Joint and Combined Variation Answers

A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?

The quantity a varies directly with b and c and inversely with d. The quantity d is tripled. Which of the following could be true if the relationship remains the same?

The kinetic energy, K, of an object varies jointly with the mass of the object and the square of the velocity of the object. A 50-kg object moving at a velocity of 20 meters per second has 10,000 joules of kinetic energy. How many joules of kinetic energy does a 25-kg object moving at a velocity of 10 meters per second have?

When a = 6 and b = 22, c = 33. If c varies directly with b and inversely with a, which equation models the situation?

When h is and j is , g is 4. If g varies jointly with h and j, what is the value of g when h is 2 and j is 3?

The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?

A quantity h varies directly with w and inversely with p. When w = 4 and p = 6, h = 2. What is the constant of variation?

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters. A second rectangular prism with the same height as the first prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism?

It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. If the amount of time varies directly with the amount of grass and inversely with the number of lawnmowers, how many hours will it take 2 lawnmowers to cut 6 acres of grass?

The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?

A quantity m varies jointly with p and r. When p is 2 and r is 4, m is 1. What is the constant of variation?