Weight of a Body The weight of a body above the surface of

If x and y are two quantities, then y is directly proportional to x if there is a nonzero number k such that

True or False If y varies directly with x,then where k is a constant.

In Problems 314, write a general formula to describe each variation.y varies directly with x; y = 2 when x = 10

In Problems 314, write a general formula to describe each variation.v varies directly with t; v = 16 when t = 2

In Problems 314, write a general formula to describe each variation.A varies directly with x when x = 2 2; A = 4p

In Problems 314, write a general formula to describe each variation.V varies directly with x when x = 3 3; V = 36p

In Problems 314, write a general formula to describe each variation.F varies inversely with d when d = 5 2; F = 10

In Problems 314, write a general formula to describe each variation.y varies inversely with 1x; y = 4 when x = 9

In Problems 314, write a general formula to describe each variation.z varies directly with the sum of the squares of x and y;z = 5 when x = 3 and y = 4

In Problems 314, write a general formula to describe each variation.T varies jointly with the cube root of x and the square of d; T = 18 when x = 8 and d = 3

In Problems 314, write a general formula to describe each variation.M varies directly with the square of d and inversely with the square root of x; when andM = 24 x = 9 d = 4

In Problems 314, write a general formula to describe each variation. z varies directly with the sum of the cube of x and the square of y; when andz = 1 x = 2 y = 3

In Problems 314, write a general formula to describe each variation. The square of T varies directly with the cube of a and inversely with the square of d; when andT = 2 a = 2 d = 4

In Problems 314, write a general formula to describe each variation. The cube of z varies directly with the sum of the squares of x and y; z = 2 when x = 9 and y = 4z = 2 when x = 9 and y = 4

In Problems 1520, write an equation that relates the quantitiesGeometry The volume V of a sphere varies directly with the cube of its radius r. The constant of proportionality is .

In Problems 1520, write an equation that relates the quantitiesGeometry The square of the length of the hypotenuse c of a right triangle varies jointly with the sum of the squares of the lengths of its legs a and b.The constant of proportionality is 1.

In Problems 1520, write an equation that relates the quantitiesGeometry The area A of a triangle varies jointly with the lengths of the base b and the height h. The constant of proportionality is

In Problems 1520, write an equation that relates the quantitiesGeometry The perimeter p of a rectangle varies jointly with the sum of the lengths of its sides l and .The constant of proportionality is 2.

In Problems 1520, write an equation that relates the quantitiesPhysics: Newtons Law The force F (in newtons) of attraction between two bodies varies jointly with their masses m and M (in kilograms) and inversely with the square of the distance d (in meters) between them. The constant of proportionality is G = 6.67 * 10-11

In Problems 1520, write an equation that relates the quantitiesPhysics: Simple Pendulum The period of a pendulum is the time required for one oscillation; the pendulum is usually referred to as simple when the angle made to the vertical is less than 5.The period T of a simple pendulum (in seconds) varies directly with the square root of its length l (in feet). The constant of proportionality is 2p 232

Mortgage Payments The monthly payment p on a mortgage varies directly with the amount borrowed B.If the monthly payment on a 30-year mortgage is $6.49 for every $1000 borrowed, find a linear equation that relates the monthly payment p to the amount borrowed B for a mortgage with the same terms. Then find the monthly payment p when the amount borrowed B is $145,000.

Mortgage Payments The monthly payment p on a mortgage varies directly with the amount borrowed B. If the monthly payment on a 15-year mortgage is $8.99 for every $1000 borrowed, find a linear equation that relates the monthly payment p to the amount borrowed B for a mortgage with the same terms. Then find the monthly payment p when the amount borrowed B is $175,000.

Physics: Falling Objects The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in 1 second, how far will it fall in 3 seconds? How long will it take an object to fall 64 feet?

Physics: Falling Objects The velocity of a falling object is directly proportional to the time t of the fall. If, after 2 seconds, the velocity of the object is 64 feet per second, what will its velocity be after 3 seconds?

Physics: Stretching a Spring The elongation E of a spring balance varies directly with the applied weight W (see the figure). If E = 3 when W = 20, find E when W = 15.

Physics: Vibrating String The rate of vibration of a string under constant tension varies inversely with the length of the string.If a string is 48 inches long and vibrates 256 times per second, what is the length of a string that vibrates 576 times per second?

Revenue Equation At the corner Shell station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is $47.40 when the number of gallons sold is 12, find a linear equation that relates revenue R to the number g of gallons of gasoline. Then find the revenue R when the number of gallons of gasoline sold is 10.5.

Cost Equation The cost C of roasted almonds varies directly with the number A of pounds of almonds purchased. If the cost is $23.75 when the number of pounds of roasted almonds purchased is 5,find a linear equation that relates the cost C to the number A of pounds of almonds purchased. Then find the cost C when the number of pounds of almonds purchased is 3.5.

Demand Suppose that the demand D for candy at the movie theater is inversely related to the price p. (a) When the price of candy is $2.75 per bag, the theater sells 156 bags of candy. Express the demand for candy in terms of its price. (b) Determine the number of bags of candy that will be sold if the price is raised to $3 a bag.

Driving to School The time t that it takes to get to school varies inversely with your average speed s. (a) Suppose that it takes you 40 minutes to get to school when your average speed is 30 miles per hour. Express the driving time to school in terms of average speed. (b) Suppose that your average speed to school is 40 miles per hour. How long will it take you to get to school?

Pressure The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 600 cubic centimeters when the pressure is 150 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.

Resistance The current i in a circuit is inversely proportional to its resistance Z measured in ohms. Suppose that when the current in a circuit is 30 amperes the resistance is 8 ohms. Find the current in the same circuit when the resistance is 10 ohms.

Weight The weight of an object above the surface of Earth varies inversely with the square of the distance from the center of Earth. If Maria weighs 125 pounds when she is on the surface of Earth (3960 miles from the center), determine Marias weight if she is at the top of Mount McKinley (3.8 miles from the surface of Earth).

Intensity of Light The intensity I of light (measured in foot-candles) varies inversely with the square of the distance from the bulb. Suppose that the intensity of a 100-watt light bulb at a distance of 2 meters is 0.075 foot-candle. Determine the intensity of the bulb at a distance of 5 meters

Geometry The volume V of a right circular cylinder varies jointly with the square of its radius r and its height h. The constant of proportionality is . See the figure. Write an equation for V.

Geometry The volume V of a right circular cone varies jointly with the square of its radius r and its height h. The constant of proportionality is See the figure. Write an equation for V.

Weight of a Body The weight of a body above the surface of Earth varies inversely with the square of the distance from the center of Earth.If a certain body weighs 55 pounds when it is 3960 miles from the center of Earth, how much will it weigh when it is 3965 miles from the center?

Force of the Wind on a Window The force exerted by the wind on a plane surface varies jointly with the area of thesurface and the square of the velocity of the wind.If the force on an area of 20 square feet is 11 pounds when the wind velocity is 22 miles per hour, find the force on a surface area of 47.125 square feet when the wind velocity is 36.5 miles per hour.

Horsepower The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute, rpm) and the cube of its diameter. If a shaft of a certain material 2 inches in diameter can transmit 36 hp at 75 rpm, what diameter must the shaft have in order to transmit 45 hp at 125 rpm?

Chemistry: Gas Laws The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P.Write an equation relating V, T, and P using k as the constant of proportionality.If a cylinder contains oxygen at a temperature of 300 K and a pressure of 15 atmospheres in a volume of 100 liters, what is the constant of proportionality k? If a piston is lowered into the cylinder, decreasing the volume occupied by the gas to 80 liters and raising the temperature to 310 K, what is the gas pressure?

Physics: Kinetic Energy The kinetic energy K of a moving object varies jointly with its mass m and the square of its velocity . If an object weighing 25 kilograms and moving with a velocity of 10 meters per second has a kinetic energy of 1250 joules, find its kinetic energy when the velocity is 15 meters per second.

Electrical Resistance of a Wire The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 432 feet long and 4 millimeters in diameter has a resistance of 1.24 ohms, find the length of a wire of the same material whose resistance is 1.44 ohms and whose diameter is 3 millimeters.

Measuring the Stress of Materials The stress in the material of a pipe subject to internal pressure varies jointly with the internal pressure and the internal diameter of the pipe and inversely with the thickness of the pipe. The stress is 100 pounds per square inch when the diameter is 5 inches, the thickness is 0.75 inch, and the internal pressure is 25 pounds per square inch. Find the stress when the internal pressure is 40 pounds per square inch if the diameter is 8 inches and the thickness is 0.50 inch

Safe Load for a Beam The maximum safe load for a horizontal rectangular beam varies jointly with the width of the beam and the square of the thickness of the beam and inversely with its length.If an 8-foot beam will support up to 750 pounds when the beam is 4 inches wide and 2 inches thick, what is the maximum safe load in a similar beam 10 feet long, 6 inches wide, and 2 inches thick?

In the early 17th century, Johannes Kepler discovered that the square of the period T of the revolution of a planet around the Sun varies directly with the cube of its mean distance a from the Sun. Go to the library and research this law and Keplers other two laws. Write a brief paper about these laws and Keplers place in history.

Using a situation that has not been discussed in the text, write a real-world problem that you think involves two variables that vary directly. Exchange your problem with another students to solve and critique.

Using a situation that has not been discussed in the text, write a real-world problem that you think involves two variables that vary inversely. Exchange your problem with another students to solve and critique.

Using a situation that has not been discussed in the text, write a real-world problem that you think involves three variables that vary jointly. Exchange your problem with another students to solve and critique.