Expert: Richard J. Raridon - 7/20/2010

Question
Part 1
Select the best answer from the choices provided. (Each question is worth one point)
1. If s is directly proportional to t, and s = 40 when t = 15, find t when s = 64. t = 0.025  t = 24
t = 170.67  t = 40

2. If a varies directly as b, and a = 75 when b = 40, find a when b = 12. a = 6.4  a = 0.4
a = 22.5  a = 2.25

3. If y is directly proportional to the square root of x, and y = 25 when x = 3, find x when y = 100.  x = 3Ö 3
 x = 48
x = 100  x = 12

4. If w varies directly as 2x - 1, and w = 9 when x = 2, find x when w = 15. x = 2  x = 36
x = 5  x = 3

5. If a, b, and c are positive, and a divided by b is equal to b divided by c, then b is called the mean proportion, or geometric mean, between a and c. Find the mean proportion between the pair of numbers: 3 and 27. b = 9  b = 81
b = 27  b = 18

6. If a, b, and c are positive, and a divided by b is equal to b divided by c, then b is called the mean proportion, or geometric mean, between a and c. Find the mean proportion between the pair of numbers: 5 and 15. 5Ö 3
 b = 3
b = 75  3Ö 5


7. The acceleration of an object varies directly as the force acting on it. If a force of 240 newtons causes an acceleration of 150 m/s², what force will cause an acceleration of 100 m/s2? 160 newtons  16 newtons
62.5 newtons  62 newtons

8. At the grocery mart, a 575g can of green beans cost $0.39. How much will an 810 g can of green beans cost? $0.52  $0.50
$0.55  $0.53

9. A public opinion poll found that out of a sample of 450 voters, 252 favored a school bond issue. If 20,000 people voted, how many are likely to vote for the bond measure? 15,714  11,200
1,120  10,100

10. The speed of an object falling from rest in a vacuum is directly proportional to the time it has fallen. After an object has fallen for 1.5 seconds, its speed is 14.7 m/s. What is the speed after it has fallen 5 seconds? 20 m/s  51 m/s
49 m/s  50 m/s

11. Newton's law of cooling states that the rate at which an object cools varies directly as the difference between its temperature and the temperature of the surrounding air. At the moment a steel plate at 270 degrees Celsius is placed in air that is at 20 degrees Celsius, its rate of cooling is 50 degrees Celsius per minute. How fast is it cooling when the plate temperature is 100 degrees Celsius? 24 degrees C/min  16 degrees C/min
14 degrees C/min  20 degrees C/min

12. The centrifugal force acting on an object moving in a circle is directly proportional to the square of the speed of the object. If the force is 2240 newtons when the object is moving 8 m/s, what is the force when the object is moving at 12 m/s? 5,040 n  420 n
840 n  504 n

13. The speed of an object falling from rest is directly proportional to the square root of the distance the object has fallen. When an object has fallen 36 ft., its speed is 48 ft/s. How much farther must it fall before its speed is 80 ft/s? 64 ft  36 ft
100 ft  54 ft

14. If z is inversely proportional to r, and z = 32 when r = 1.5, find r when z = 8. r = 40  r = 0.17
r = 6  r = .4

15. If p varies inversely as the square root of q, and p = 12 when q = 36, find p when q = 16. p = 4.5  p = 0.056
p = 18  p = 1.8

16. If w is jointly proportional to u and v, and w =2 when u=4 and v=6, what is w when u=3 and v=8? w = 2  w = 4
w = 13  w = 1

17. Suppose that r varies directly as p and inversely as q2, and that r = 27 when p = 3 and q = 2. Find r when p = 2 and q = 3. r = 8  r = 14.4
r = 12  r = 6.2

18. By Ohm's law The current flowing in a wire is inversely proportional to the resistance of the wire. If the current is 5 amperes (A) when the resistance is 24 ohms (Ω), for what resistance will the current be 8 amperes? 21 Ω  112 Ω
100 Ω  15 Ω

19. The conductance of a wire varies directly as the square of the wire's diameter and inversely as its length. Fifty meters of wire with a diameter 2 mm has a conductance of 0.12 ohms. If a wire of the same material has length of 75 m and diameter of 2.5 mm, what is its conductance? 0.05 ohms  0.167 ohms
0.125 ohms  0.5 ohms

20. If p is inversely proportional to q, and p = 28 when q = 1.5, find q when p = 7. q = 6  q = 42
q = 7  q = 0.38

21. The volume of a cone varies jointly as the height and the square of the radius of the base. A cone height 8 cm and a base of diameter 9 cm has volume 54π. Find the constant of variation and use it to develop the general formula for the volume of a cone. V = 0.33π  V = 54πr2h
V = 0.33πr2h  V = 3πr

22. If y varies inversely as x and y = 24 when x = 3, what is y when x = 8? 5  8
3  9

23. If y varies inversely as x and y = 4 when x = 9, what is x when y = 72? 2  4
0.4  0.5

24. The current in an electric circuit of constant voltage varies inversely as the resistance. When the current is 30 amps, the resistance is 20 ohms. Find the current when the resistance is 25 ohms. 24 amps  22 amps
20 amps  16 amps

25. The length of a rectangle with constant area varies inversely as the width. When the length is 18, the width is 8. Find the length when the width is 9. 12  14
16  18

26. A number y varies inversely as the square of x. If y = 2 when x = 6, what is y when x = 3? 6  8
10  12

27. A number y varies inversely as the square root of x. If y = 3 when x = 64, what is x when y = 6? 12  14
16  18

28. The illumination I from a light varies inversely as the square of its distance d from the illuminated object. If I = 8.00 ft-candles when d = 5.00 ft, what is I when d = 4.00 ft? 10.5 ft-candles  11.5 ft-candles
12.5 ft-candles  13.5 ft-candles

29. The height of a cylinder with constant volume is inversely proportional to the square of its radius. If h = 8 when r = 4, what is r when h = 2? 2  4
6  8

30. The volume V of a given mass of gas varies directly as the absolute temperature T and inversely as the pressure P. If V = 462 cm3 when T = 42 degrees and P = 40 kg/cm2, what is the volume when T = 30 degrees and P = 30 kg/cm2? 400 cm3  410 cm3
420 cm3  440 cm3

Part 3
Type the answer to the problem in the text box below each item. Be sure legibly show all work in your notebook. Remember to include any applicable units. If there is no solution, type "no solution". If there is not enough information present to solve the problem, type "not enough information". (Each question is worth two points)
31. For the following direct variation, give an equation that relates the two variables and includes a variation constant.

The kinetic energy (KE) of a 1 kg mass is directly proportional to the square of the speed (v). Variation constant = 1/2.


32. If w varies directly as 3x + 2, and w = 56 when x = 4, find x when w = 92.

33. Suppose that w varies directly as z2 and inversely as xy. When w = 10, x = 15, y = 2, and z = 5. Find z when w = 2, x = 8, and y = 27.

34. Give the equation of the variation described. Use k for the constant of variation.

i is inversely proportional to the square of j.


35. Give the equation of the variation described. Use k for the constant of variation.

w varies jointly as x and y and inversely as z.

Answer
1. t=24
2. a=22.5
3. 48
4. x=3
5. b=9
6. b=5(3^1/2)
7. x=160N
8. $0.55
9. 11,200
10. 49m/s
11. x=16degC/min
12. x=5040N
13. x=100
14. r=6
15. p=18
16. w=2
17. r=8
18. 15 ohms
19. C=0.125
20. q=6
21. V = (1/3)(pi)r^2h
22. 9
23. 0.5
24. 24 amps
25. 16
26. y=8
27. x=16
28. 12.5 ft-candles
29. r=8
30. V=440cm^3
31. KE = (1/2)mv^2
32. x=7
33. z=6
34. i=k/j^2
35. w = kxy/z