Solve each of the following problems. The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of 200 meters of wire that has a diameter of 1/2 centimeter is 1.5 ohms, find the resistance of 400 meters of wire with a diameter of 1/4 centimeter.

Q: Solve each of the following problems. If y is inversely proportional to x, and y = 1/9 when x = 12,…

A:

Q: The time (T) required to do a job varies inversely with the square of the number of people (P)…

A:

Q: Suppose that y varies inversely as the square of x, and that y=5 when x=10. What is y when x=12?…

A: Given,  y varies inversely as the square of x

Q: Solve the following situational problems involving circular functions. 1.The radius of the wheel of…

A: Solve the following situational problems involving circular functions. 1.The radius of the wheel of…

Q: Solve each of the following problems. The volume of a gas at a constant temperature varies inversely…

A: Let V be the volume of the gas and P be the pressure of a gas at constant temperature. It is given…

Q: Suppose that y varies inversely as the square of x, and that y=5 when x=16. What is y when x=6?…

A: Given, y varies inversely as square of x              ⇒ y ∝ 1x2

Q: e load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies…

A:

Q: Find a model for the Body Mass Index (BMI) of a person, given that BMI varies directly as a person’s…

A: Given: Body Mass Index (BMI) varies directly as a person’s weight in pounds and inversely as the…

Q: Solve each of the following problems. If y is directly proportional to x and inversely proportional…

A:

Q: The resistance, R, of a wire varies directly as its length and inversely as the square of its…

A:

Q: Suppose that y varies inversely as the square of x, and that y=4 when x=2. What is y when x=6? Round…

A: y ∝ 1x2 y = kx2 k = yx2         ............................(1)

Q: Suppose the quantity x of Super Titan radial tires made available each week in the marketplace is…

A: Given data:   The expression for the price of Super Titan radial tires is p-x2/2=48. The given rate…

Q: what will be its volume if the pressure is increased to 7 pounds per square inch?

A: Since P∝1V. Therefore, PV=constant.   For two gases, P1V1=P2V2

Q: The intensity I of light from a light bulb varies inversely as the square of the distance d from the…

A: As the intensity I of light from a light bulb is inversely proportional to the square of the…

Q: If y varies directly with the square of x and inversely as z, what is the change in y when both x…

A: Here, y varies directly with the square of x and inversely as z. The mathematical equation of the…

Q: The quantity demanded per month, x, of a certain make of tablet computer is related to the average…

A:

Q: If the monthly total cost of producing 27-inch television sets is given by C(x) = 40,000 + 103x,…

A: Consider the given functions, Total Monthly Cost, Cx=40,000+103xCost per unit, Cx=40,000+103xx…

Q: Find a model for the Body Mass Index (BMI) of a person, given that BMI varies directly as a person's…

A:

Q: Solve each of the following problems. The volume (V) of a gas varies directly as the temperature (T…

A:

Q: Solve each of the following problems. If y is inversely proportional to x, and y = 1/35 when x = 14,…

A: Since, it is given that y is inversely proportional to x.Then, y∝1x⇒y=ax-(i), where a is…

Q: Solve each of the following problems. The period (the time required for one complete oscillation) of…

A: Given: The period of a simple pendulum varies directly as the square root of its length. A pendulum…

Q: If y varies inversely with the square of x, and y=6 when x=2,find y when x=0.4

A: If y varies inversely with the square of x and y = 6 when x = 2we find y when x = 0.4

Q: If s varies directly as the square of t, and s = 10, what is the constant of variation?

A: To determine the constant of variation from the given data

Q: If y is inversely proportional to the square root of x and y is 2 when x is 9, what is when x is 4?

A:

Q: Solve each of the following problems. If y is directly proportional to x, and y = 42 when x = 28,…

A: Given- If y is directly proportional to x, and y=42, when x=28. To Find- The value of y when x=38.

Q: The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies…

A: given for PendulumpαLthereforep=kLp1=1.7sL1=2 ftL2=7 ftp2=?

Q: The intensity of illumination falling on a surface from a given source of light is inversely…

A: We have given intencity of illumiantion I falling on a surface from a given source of light is…

Q: Answer the following problem. Show your complete solution. 3. The amount of gasoline used by a car…

A:

Q: Solve each of the following problems. The volume of a cylinder varies jointly as its altitude and…

A: For getting a variation equation following things should be kept in mind. For a variable C to vary…

Q: The number of minutes needed to solve an Exercise Set of variation problems varies directly as the…

A: Let the number of minutes m varies directly as the number of problems n and inversely as the number…

Q: The number of hours worked varies inversely with the amount of money paid per hour. Bill can earn…

A: According to question given that the number of hours worked Varies inversely with the amount of…

Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

A: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

Q: Suppose that y varies directly as the square root of x, and that y equals 12 when x= 36. Find x when…

A: y varies directly as the square root of x. y∝xy=kx where k=proportionality constant Substitute x=36…

Q: Solve each of the following problems. If y is inversely proportional to the square root of x, and if…

A: Given- y is inversely proportional to the square root of x  and if y=0.08 when x=225. To Find- The…

Q: Solve each of the following problems. The time required for a car to travel a certain distance…

A: Suppose that the time required for a car to travel a certain distance is t and the rate at which it…

Q: Solve each of the following problems. The period (the time required for one complete oscillation) of…

A: For a given variation problem, the variation equation can be written keeping following things in…

Q: Solve each of the following problems. If y is directly proportional to x, and y = 36 when x = 48,…

A: y∝xy=kxWhen value ofx=48 and y=3636=k(48)k=3648=34

Q: The time it takes to cover the distance between two cities by car varies inversely with the speed of…

A:

Q: Solve each of the following problems. The distance that a freely falling body falls varies directly…

A: Let -Distance = dTime = tAccording to question - Distance varies directly as the square of the…

Q: The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies…

A: The solution is given below

Q: If a varies directly with the square of b, and b in turn varies inversely with d, if  a is 90 when d…

A: Given that, a varies directly with the square of b. b varies inversely with d. a is 90 when d is 5.…

Q: Find a model for the Body Mass Index (BMI) of a person, given that BMI varies directly as a person's…

A:

Q: The period of a pendulum varies directly as the square root of the length of the pendulum and…

A:

Q: The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies…

A:

Q: The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies…

A: Given: the time it takes for the pendulum to make one complete swing, varies directly as the square…

Q: During a nationwide program to immunize the population against a new strain of the flu, public…

A: Consider the given function, C(x)=1.85x100-x  Put x=30% in the function.…

Q: At a fixed temperature, the volume of a given mass of gas varies inversely as the pressure applied…

A: Given that, At a fixed temperature, the volume (V) of a given mass of gas varies inversely as the…

Q: A large meteor is spotted by the Hubble Telescope passing the moon and on track to strike earth…

A: Two quantities can either be directly proportional to each other or inversely proportional to each…

Q: Suppose  c  is inversely proportional to the square of  d. If  c=8  when  d=2⁢, find the constant of…

A: Given, c is inversely proportional to the square of d.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.