Joint and Combined Variation
The amount of time it takes p people to paint d doors varies directly with the number of doors and inversely with the number of people. Four people can paint 10 doors in 2 hours. How many people will it take to paint 25 doors in 5 hours?
A) 4
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 prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism?
A) 576 cubic centimeters
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?
B) 1,250 joules
The quantity a varies directly with b and c and inversely with d. The quantity d is tripled. Which of the following must be true for the relationship to remain the same?
B) The product of c and b must be tripled.
A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?
B) mc005-1.jpg p/rs
A quantity b varies jointly with c and d and inversely with e. When b is 18, c is 4, d is 9, and e is 6. What is the constant of variation?
C) 3
A quantity h varies directly with w and inversely with p. If h = 2, w = 4, and p = 6. What is the constant of variation?
C) 3
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?
D) 12
When a = 6 and b = 22, c = 33. If c varies directly with b and inversely with a, which equation models the situation?
NOT B
A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation, k?
NOT B (A) mc006-1.jpg) xz/y
