Question 1

Solve.
-The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 6 amperes when the resistance is 646 ohms. What is the current when the resistance is 884 ohms? Round to the
Nearest hundredths when necessary.
A) 0.23 amperes
B) 0.12 amperes
C) 8.21 amperes
D) 4.38 amperes

Accepted Answer

The relationship is I = k/R, where k is a constant. Given I = 6 when R = 646, k = 6 * 646 = 3876. For R = 884, I = 3876 / 884 ≈ 4.38 amperes.

Question 2

Solve.
-The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 34,000 mi has  in of tread left. How much tread will be left on a tire that has traveled 13,000 mi?
Express the answer as a fraction in simplest form.
A) 832 in.
B) 
C) 
D)

Accepted Answer

The answer of Solve.
-The amount of tread left on a...

Question 3

Find an equation of variation in which the following are true.
-x varies inversely as  , and x = 7 when y = 15.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 4

Solve.
-It takes 9 hours for 8 people to paint a house. How long will it take 2 people to do the job?
A) 2.5 hr
B) 32.4 hr
C) 36 hr
D) 2.3 hr

Accepted Answer

The job takes 9 hours for 8 people, so for 2 people, it would take 4 times longer since 8/2 = 4. Therefore, 9 hours * 4 = 36 hours.

Question 5

Solve.
-The volume V of a gas varies inversely as the pressure P on it. The volume of a gas is 180  under a pressure of 18  What will be its volume under a pressure of 30  ?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve.
-The volume V of a gas varies...

Question 6

Solve.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft
Apart?
A) 4 lb
B) 1 lb
C) 3 lb
D) 2 lb

Accepted Answer

The gravitational attraction between two masses is given 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 9 lb when the distance is 2 ft, we can find $k$ by plugging these values into the formula: $9 = \frac{k}{2^2}$, so $k = 36$. To find the attraction when the distance is 6 ft, we use the same formula with $d = 6$: $A = \frac{36}{6^2} = \frac{36}{36} = 1$ lb.

Question 7

Solve.
-The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 60 seconds are required to make a 3-by-5 enlargement, find the time required for a 5-by-8
Enlargement.
A) 160 sec
B) 240 sec
C) 200 sec
D) 120 sec

Accepted Answer

The area of the 3-by-5 enlargement is 3 * 5 = 15 square inches. The area of the 5-by-8 enlargement is 5 * 8 = 40 square inches. Since the time varies directly as the area, the time required for the 5-by-8 enlargement is 60 * 40 / 15 = 160 seconds.

Question 8

Solve.
-The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 2-m beam can support 580 kg. How many kilograms can a 5-m beam support?
A) 0.0172 kg
B) 58 kg
C) 0.0043 kg
D) 232 kg

Accepted Answer

The weight a beam can support is inversely proportional to its length, so if a 2-m beam supports 580 kg, a 5-m beam supports $580 \times \frac{2}{5} = 232$ kg.

Question 9

Find an equation of variation in which the following are true.
-y varies directly as the square of x, and y = 5.6 when x = 4.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 10

Find an equation of variation in which y varies inversely as x and the following is true.
-y = 0.75, when x = 24
A) 
B) 
C) 
D) y = 18x

Accepted Answer

The answer of Find an equation of variation in which...

Question 11

Find an equation of variation in which y varies inversely as x and the following is true.
-y = 0.6, when x = 0.2
A) 
B) 
C) 
D) y = 3x

Accepted Answer

The answer of Find an equation of variation in which...

Question 12

Find an equation of variation in which y varies inversely as x and the following is true.
-y = 7.25, when x = 0.52
A) 
B) 
C) 
D) y = 13.94x

Accepted Answer

The answer of Find an equation of variation in which...

Question 13

Find an equation of variation in which y varies inversely as x and the following is true.
-y = 21, when x = 3
A) y = 7x
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 14

Solve.
-The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 482 vibrations per second and a wavelength of 12 ft. Find the wavelength of another tone that has a pitch of 348 vibrations per
Second. Round to the nearest hundredths when necessary.
A) 0.06 ft
B) 13,978 ft
C) 16.62 ft
D) 1.66 ft

Accepted Answer

The relationship between pitch (P) and wavelength (W) is inversely proportional, so $P = k/W$, where $k$ is a constant. For the first tone, $482 = k/12$, so $k = 482 \times 12$. For the second tone with a pitch of 348 vibrations per second, $348 = (482 \times 12)/W$. Solving for $W$ gives $W \approx 16.62$ ft.

Question 15

Find an equation of variation in which y varies inversely as x and the following is true.
-y = 10, when x = 19
A) 
B) y = 190x
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 16

Solve.
-The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 g, find the weight of the liquid in a cubical container 3 cm on a side.
A) 81 g
B) 15 g
C) 27 g
D) 9 g

Accepted Answer

The weight of the liquid is directly proportional to its volume. The volume of a cube is given by $V = s^3$, where $s$ is the side length. For the first container, $V_1 = 4^3 = 64$ cm$^3$, and the weight is 192 g, establishing a ratio of weight to volume as $192g / 64cm^3 = 3g/cm^3$. For the second container, $V_2 = 3^3 = 27$ cm$^3$. Thus, the weight of the liquid in the second container is $27cm^3 * 3g/cm^3 = 81g$.

Question 17

Solve.
-The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 60 miles per hour in 50 minutes, how fast must it travel to cover the same distance in 10
Minutes?
A) 
B) 12 miles per hour
C) 
D) 300 miles per hour

Accepted Answer

The answer of Solve.
-The speed of a vehicle is inversely...

Question 18

Solve.
-The number of miles per gallon of gasoline that a car averages varies inversely as the average speed the car travels. A car gets 26 miles per gallon at 39 mph. How many miles per gallon will it get at 67 mph?
A) 0.07 miles per gallon
B) 0.02 miles per gallon
C) 15.1 miles per gallon
D) 44.7 miles per gallon

Accepted Answer

The relationship between miles per gallon (mpg) and speed (s) can be described by the formula mpg = k/s, where k is a constant. Given that at 39 mph the car gets 26 mpg, we can find k by multiplying these two values (k = 26 * 39). To find the mpg at 67 mph, we divide this constant by 67 mph, resulting in approximately 15.1 miles per gallon.

Question 19

Solve.
-The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 195 lb on earth weighs 39 lb on the Moon. How much would a 115-lb person weigh on the Moon?
A) 349 lb
B) 575 lb
C) 0.2 lb
D) 23 lb

Accepted Answer

The weight on the Moon is calculated as a fraction of the weight on Earth. Given that a 195 lb person weighs 39 lb on the Moon, we can find the ratio of Moon weight to Earth weight: 39/195 = 0.2. To find the weight of a 115-lb person on the Moon, multiply their Earth weight by this ratio: 115 * 0.2 = 23 lb.

Question 20

Find an equation of variation in which y varies inversely as x and the following is true.
-y = 50, when x = 26
A) y = 1.92x
B) 
C) 
D) y = 1300x

Accepted Answer

The answer of Find an equation of variation in which...

Quiz 7: Rational Expressions and Equations

Solve. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 6 amperes when the resistance is 646 ohms. What is the current when the resistance is 884 ohms? Round to the Nearest hundredths when necessary.

Solve. -The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 34,000 mi has in of tread left. How much tread will be left on a tire that has traveled 13,000 mi? Express the answer as a fraction in simplest form.

Find an equation of variation in which the following are true. -x varies inversely as , and x = 7 when y = 15.

Solve. -It takes 9 hours for 8 people to paint a house. How long will it take 2 people to do the job?

Solve. -The volume V of a gas varies inversely as the pressure P on it. The volume of a gas is 180 under a pressure of 18 What will be its volume under a pressure of 30 ?

Solve. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft Apart?

Solve. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 60 seconds are required to make a 3-by-5 enlargement, find the time required for a 5-by-8 Enlargement.

Solve. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 2-m beam can support 580 kg. How many kilograms can a 5-m beam support?

Find an equation of variation in which the following are true. -y varies directly as the square of x, and y = 5.6 when x = 4.

Find an equation of variation in which y varies inversely as x and the following is true. -y = 0.75, when x = 24

Find an equation of variation in which y varies inversely as x and the following is true. -y = 0.6, when x = 0.2

Find an equation of variation in which y varies inversely as x and the following is true. -y = 7.25, when x = 0.52

Find an equation of variation in which y varies inversely as x and the following is true. -y = 21, when x = 3

Solve. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 482 vibrations per second and a wavelength of 12 ft. Find the wavelength of another tone that has a pitch of 348 vibrations per Second. Round to the nearest hundredths when necessary.

Find an equation of variation in which y varies inversely as x and the following is true. -y = 10, when x = 19

Solve. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 g, find the weight of the liquid in a cubical container 3 cm on a side.

Solve. -The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 60 miles per hour in 50 minutes, how fast must it travel to cover the same distance in 10 Minutes?

Solve. -The number of miles per gallon of gasoline that a car averages varies inversely as the average speed the car travels. A car gets 26 miles per gallon at 39 mph. How many miles per gallon will it get at 67 mph?

Solve. -The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 195 lb on earth weighs 39 lb on the Moon. How much would a 115-lb person weigh on the Moon?

Find an equation of variation in which y varies inversely as x and the following is true. -y = 50, when x = 26