See Problem 4.

20. Painting The number of buckets of paint n needed to paint a fence varies directly with the total area a of the fence and inversely with the amount of paint p in a bucket. It takes three 1-gallon buckets of paint to paint 72 square feet of fence. How many 1-gallon buckets will be needed to paint 90 square feet of fence?

See Problem 5.

21. Potential Energy On Earth with a gravitational acceleration g, the potential energy stored in an object varies directly with its mass m and its vertical height h. What is the equation of the potential energy of a 2 kg skateboard that is sliding down a ramp?
22. Think About a Plan The table shows data about how the life span s of a mammal relates to its heart rate r. The data could be modeled by an equation of the form r s = k . r s equals k .  Estimate the life span of a cat with a heart rate of 126 beats/min.
    • How can you estimate a constant of the inverse variation?
    • What expression would you use to find the life span?

    Heart Rate and Life Span

    Mammal	Heart rate (beats/min)	Life span (min)
    Mouse	634	1,576,800
    Rabbit	158	6,307,200
    Lion	76	13,140,000

    SOURCE: The Handy Science Answer Book

23. Physics The force F of gravity on a rocket varies directly with its mass m and inversely with the square of its distance d from Earth. Write a model for this combined variation.

B Apply

24. The spreadsheet shows data that could be modeled by an equation of the form P V = k . p v equals k .  Estimate P when V = 62. v equals 62.
25. Chemistry The formula for the Ideal Gas Law is P V = n R T , p v equals n r t comma  where P is the pressure in kilopascals (kPA), V is the volume in liters (L), T is the temperature in Kelvin (K), n is the number of moles of gas, and R = 8.314 r equals , 8.314  is the universal gas constant.
    1. What volume is needed to store 5 moles of helium gas at 350 K under the pressure 190 kPA?
    2. A 10 L cylinder is filled with hydrogen gas to a pressure of 5,000 kPA. The temperature of gas is 300 K. How many moles of hydrogen gas are in the cylinder?

    	A	B
    1	P	V
    2	140.00	100
    3	147.30	95
    4	155.60	90
    5	164.70	85
    6	175.00	80
    7	186.70	75

Write the function that models each variation. Find z when x = 4 and y = 9.

26. z varies directly with x and inversely with y. When x = 6 x equals 6  and y = 2 , z = 15 . y equals 2 comma z equals 15 .
27. z varies jointly with x and y. When x = 2 x equals 2  and y = 3 , z = 60 . y equals 3 comma z equals 60 .
28. z varies inversely with the product of x and y. When x = 2 x equals 2  and y = 4 , z = 0.5 . y equals 4 comma z equals 0.5 .

Each pair of values is from a direct variation. Find the missing value.

29. (2, 5), (4, y)
30. (4, 6), (x, 3)
31. (3, 7), (8, y)
32. (x, 12), (4, 1.5)

Each ordered pair is from an inverse variation. Find the constant of variation.

33. (6, 3)
34. (0.9, 4)
35. ( 3 8 , 2 3 ) open . 3 eighths , comma , 2 thirds . close
36. ( 2 , 18 ) open . square root of 2 comma square root of 18 . close

Each pair of values is from an inverse variation. Find the missing value.

37. (2, 5), (4, y)
38. (4, 6), (x, 3)
39. (3, 7), (8, y)
40. (x, 12), (4, 1.5)

Table of Contents