Algebra 2: Rational Expressions, Equations, and

Algebra 2: Rational Expressions, Equations, and Functions
Topic F8: Variation | VERSION B Name: ______________________________________________________ 1.
𝑦 varies directly with 𝑥. If 𝑦 = −15 when 𝑥 = 5, find 𝑦 when 𝑥 = 5. 𝑦 = 2.
𝑦 varies directly with the square 𝑥. If 𝑦 = 32 when 𝑥 = −4, find 𝑦 when 𝑥 = 5. 𝑦 = 3.
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𝑧 varies jointly with 𝑦 and the square of 𝑥. If 𝑥 = 3 when 𝑦 = −2 and 𝑧 = 36, find 𝑥 when 𝑧 = 256 and 𝑦 = −8. 𝑥 = 7.
𝐹 varies directly with 𝑚 and inversely with the square of 𝑑. If 𝐹 = 100 when 𝑚 = 200 and 𝑑 = 2, find 𝐹 when 𝑚 = 80 and 𝑑 = 2. 𝐹 = 8.
𝐹 varies directly with 𝑚 and inversely with the square of 𝑑. If 𝑑 = 6 when 𝑚 = 1440 and 𝐹 = 120, find 𝑑 when 𝑚 = 1280 and 𝐹 = 60. 𝑑 = 9.
The length a spring stretches is directly proportional to the force applied. If a force of 2 pounds stretches a spring 10 inches, how much force is necessary to stretch the same spring 3 inches? ____________________ pounds are needed. 𝑦 varies inversely with the square 𝑥. If 𝑦 = −8 when 𝑥 = 6, find 𝑦 when 𝑥 = −2. 𝑦 = 𝑦 varies inversely with the cube of 𝑥. If 𝑦 = 135 !
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when 𝑥 = , find 𝑦 when 𝑥 = . 𝑦 = 5.
𝑧 varies jointly with 𝑦 and the square of 𝑥. If 𝑧 = −96 when 𝑦 = −3 and 𝑥 = 2, find 𝑧 when 𝑥 = 3 and 𝑦 = −7. 𝑧 = www.varsitylearning.com 1 Algebra 2: Rational Expressions, Equations, and Functions
Topic F8: Variation | VERSION B Name: ______________________________________________________ 10. The weight of a certain material varies directly with the surface area of that material. If 8 square feet weighs half a pound, how much will 6 square feet weigh? It will weigh pounds. 11. The volume of a gas is inversely proportional to the pressure. If a pressure of 28 pounds per square inch corresponds to a volume of 18 cubic feet, what pressure is needed to produce a volume of 42 cubic feet? pounds per square inch 12. The frequency of an electromagnetic wave varies inversely with the wavelength. If a wavelength of 200 meters has a frequency of 800 kilocycles per second, what frequency will be associated with a wavelength of 320 meters? kilocycles per second will be associated with a wavelength of 400 meters. 13. The capacity of a cylinder varies jointly with its height and the square of its radius. If a cylinder with a radius of 3 centimeters and a height of 6 centimeters has a capacity of 169.56 cubic centimeters, what will the capacity be of a cylinder with radius 6 centimeters and height 2 centimeters? The capacity of the cylinder is cubic centimeters. 14. The resistance of a wire varies directly with its length and inversely with the square of its diameter. If 100 feet of wire with diameter 0.01 inch has a resistance of 10 ohms, what is the resistance of 150 feet of the same type of wire if its diameter is 0.03 inch? Round to the nearest hundredth. The resistance is ohms. 15. The volume of a gas varies directly with its temperature and inversely with the pressure. If the volume of a certain gas is 15 cubic feet at a temperature of 300 K and a pressure of 40 pounds per square inch, what is the volume of the same gas at 320 K when the pressure is 25 pounds per square inch? cubic feet. www.varsitylearning.com 2 Algebra 2: Rational Expressions, Equations, and Functions
Topic F8: Variation | VERSION B Name: ______________________________________________________ 1.
𝑦 varies directly with 𝑥. If 𝑦 = −15 when 𝑥 = 5, find 𝑦 when 𝑥 = 5. 𝑦 = −15 2.
𝑦 varies directly with the square 𝑥. If 𝑦 = 32 when 𝑥 = −4, find 𝑦 when 𝑥 = 5. 𝑦 = 50 3.
4.
6.
𝑧 varies jointly with 𝑦 and the square of 𝑥. If 𝑥 = 3 when 𝑦 = −2 and 𝑧 = 36, find 𝑥 when 𝑧 = 256 and 𝑦 = −8. 𝑥 = −4, 4 7.
𝐹 varies directly with 𝑚 and inversely with the square of 𝑑. If 𝐹 = 100 when 𝑚 = 200 and 𝑑 = 2, find 𝐹 when 𝑚 = 80 and 𝑑 = 2. 𝐹 = 40 8.
𝐹 varies directly with 𝑚 and inversely with the square of 𝑑. If 𝑑 = 6 when 𝑚 = 1440 and 𝐹 = 120, find 𝑑 when 𝑚 = 1280 and 𝐹 = 60. 𝑑 = −8, 8 9.
The length a spring stretches is directly proportional to the force applied. If a force of 2 pounds stretches a spring 10 inches, how much force is necessary to stretch the same spring 3 inches? 𝑦 varies inversely with the square 𝑥. If 𝑦 = −8 when 𝑥 = 6, find 𝑦 when 𝑥 = −2. 𝑦 = −72 𝑦 varies inversely with the cube of 𝑥. If 𝑦 = 135 !
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when 𝑥 = , find 𝑦 when 𝑥 = . 𝑦 = 320 5.
𝑧 varies jointly with 𝑦 and the square of 𝑥. If 𝑧 = −96 when 𝑦 = −3 and 𝑥 = 2, find 𝑧 when 𝑥 = 3 and 𝑦 = −7. 𝑧 = −504 !
pounds are needed. !
www.varsitylearning.com 3 Algebra 2: Rational Expressions, Equations, and Functions
Topic F8: Variation | VERSION B Name: ______________________________________________________ 10. The weight of a certain material varies directly with the surface area of that material. If 8 square feet weighs half a pound, how much will 6 square feet weigh? It will weigh !
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pounds. 11. The volume of a gas is inversely proportional to the pressure. If a pressure of 28 pounds per square inch corresponds to a volume of 18 cubic feet, what pressure is needed to produce a volume of 42 cubic feet? 12 pounds per square inch 12. The frequency of an electromagnetic wave varies inversely with the wavelength. If a wavelength of 200 meters has a frequency of 800 kilocycles per second, what frequency will be associated with a wavelength of 320 meters? 500 kilocycles per second will be associated with a wavelength of 400 meters. 13. The capacity of a cylinder varies jointly with its height and the square of its radius. If a cylinder with a radius of 3 centimeters and a height of 6 centimeters has a capacity of 169.56 cubic centimeters, what will the capacity be of a cylinder with radius 6 centimeters and height 2 centimeters? The capacity of the cylinder is 226.08 cubic centimeters. 14. The resistance of a wire varies directly with its length and inversely with the square of its diameter. If 100 feet of wire with diameter 0.01 inch has a resistance of 10 ohms, what is the resistance of 150 feet of the same type of wire if its diameter is 0.03 inch? Round to the nearest hundredth. The resistance is 1.67 ohms. 15. The volume of a gas varies directly with its temperature and inversely with the pressure. If the volume of a certain gas is 15 cubic feet at a temperature of 300 K and a pressure of 40 pounds per square inch, what is the volume of the same gas at 320 K when the pressure is 25 pounds per square inch? !"#
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cubic feet. www.varsitylearning.com 4

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