## Proportionality Mathematics Questions and Answers

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If y varies inversely as x and y equals 18 when x equals 5, find y when x equals 3.

How high is a tree that casts a 22-ft shadow at the same time a 4-ft post casts a shadow that is 6-ft long?

Determine if the statement is true or false. |3 \sin 6x| \leq 3 for all x.

Levi must paint the inside of his house, the inside of his house has a paintable surface area of 3500 ft^2. Levi went to the European "Home Depot" to buy his paint when he returned home, he realized each bucket of paint covers 5 m^2, Levi has 140 buckets

Farmer Brown had ducks and cows. One day he noticed that the animals had a total of 16 heads and 42 feet. How many of the animals were cows?

The temperature, T, of a given mass of gas, varies inversely with its volume, V. The temperature of 20 cm^3 of a certain gas is 15^\circ C. What will the temperature be when it is compressed to a volu

If y varies jointly with x and z, and y = 24 when x = 3 and z = 2, then the value of x when y = 6 and z = 0.5 is (blank).

Given y varies directly with x. When y = 20, x = 50. Find x when y = 36.

A sample of 144 firecrackers contained 8 duds. How many duds would you expect in a sample of 2016 firecracker?

The time required to do a job varies inversely as the number of people working. It takes 5 hours for 7 bricklayers to build a park well. How long will it take 10 bricklayers to complete the job?

A particular hybrid car travels approximately 288 mi on 6 gal of gas. Find the amount of gas required for a 912-mi trip.

The number of calculators Mrs. Hopkins can buy for the classroom varies inversely as the cost of each calculator. She can buy 24 calculators that cost $60 each. How many calculators can she buy if the

The number of kilograms of water in a human body varies directly as the mass of the body. An 87 kg person contains 58 kg of water. How many kilograms of water are in a 72 kg person?

Does the equation 7x - 4y = 0 represent a direct variation? If so, find the constant of variation. A) yes; { k= \frac{7}{4} } B) yes, k= -4 C) No D) yes; { k= \frac{-7}{4} }

The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat

Determine whether the equation represents direct, inverse, joint, or combined variation. { y=\frac{31x}{wz} } .

Solve using variation of parameters. A) y'' + y = 3 \sec x - x^2 + 1 B) 2y'' + y = \tan x + e^{2x} - 2 Differential equations.

The U-Drive Rent-A-Truck company plans to spend $16 million on 320 new vehicles. Each commercial van will cost $25,000, each small truck $80,000, and each large truck $70,000. Past experience shows

The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, infinity). Find the general solution of the given non homogeneous equation.

x varies directly as the square of y and x = 12 when y = 4. What is the value of x when y = 6?

Frank runs 10 miles in 75 minutes. At the same rate, how many miles would he run in 69 minutes?

Which of the following proportions will allow you to correctly compute the answer to the question: 51 in. = _ ft.? 1. \frac{51}{x} = \frac{1}{12} 2. \frac{x}{51} = \frac{12}{1} 3. \frac{51}{12} = \fra

Solve the proportion. \frac{2}{7} = \frac{x}{42} A.) \frac{1}{2} B.) 12 C.) \frac{2}{7} D.) 6

Determine whether y varies directly with x if so, solve for the constant of variation k. 3y= -7x-18

The variable z varies jointly with y and the square of x. If x= -2 when y= 7 and z= -84, find x when z= -96 and y= 2.

You rollerblade at an average speed of 8 miles per hour. The number of miles m you rollerblade during h hours is modeled by m= 8h. Do these two quantities have a direct variation?

Suppose that y is directly proportional to x and that y= 10 when x= 3. Find the constant of proportionality k.

The American Association of Individual Investors (AAII) polls its subscribers on a weekly basis to determine the number who are bullish, bearish, or neutral on the short-term prospects for the stock m

The variables x and y are directly proportional, and y = 2 when x = 3. What is the value of y when x = 9?

Three quantities R, S, and T are such that R varies directly as S and inversely as the square of T. (a) Given that R = 480 when S = 150 and T = 5, write an equation connecting R, S, and T. (b) (i) Find the value of R when S = 360 and T = 1.5. (ii) Find th

The amount of taxes a city collect is proportional to the population of the city. If the city collects $6 billion in 1982 when the population was 2 million people, how much did the city collect in 1990 when the population was 3 million people?

Solve: If y is proportional to x and x is 4 when y is 22, then what is y when: (g)x = \frac{1}{w}? y =

Solve the following proportion. 2 / 15 = 13 / x.

Translate the statement of variation into an equation; use k as the constant of variation. V varies jointly as s and the fourth power of u.

A three quarter inch wire has 12 ohms resistance. How much resistance has the same length of half-inch wire, if resistance varies inversely as the square of the diameter?

You pay $1 to rent a movie plus an additional $0.50 per day until you return to the movie. Your friend pays $1.25 per day to rent a movie. a. Make tables showing the costs to rent a movie for up to 5

A walker's speed, v, is proportional to the ratio of his leg length, L, and the period of the repeating motion of his legs, T, that is, v is proportional to L/T. If the period is measured to be propor

In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the responses, 1290 answered "no" , 454 answered "yes", and 400 had no opinion. What is the sample portion of ye

If y varies directly as x, and y = 9 when x= 5, find y when x = 10.

Ben bought 2 sandwiches for $5.00. Let x represent the number of sandwiches purchased and let y represent the total cost. Graph this proportional relationship.

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) y is inversely proportional to x^3. (y = 5 when x = 2.)

The number of ants in Bob's kitchen increase at a rate that is proportional to the number of ants present each day. If there are 20 ants on day 0 and 60 ants on day 4, how many ants will there be on day 14? Round to the nearest ant.

Suppose r varies directly as the square of m, and inversely as s. If r = 15 when m = 15 and s = 9, find r when m = 60 and s = 9.

If burning one mole releases 1310.0 kj, then how many moles will release 227.30?

What is the solution of the proportion? 3y - 8/12 = y/5

If y varies directly as the square root of x and y = 8 when x = 81, find y if x = 6561. (Round off your answer to the nearest hundredth.)

A recipe calls for of a cup of milk for 11 cookies. How many cups of milk are needed to make 132 cookies?

The total population of animals is directly proportional to the size of the habitat (in acres) polled. Write an equation using only one variable that could be used to solve for the constant of variation k .

Find the value of y for a given value of x, if y varies directly with x. If y = 39 when x = -117, what is y when x = -132?

Solve for n. \frac{3}{7 - n}= \frac{1}{n}

Solve for x. fraction{3}{x - 7}= fraction{2}{2x+1}

If z varies inversely as w, and z = 40 when w = .06, find z when w = 20.

The quantity y varies directly with the square of x. If y = 3 when x = 9, find y when x is 11. Round answer to the nearest hundredth.

Suppose that y varies directly with x and inversely with z. If y= 25 when x= 35 and z= 7, write the equation that models the relationship. Then find y when x= 12 and z= 4.

An example of a useful somaclonal variation is Shi 1 answer below An example of a useful somaclonal variation is Shikonin dye production Short crop duration in sugarcane Male sterility White rust re

Suppose that S varies directly as the 2/5 power of T, and that S=8 when T=32. Find S when T=243.

Solve the proportion u / 4 = 11 / 17.

Solve and find the value of x. \frac{2}{3}=\frac{1.2}{x}

If y is inversely proportional to x, and y = 8 when x = 2, find y when x = 5.

Are 84/105 and 128/160 proportional?