Question 1

Solve the problem.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2 sec when the length is 16 inches, what is the period when L = 1.5625 inches?
A) 2.5 sec
B) 0.625 sec
C) 2.75 sec
D) 3 sec

Accepted Answer

The period of vibration $P$ is directly proportional to the square root of the length $L$, so $P = k\sqrt{L}$, where $k$ is the constant of proportionality. Given $P = 2$ sec when $L = 16$ inches, we can find $k$ by substituting these values into the equation: $2 = k\sqrt{16}$, which simplifies to $2 = 4k$, so $k = 0.5$. For $L = 1.5625$ inches, $P = 0.5\sqrt{1.5625} = 0.5 \times 1.25 = 0.625$ sec.

Question 2

Solve the problem.
-The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4?
A) The weight is multiplied by 4.
B) The weight is divided by 16.
C) The weight is divided by 4.
D) The weight is multiplied by 16.

Accepted Answer

The weight of a body is inversely proportional to the square of its distance from the center of the earth. Therefore, if the distance is multiplied by 4, the weight is divided by $4^2 = 16$.

Question 3

Solve the problem.
-The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 45 seconds are required to make a 3-by-5 enlargement, find the time required for a 4-by-7
Enlargement.
A) 140 sec
B) 56 sec
C) 84 sec
D) 112 sec

Accepted Answer

The area of the 3-by-5 enlargement is 15 square units, and it takes 45 seconds. The area of the 4-by-7 enlargement is 28 square units. Since time varies directly with area, we set up the proportion: 45/15 = T/28. Solving for T gives T = 84 seconds.

Question 4

Solve the problem.
-The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 4 foot candles, find the intensity on a screen 20 ft from the light.
A) 2 foot-candles
B)  foot-candle
C)  foot-candles
D)  foot-candle

Accepted Answer

The answer of Solve the problem.
-The intensity I of light...

Question 5

Solve the problem.
-The shadow cast by an object on a sunny day varies directly as the height of the object. If a person 58 inches tall casts a shadow 84 inches long, how tall is a tree which casts a shadow 44 feet in length? Round to the nearest
Hundredth when necessary.
A) 63.72 feet
B) 110.73 feet
C) 71 feet
D) 30.38 feet

Accepted Answer

The answer of Solve the problem.
-The shadow cast by an...

Question 6

Provide an appropriate response.
-Give the equation that describes the graph shown. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Provide an appropriate response.
-Give the equation that...

Question 7

Determine whether the first variable varies directly or inversely with the other variable.
-The height of a building in inches, the height of the same building in feet
A) Inversely
B) Directly

Accepted Answer

The height of a building in inches varies directly with the height of the same building in feet because as one increases, the other also increases proportionally.

Question 8

Solve the problem.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft
Apart?
A) 3 lb
B) 1 lb
C) 2 lb
D) 4 lb

Accepted Answer

The gravitational attraction between two masses can be represented by the formula $A = \frac{k}{d^2}$, where $A$ is the attraction, $d$ is the distance between the masses, and $k$ is a constant. Given that the attraction is 2.25 lb when the distance is 4 ft, we can find $k$ by rearranging the formula to $k = A \cdot d^2 = 2.25 \cdot 4^2 = 2.25 \cdot 16 = 36$. To find the attraction when the distance is 6 ft, we use the formula again with $d = 6$: $A = \frac{36}{6^2} = \frac{36}{36} = 1$ lb.

Question 9

Solve the problem.
-The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If  , what is the volume when T = 
A) 133.3 in.3
B) 163.3 in.3
C) 143.3 in.3
D) 153.3 in.3

Accepted Answer

The answer of Solve the problem.
-The volume V of a...

Question 10

Solve the problem.
-The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 24 seconds are required to make a 3-by-4 enlargement, find the time required for a 6-by-6
Enlargement.
A) 144 sec
B) 72 sec
C) 36 sec
D) 108 sec

Accepted Answer

The time $T$ varies directly with the area $A$, so $T = kA$ for some constant $k$. For a 3-by-4 enlargement, the area is $3 \times 4 = 12$ square units, and it takes 24 seconds. Thus, $24 = k \times 12$, so $k = 2$. For a 6-by-6 enlargement, the area is $6 \times 6 = 36$ square units. Therefore, the time required is $T = 2 \times 36 = 72$ seconds.

Question 11

Determine whether the first variable varies directly or inversely with the other variable.
-The depth of a diver in the ocean, the pressure exerted by the water on the diver.
A) Directly
B) Inversely

Accepted Answer

The depth of a diver in the ocean and the pressure exerted by the water on the diver vary directly because as the depth increases, the pressure also increases.

Question 12

Solve the problem.
-If y varies directly as x and inversely as the square root of w, and y = 72 when x = 8 and w = 12, find y when x = 5 and w = 27.
A) y = 30
B) 
C) 
D) y = 60

Accepted Answer

The answer of Solve the problem.
-If y varies directly as...

Question 13

Determine whether the first variable varies directly or inversely with the other variable.
-The number of hot dogs that you can buy for $75, the price per hot dog
A) Directly
B) Inversely

Accepted Answer

The number of hot dogs you can buy varies inversely with the price per hot dog; as the price per hot dog increases, the number of hot dogs you can buy with $75 decreases, and vice versa.

Question 14

Provide an appropriate response.
-One of the graphs is that of y = f(x) and the other is that of  State which is the graph of y =  
A) i
B) ii

Accepted Answer

The answer of Provide an appropriate response.
-One of the graphs...

Question 15

Determine whether the first variable varies directly or inversely with the other variable.
-The time it takes an athlete to run 100 meters, her average speed
A) Inversely
B) Directly

Accepted Answer

The time it takes an athlete to run 100 meters varies inversely with her average speed; as the speed increases, the time decreases.

Question 16

Provide an appropriate response.
-True or false? In order to graph y =  , the graph is the same as that of y = f(x) for values of f(x) that are
negative, and for nonnegative values of y = f(x), the graph is reflected across the x-axis.

Accepted Answer

The answer of Provide an appropriate response.
-True or false? In...

Question 17

Provide an appropriate response.
-Which function represents a vertical translation of the parabola 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Provide an appropriate response.
-Which function represents a...

Question 18

Solve the problem.
-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 4 cm on a side.
A) 128 g
B) 44 g
C) 8 g
D) 64 g

Accepted Answer

The weight of the liquid varies directly as its volume, so the weight of the liquid in a cubical container 4 cm on a side is 250 g * (4/5)^3 = 128 g.

Question 19

Provide an appropriate response.
-Which of the following is a horizontal translation and a reflection of the function  about the x-axis? Use your graphics calculator to verify your result.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Provide an appropriate response.
-Which of the following...

Question 20

Solve the problem.
-If x varies inversely as  , and x = 2 when y = 18, find x when y = 6.
A) x = 12
B) x = 72
C) x = 18
D) x = 3

Accepted Answer

The answer of Solve the problem.
-If x varies inversely as...

Quiz 2: Functions and Graphs

Solve the problem. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2 sec when the length is 16 inches, what is the period when L = 1.5625 inches?

Solve the problem. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4?

Solve the problem. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 45 seconds are required to make a 3-by-5 enlargement, find the time required for a 4-by-7 Enlargement.

Solve the problem. -The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 4 foot candles, find the intensity on a screen 20 ft from the light.

Solve the problem. -The shadow cast by an object on a sunny day varies directly as the height of the object. If a person 58 inches tall casts a shadow 84 inches long, how tall is a tree which casts a shadow 44 feet in length? Round to the nearest Hundredth when necessary.

Provide an appropriate response. -Give the equation that describes the graph shown.

Determine whether the first variable varies directly or inversely with the other variable. -The height of a building in inches, the height of the same building in feet

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft Apart?

Solve the problem. -The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If , what is the volume when T =

Solve the problem. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 24 seconds are required to make a 3-by-4 enlargement, find the time required for a 6-by-6 Enlargement.

Determine whether the first variable varies directly or inversely with the other variable. -The depth of a diver in the ocean, the pressure exerted by the water on the diver.

Solve the problem. -If y varies directly as x and inversely as the square root of w, and y = 72 when x = 8 and w = 12, find y when x = 5 and w = 27.

Determine whether the first variable varies directly or inversely with the other variable. -The number of hot dogs that you can buy for $75, the price per hot dog

Provide an appropriate response. -One of the graphs is that of y = f(x) and the other is that of State which is the graph of y =

Determine whether the first variable varies directly or inversely with the other variable. -The time it takes an athlete to run 100 meters, her average speed

Provide an appropriate response. -True or false? In order to graph y = , the graph is the same as that of y = f(x) for values of f(x) that are negative, and for nonnegative values of y = f(x), the graph is reflected across the x-axis.

Provide an appropriate response. -Which function represents a vertical translation of the parabola

Solve the problem. -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 4 cm on a side.

Provide an appropriate response. -Which of the following is a horizontal translation and a reflection of the function about the x-axis? Use your graphics calculator to verify your result.

Solve the problem. -If x varies inversely as , and x = 2 when y = 18, find x when y = 6.