L13 - Lecture 13, part I: Section 1.10 Variation Def. A...

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Unformatted text preview: Lecture 13, part I: Section 1.10 Variation Def. A quantity u1D466 varies directly with quantity u1D465 , or u1D466 is directly proportional to u1D465 , if there is a nonzero number u1D458 such that The number u1D458 is called the constant of propor- tionality or the constant of variation . ex. The property tax in Florida is directly propor- tional to an assessed value of a property. If a house that has an assessed value of $150,000 has a prop- erty tax of $4500, find a formula for the amount of property tax u1D466 in terms of the assessed value u1D465 of the property. Use the formula to find the property tax on a house that has an assessed value of $200,000. Inverse Variation The nonzero quantity u1D466 varies inversely with quan- tity u1D465 , or u1D466 is inversely proportional to u1D465 if there is a nonzero constant u1D458 such that ex. Boyles Law states that for a constant tempera- ture, the pressure u1D443 of a gas is inversely proportional to the volume u1D449 of the gas. The pressure of a cer- tain gas in a spherical balloon with radius 3 inches is 10 lb/in 2 . If the radius of the balloon increases to 6 inches, approximate the new pressure of the gas. Joint and Combined Variation When a quantity...
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L13 - Lecture 13, part I: Section 1.10 Variation Def. A...

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