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Question : s varies directly as m A) m = ks B) m = (k/s) C) s = km D) s = (k/m) : 2151703

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write an equation to describe the variation. Use k for the constant of proportionality.

1) s varies directly as m

A) m = ks

B) m = (k/s)

C) s = km

D) s = (k/m)

If y varies directly as x, find the direct variation equation for the situation.

2) y = 7 when x = 42

A) y = (1/6)x

B) y = (1/7)x

C) y = 6x

D) y = x + 35

3) y = 12 when x = 16

A) y = (3/4)x

B) y = 4x

C) y = (4/3)x

D) y = x - 4

4) y = 2 when x = (1/3)

A) y = (1/2)x

B) y = (1/6)x

C) y = x + (5/3)

D) y = 6x

5) y = 1.5 when x = 0.3

A) y = 5x

B) y = x + 1.2

C) y = 0.3x

D) y = 0.2x

6) y = 0.3 when x = 1.5

A) y = 0.3x

B) y = x - 1.2

C) y = 5x

D) y = 0.2x

Solve.

7) Suppose that y varies directly as the square of x. If x is doubled, what is the effect on y?

A) It's multiplied by 4.

B) It's multiplied by 8.

C) It's squared.

D) It's multiplied by 2.

8) The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 20 minutes requires 16 gallons of water. Find the amount of water used in a shower lasting 4 minutes.

A) 4 gallons

B) 80 gallons

C) 3.2 gallons

D) 2.4 gallons

9) If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 5 volts are applied to a circuit, 50 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 8 volts.

A) 40 milliamperes

B) 90 milliamperes

C) 80 milliamperes

D) 72 milliamperes

10) The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 2 hours and uses 28 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 6 hours.

A) 84 gallons

B) 98 gallons

C) 90 gallons

D) 12 gallons

11) The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls 39.2 meters in 2 seconds. Find the distance the object falls in 3 seconds.

A) 29.4 meters

B) 88.2 meters

C) 58.8 meters

D) 6 meters

12) For a resistor in a direct current circuit that does not vary its resistance, the power that a resistor must dissipate is directly proportional to the square of the voltage across the resistor. The resistor must dissipate (1/16) watt of power when the voltage across the resistor is 14 volts. Find the power that the resistor must dissipate when the voltage across it is 28 volts.

A) (7/8) watt

B) (1/8) watt

C) (1/4) watt

D) (49/4) watts

Write an equation to describe the variation. Use k for the constant of proportionality.

13) a varies inversely as w

A) a = (k/w)

B) w = (a/k)

C) w = ka

D) a = (w/k)

If y varies inversely as x, find the inverse variation equation for the situation.

14) y = 7 when x = 3

A) y = (7/3)x

B) y = (x/21)

C) y = (1/21x)

D) y = (21/x)

15) y = 90 when x = 6

A) y = (1/540x)

B) y = (540/x)

C) y = (x/540)

D) y = 15x

16) y = 45 when x = (1/9)

A) y = (x/5)

B) y = (1/5x)

C) y = 405x

D) y = (5/x)

17) y = (1/9) when x = 18

A) y = (1/162)x

B) y = (x/2)

C) y = (1/2x)

D) y = (2/x)

18) y = 0.4 when x = 0.2

A) y = 12.5x

B) y = 2x

C) y = (12.5/x)

D) y = (0.08/x)

Solve.

19) When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 294 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 42 cubic inches.

A) 3 pounds per square inch

B) 84 pounds per square inch

C) 91 pounds per square inch

D) 98 pounds per square inch

20) The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 100 seconds with an average speed of 3 feet per second. Find the average speed of the swimmer if it takes 75 seconds to finish the race.

A) 5 feet per second

B) 6 feet per second

C) 3 feet per second

D) 4 feet per second

21) If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 21 kilograms accelerates at a rate of 8 meters per second per second by a force, find the rate of acceleration of an object with a mass of 7 kilograms that is pulled by the same force.

A) 24 meters per second per second

B) 16 meters per second per second

C) (8/3) meters per second per second

D) 21 meters per second per second

22) If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 420 milliamperes when the resistance is 2 ohms, find the current when the resistance is 12 ohms.

A) 2514 milliamperes

B) 2520 milliamperes

C) 70 milliamperes

D) 140 milliamperes

23) While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 20 feet per second per second when the radius of the turn is 90 feet, find the acceleration the passengers feel when the radius of the turn is 360 feet.

A) 6 feet per second per second

B) 7 feet per second per second

C) 5 feet per second per second

D) 8 feet per second per second

Write an equation to describe the variation. Use k for the constant of proportionality.

24) x varies jointly as y and z.

A) x = kyz

B) xyz = k

C) x + y + z = k

D) x = k + y + z

25) P varies jointly as R and the square of S.

A) P = kRS^{2}

B) P = k + R + S^{2}

C) PRS^{2} = k

D) P + R + S^{2} = k

26) w varies jointly as x and the cube of y.

A) w = k + x + y^{3}

B) wxy^{3} = k

C) w = kxy^{3}

D) w + x + y^{3} = k

27) p varies jointly as the square of q and the square of r.

A) p + q^{2} + r^{2} = k

B) pq^{2}r^{2} = k

C) p = kq^{2}r^{2}

D) p = k + q^{2} + r^{2}

Find the variation equation for the variation statement.

28) z varies jointly as y and the cube of x; z = 1792 when x = 4 and y = -4

A) y = -7xy^{3}

B) y = 7x^{3}y

C) y = 7xy^{3}

D) y = -7x^{3}y

Solve.

29) The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 65 feet and 8-foot walls requires 5.2 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 35 feet and 6-foot walls.

A) 210 quarts

B) 21 quarts

C) 2.1 quarts

D) 4.2 quarts

30) The amount of simple interest earned on an investment over a fixed amount of time is jointly proportional to the principle invested and the interest rate. A principle investment of $4000.00 with an interest rate of 3% earned $240.00 in simple interest. Find the amount of simple interest earned if the principle is $2400.00 and the interest rate is 1%.

A) $4800.00

B) $144.00

C) $80.00

D) $48.00

31) The voltage across a resistor is jointly proportional to the resistance of the resistor and the current flowing through the resistor. If the voltage across a resistor is 12 volts for a resistor whose resistance is 2 ohms and when the current flowing through the resistor is 6 amperes, find the voltage across a resistor whose resistance is 4 ohms and when the current flowing through the resistor is 5 amperes.

A) 24 volts

B) 30 volts

C) 20 volts

D) 10 volts

32) The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 75 watts of power when 5 amperes of current is flowing through the resistor whose resistance is 3 ohms, find the power that a resistor needs to dissipate when 8 amperes of current are flowing through a resistor whose resistance is 3 ohms.

A) 24 watts

B) 120 watts

C) 72 watts

D) 192 watts

33) While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 324 newtons when the car is moving at a speed of 60 kilometers per hour and the passenger has a mass of 100 kilograms, find the force a passenger experiences when the car is moving at 70 kilometers per hour and the passenger has a mass of 80 kilograms.

A) 392 newtons

B) 441 newtons

C) 352.8 newtons

D) 313.6 newtons

34) The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the temperature and inversely as the volume of the gas. If the pressure is 1152 kPa (kiloPascals) when the number of moles is 6, the temperature is 320° Kelvin, and the volume is 720 cc, find the pressure when the number of moles is 9, the temperature is 280° K, and the volume is 1080 cc.

A) 2232

B) 2016

C) 1008

D) 900

Write an equation to describe the variation. Use k for the constant of proportionality.

35) s varies directly as t and inversely as u.

A) s = (ku/t)

B) stu = k

C) s = (kt/u)

D) s + t - u = k

36) s varies directly as t and inversely as the square of u.

A) stu^{2} = k

B) s + t - u^{2} = k

C) s = (ku^{2}/t)

D) s = (kt/u^{2})

37) r varies directly as the square of s and inversely as the cube of t.

A) r = (kt^{3}/s^{2})

B) r + s^{2} - t^{3} = k

C) r = (ks^{2}/t^{3})

D) rs^{2}t^{3} = k

38) q varies directly as the square of r and inversely as s.

A) q = (kr^{2}/s)

B) q = k + r^{2} - s^{2}

C) q = kr^{2}s

D) q = (ks/r^{2})

Find the variation equation for the variation statement.

39) z varies directly as x and inversely as y; z = 5 when x = 45 and y = 45

A) z = (5/xy)

B) z = 5xy

C) z = (x/5y)

D) z = (5x/y)

40) y varies directly as the square of x; y = 150 when x = 5

A) y = 30x

B) y = 25x

C) y = 150x

D) y = 6x^{2}

41) y varies directly as the square of x; y = - (81/5) when x = 9

A) y = - (1/5)x^{2}

B) y = - (81/5)x

C) y = (- (81/5)x)^{2}

D) y = (- (1/5)x)^{2}

42) y varies inversely as the square of x; y = 3 when x = 6

A) y = (108/x)

B) y = (x/108)

C) y = (108/x^{2})

D) y = (x^{2}/108)