Combined Variation

Multiple Choice

The formula for Combined Variation is represented as:

• y = kx

• y = k/x

• y = kxz

• y = kx/z

Multiple Choice

It is given that m varies directly as the square of n and inversely as p.

Given m = 10.8 when n = 18 and p=6. Express m in terms of n and p.

• $$m=5n^2p$$  

• $$m=\frac{5n^2}{p}$$  

• $$m=\frac{n^2}{5p}$$  

• $$m=\frac{27n^2}{5p}$$  

Multiple Choice

y varies directly as x and inversely as z. It is given that y = 51 when x = 1.7 and z = 5. Express y in terms of x and z.

• $$y=\frac{150x}{z}$$

• $$y=\frac{6x}{z}$$

• $$y=\frac{x}{6z}$$

• $$y=\frac{x}{150z}$$

Multiple Select

The time T taken (in minutes) to boil water varies directly as the water's weight, w (in kg), and inversely as the kettle's power P (in watts).

Jonie takes 4 minutes to boil 2 kg water using a kettle with a power of 1 500 watts.

(T = 4, w = 2, P = 1 500)

(I) Express T in terms of w and P.

• $$T\ =\ \frac{3\ 000w}{P}$$

• $$T\ =\ \frac{750w}{P}$$

• T = 1.13 minutes

• T = 4.5 minutes

Multiple Select

The time T taken (in minutes) to boil water varies directly as the water's weight, w (in kg), and

inversely as the kettle's power P (in watts).

Jonie takes 4 minutes to boil 2 kg water using a kettle with a power of 1 500 watts. (T = 4, w = 2, P = 1 500)

(II) If the kettle's power is 1 200 watts, how much time (in minutes) is needed to boil 1.8 kg water?
(Find T, when P = 1 200, w = 1.8)

• T = 1.13 minutes

• T = 1.25 minutes

• T = 4 minutes

• T = 4.5 minutes

Multiple Choice

z varies inversely with x and directly with y. If x = 4, y = 48 and z = -2, find x when z = 8 and y = 96.

• -2

• -1

• 0

• 1

Multiple Choice

z varies inversely with x and directly with y. If x = 1/2, y = 5 and z = 20, find x when z = -4 and y = 8.

• 1

• 2

• 3

• 4

Multiple Choice

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

• 4

• 5

• 8

• 10

Multiple Choice

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

• 4

• 5

• 8

• 10

Multiple Choice

If y varies jointly as a and b and inversely as the square root of c, and y = 12 when a = 3, b = 2, and c = 64, find y when a = 5, b = 2, and c = 25.

• 8

• 16

• 24

• 32

Multiple Choice

The time it takes you to complete a puzzle is directly proportional to the number of pieces and inversely proportional to how many people are working on it. You and your three friends can complete a 1,000 piece puzzle in 2 hours. How long would it take you to complete a 2,500 piece puzzle?

• 8 hours

• 9 hours

• 10 hours

• 11 hours

Multiple Choice

The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working on the solutions. It takes 4 people 36 minutes to solve 18 problems. How many minutes will it take 6 people to solve 42 problems.

• 56 minutes

• 52 minutes

• 48 minutes

• 44 minutes

Multiple Choice

If p varies directly as the square of q and inversely as the square root of r, and p = 60 when q = 6 and r = 81, find p when q = 8 and r = 144.

• 70

• 80

• 90

• 100

Multiple Choice

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 250 g, find the weight of the liquid in a cubical container 3 cm on a side.

• 12 g

• 6 g

• 27 g

• 54 g

Multiple Choice

The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?

• 308.05 ft

• 295.75 ft

• 296.09 ft

• 253.5 ft