Question 1

Determine whether the situation or equation represents direct or inverse variation.
-The frequency that you brush your teeth and the length of time that you retain all your teeth

Accepted Answer

The answer of Determine whether the situation or equation represents...

Question 2

Determine whether the situation or equation represents direct or inverse variation.
-The ability of a truck to climb hills and the weight of its cargo

Accepted Answer

The ability of a truck to climb hills decreases as the weight of its cargo increases, indicating an inverse relationship between the two variables.

Question 3

Determine whether the situation or equation represents direct or inverse variation.
-The cross-sectional area of a tree and its age

Accepted Answer

The cross-sectional area of a tree and its age represent direct variation because as a tree ages, its cross-sectional area typically increases.

Question 4

Determine whether the situation or equation represents direct or inverse variation.
-The number of errors that a rookie makes as a fielder and the probability that he will remain a starting player

Accepted Answer

The number of errors a rookie makes as a fielder and the probability that he will remain a starting player have an inverse relationship. As the number of errors increases, the probability of remaining a starting player decreases.

Question 5

Determine whether the situation or equation represents direct or inverse variation.
-y =

Accepted Answer

The answer of Determine whether the situation or equation represents...

Question 6

Determine whether the situation or equation represents direct or inverse variation.
-y = 4

Accepted Answer

The answer of Determine whether the situation or equation represents...

Question 7

Solve the problem involving direct or inverse variation.
-If m varies directly as p, and m = 18 when p = 6, find m when p is 7.

Accepted Answer

Since m varies directly as p, the formula is m = kp, where k is the constant of variation. Given m = 18 when p = 6, we find k = 18/6 = 3. To find m when p = 7, substitute p = 7 into m = 3p to get m = 3*7 = 21.

Question 8

Solve the problem involving direct or inverse variation. -If s varies directly as t², and s = 144 when t = 4, find s when t is 6.

Accepted Answer

The answer of Solve the problem involving direct or inverse...

Question 9

Solve the problem involving direct or inverse variation.
-If x varies inversely as v, and x = 36 when v = 9, find x when v = 81.

Accepted Answer

Since x varies inversely as v, the relationship can be described by the equation x = k/v, where k is a constant. Given x = 36 when v = 9, we can find k by substituting these values into the equation: 36 = k/9, which gives k = 324. To find x when v = 81, substitute k = 324 and v = 81 into the equation: x = 324/81, which simplifies to x = 4.

Question 10

Solve the problem involving direct or inverse variation. -If x varies inversely as y², and x = 3 when y = 15, find x when y = 3.

Accepted Answer

Since x varies inversely as y^2, we have x = k/y^2 for some constant k. Given x = 3 when y = 15, we find k = 3 * 15^2 = 675. When y = 3, x = 675/3^2 = 675/9 = 75.

Question 11

Solve the variation problem.
-The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the water of the earth. What is the effect on the weight when the distance is multiplied by 3?

Accepted Answer

Since weight is inversely proportional to the square of the distance, tripling the distance results in the weight being divided by $3^2 = 9$.

Question 12

Solve the variation problem.
-The time necessary to make an enlargement of a photo negative varies directly as the area of the enlargement. If 126 sec are required to make a  enlargement, find the time required for a  enlargement.

Accepted Answer

The answer of Solve the variation problem.
-The time necessary to...

Question 13

Solve the variation problem.
-The distance that a spring is stretched by a hanging object varies directly as the mass of the object. If an object with a mass of 6 kg stretches a spring 30 cm, find the stretch when the object has a mass of 10 kg.

Accepted Answer

The distance stretched varies directly with the mass, so we use the formula $y = kx$, where $y$ is the distance stretched, $x$ is the mass, and $k$ is the constant of variation. Given that 30 cm corresponds to 6 kg, we find $k = 30/6 = 5$. For a mass of 10 kg, the stretch is $5 \times 10 = 50$ cm.

Question 14

Solve the variation problem.
-The number of gears a machine can make varies directly as the time it operates. If it can make 4196 gears in 19 hr, how many gears can it make in 3 hr?

Accepted Answer

The number of gears varies directly with time, so we use the formula: gears = k * time. First, find k using 4196 gears in 19 hours: k = 4196 / 19 = 220.84. Then, calculate gears for 3 hours: gears = 220.84 * 3 = 662.52, which rounds to 662.53.

Question 15

Solve the variation problem.
-According to Ohm's law, the electric current, in amperes (A), in a circuit varies directly as the voltage, in volts (V). When 18 V are applied, the current is 2 A. What is the current when 25 V are applied?

Accepted Answer

Ohm's law states that current (I) varies directly with voltage (V), so I = kV, where k is a constant. With 18V and 2A, k = 2A/18V = 1/9. For 25V, I = (1/9) * 25V = 2.78A.

Question 16

Solve the variation problem.
-The weight of an object on the moon varies directly as its weight on earth. A person who weighs 123 lb on earth weighs 24.6 lb on the moon. How much would a 186-lb person weigh on the moon?

Accepted Answer

The weight of an object on the moon is directly proportional to its weight on Earth. Given that a 123 lb person weighs 24.6 lb on the moon, we can find the proportionality constant by dividing the moon weight by the Earth weight: 24.6 lb / 123 lb = 0.2. To find the weight of a 186-lb person on the moon, we multiply their Earth weight by this constant: 186 lb * 0.2 = 37.2 lb.

Question 17

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-Consider an equation of direct variation y = kx. When x increases, does y increase or decrease?

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-Consider an equation of inverse variation y =  . When x increases, does y increase or decrease?

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-State whether the following situation represents direct variation, inverse variation, or neither, and explain why: The cost of mailing a letter in the United States and the distance that it travels.

Accepted Answer

The answer of Write the word or phrase that best...

Question 20

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-State whether the following situation represents direct variation, inverse variation, or neither, and explain why: A runner's speed in a race and the time it takes to run the race

Accepted Answer

The answer of Write the word or phrase that best...

Quiz 8: Roots and Radicals

Determine whether the situation or equation represents direct or inverse variation. -The frequency that you brush your teeth and the length of time that you retain all your teeth

Determine whether the situation or equation represents direct or inverse variation. -The ability of a truck to climb hills and the weight of its cargo

Determine whether the situation or equation represents direct or inverse variation. -The cross-sectional area of a tree and its age

Determine whether the situation or equation represents direct or inverse variation. -The number of errors that a rookie makes as a fielder and the probability that he will remain a starting player

Determine whether the situation or equation represents direct or inverse variation. -y =

Determine whether the situation or equation represents direct or inverse variation. -y = 4

Solve the problem involving direct or inverse variation. -If m varies directly as p, and m = 18 when p = 6, find m when p is 7.

Solve the problem involving direct or inverse variation. -If s varies directly as t², and s = 144 when t = 4, find s when t is 6.

Solve the problem involving direct or inverse variation. -If x varies inversely as v, and x = 36 when v = 9, find x when v = 81.

Solve the problem involving direct or inverse variation. -If x varies inversely as y², and x = 3 when y = 15, find x when y = 3.

Solve the variation problem. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the water of the earth. What is the effect on the weight when the distance is multiplied by 3?

Solve the variation problem. -The time necessary to make an enlargement of a photo negative varies directly as the area of the enlargement. If 126 sec are required to make a enlargement, find the time required for a enlargement.

Solve the variation problem. -The distance that a spring is stretched by a hanging object varies directly as the mass of the object. If an object with a mass of 6 kg stretches a spring 30 cm, find the stretch when the object has a mass of 10 kg.

Solve the variation problem. -The number of gears a machine can make varies directly as the time it operates. If it can make 4196 gears in 19 hr, how many gears can it make in 3 hr?

Solve the variation problem. -According to Ohm's law, the electric current, in amperes (A) , in a circuit varies directly as the voltage, in volts (V) . When 18 V are applied, the current is 2 A. What is the current when 25 V are applied?

Solve the variation problem. -The weight of an object on the moon varies directly as its weight on earth. A person who weighs 123 lb on earth weighs 24.6 lb on the moon. How much would a 186-lb person weigh on the moon?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Consider an equation of direct variation y = kx. When x increases, does y increase or decrease?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Consider an equation of inverse variation y = . When x increases, does y increase or decrease?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -State whether the following situation represents direct variation, inverse variation, or neither, and explain why: A runner's speed in a race and the time it takes to run the race

Quiz 8: Roots and Radicals

Determine whether the situation or equation represents direct or inverse variation. -The frequency that you brush your teeth and the length of time that you retain all your teeth

Determine whether the situation or equation represents direct or inverse variation. -The ability of a truck to climb hills and the weight of its cargo

Determine whether the situation or equation represents direct or inverse variation. -The cross-sectional area of a tree and its age

Determine whether the situation or equation represents direct or inverse variation. -The number of errors that a rookie makes as a fielder and the probability that he will remain a starting player

Determine whether the situation or equation represents direct or inverse variation. -y =

Determine whether the situation or equation represents direct or inverse variation. -y = 4

Solve the problem involving direct or inverse variation. -If m varies directly as p, and m = 18 when p = 6, find m when p is 7.

Solve the problem involving direct or inverse variation. -If s varies directly as t2, and s = 144 when t = 4, find s when t is 6.

Solve the problem involving direct or inverse variation. -If x varies inversely as v, and x = 36 when v = 9, find x when v = 81.

Solve the problem involving direct or inverse variation. -If x varies inversely as y2, and x = 3 when y = 15, find x when y = 3.

Solve the variation problem. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the water of the earth. What is the effect on the weight when the distance is multiplied by 3?

Solve the variation problem. -The time necessary to make an enlargement of a photo negative varies directly as the area of the enlargement. If 126 sec are required to make a enlargement, find the time required for a enlargement.

Solve the variation problem. -The distance that a spring is stretched by a hanging object varies directly as the mass of the object. If an object with a mass of 6 kg stretches a spring 30 cm, find the stretch when the object has a mass of 10 kg.

Solve the variation problem. -The number of gears a machine can make varies directly as the time it operates. If it can make 4196 gears in 19 hr, how many gears can it make in 3 hr?

Solve the variation problem. -According to Ohm's law, the electric current, in amperes (A) , in a circuit varies directly as the voltage, in volts (V) . When 18 V are applied, the current is 2 A. What is the current when 25 V are applied?

Solve the variation problem. -The weight of an object on the moon varies directly as its weight on earth. A person who weighs 123 lb on earth weighs 24.6 lb on the moon. How much would a 186-lb person weigh on the moon?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Consider an equation of direct variation y = kx. When x increases, does y increase or decrease?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Consider an equation of inverse variation y = . When x increases, does y increase or decrease?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -State whether the following situation represents direct variation, inverse variation, or neither, and explain why: A runner's speed in a race and the time it takes to run the race

Solve the problem involving direct or inverse variation. -If s varies directly as t², and s = 144 when t = 4, find s when t is 6.

Solve the problem involving direct or inverse variation. -If x varies inversely as y², and x = 3 when y = 15, find x when y = 3.