We also say that P varies jointly as Q and R The constant k is called the constant of proportionality An example ofjoint variation The area A of a triangle is equal to half the base b times the height h A is a function of two independent variables1b and h We can say that A varies jointly as b and h and write A bh 2 Example 1 Write a formula to express the following statement B varies directly as the square root of C Example 2 Write a formula to express the following statement G varies jointly as H and J Example 3 Write a formula to express the following statement Then find the constant of proportionality k a y varies inversely as the cube of x b lfx 3 then y 2 Use this information and the formula in part a to find the constant of proportionality k Example 4 Write a formula to express the following statement Then find the constant of proportionality k a x varies jointly as y and z and inversely as the square of w b lfy 5 z 4 and w 3 then x 2 Use this information and the formula in part a to find the constant of proportionality k Example 5 At Fred s Flooring the cost of carpet is directly proportional to the area to be covered by carpet If a room measuring 120 square feet costs 480 to carpet find the cost of carpeting a room that measures 156 square feet a Write a formula to express the situation b Find the constant of proportionality k c Use part a and b to solve for the indicated quantity Example 6 Buy Right Electronics sells a popular computer game at a price that is inversely proportional to the number of games sold per month When they are selling 800 games per month the price is 50 each If they sell 1000 games per month then what should the new price of the computer game be a Write a formula to express the situation b Find the constant of proportionality k c Use part a and b to solve for the indicated quantity

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