8.1 HOMEWORK Direct Inverse and Joint Variation Name______
Advanced Algebra Period______
Formulas:
Direct Inverse Joint
1. For rectangles with the same area, the length varies inversely as the width. One rectangle has a length of 12 cm and a width of 5 cm. Find the length of another rectangle with the same area whose width is 4 cm.
2. The amount of money earned on a job is proportional to the number of hours worked. If $36 is earned for 8 hours of work, how much is earned for 30 hours of work?
3. The current in an electrical circuit varies inversely as the amount of resistance in the circuit. The current is 10 amps when the resistance is 24 ohms. Find the current when the resistance is 30 ohms.
4. The cost per person to rent a mountain cabin is proportional to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?
5. The height that a ball bounces varies with the height from which it is dropped. A certain ball bounces 30 cm when dropped from a height of 50 cm. How high will the ball bounce if dropped from a height of 120 cm?
6. The amount that a spring stretches is proportional to the weight of the object attached to it. If a spring is stretched 10 cm by a weight of 8 kg, how much will it be stretched by a weight of 3 kg?
7. The area of a trapezoid varies jointly with the height and the sum of the lengths of the bases. When the sum of the lengths of the bases is 18 inches and the height is 4 inches, the area is 36 square inches. Find the formula for the area of a trapezoid.
8. The volume of a gas varies inversely as the pressure. A helium-filled balloon has a volume of 21 m³ at sea level, where the pressure is 1 atmosphere. The balloon rises to an altitude where the pressure is 0.7 atmospheres. What is the volume?
9. The number of chairs on a ski lift is inversely proportional to the distance between them. A lift has 70 chairs when they are spaced 24 m apart. If 80 evenly-spaced chairs are used on the lift, how much space will be left between them?
10. The number of calories in a container of milk is proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in the 15-ounce glass of milk.
11. The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person with a mass of 50 kg?
12. The distance, d, that a free-falling body falls varies directly as the square of the time, t, that it falls. If d = 36 m when t = 3 sec. Find d when t = 5 sec.
13. The amount of material, M, needed to cover a ball is directly proportional to the square of the radius, r. If M = 60 cm² when r = 2 cm, Find M when r = 7
14. The brightness of illumination, I, of an object varies inversely as the square of its distance, d, from the source of illumination. If I = 18 luxes when d = 4 m. Find l when d = 3 m
15. The time t, needed to fill the gas tank of a car varies with the square of the diameter, d, of the hose. If t = 5 min when d = 3 cm. Find t when d = 2 cm.
16. If y varies jointly as x and z and y = 12 when x - -2 and z = 3, find y when x = 6 and z = 8.
17. The area A of a trapezoid varies jointly as its height and the sum of its bases. If the area is 480 square meters when the height is 20 meters and the bases are 28 meters and 20 meters, what is the area of a trapezoid when its height is 8 meters and its bases are 10 meters and 15 meters?