Relative Aperture. The relative aperture, or f-stop, of a 23.5-mm diameter lens is

Find the variation constant and an equation of variation for the given situation.y varies directly as x, and y = 54 when x = 12

Find the variation constant and an equation of variation for the given situation.y varies directly as x, and y = 0.1 when x = 0.2

Find the variation constant and an equation of variation for the given situation.y varies inversely as x, and y = 3 when x = 12

Find the variay varies inversely as x, and y = 12 when x = 5tion constant and an equation of variation for the given situation.

Find the variation constant and an equation of variation for the given situation.y varies directly as x, and y = 1 when x = 1 4

Find the variation constant and an equation of variation for the given situation.y varies inversely as x, and y = 0.1 when x = 0.5

Find the variation constant and an equation of variation for the given situation.y varies inversely as x, and y = 32 when x = 1 8

Find the variation constant and an equation of variation for the given situation.y varies directly as x, and y = 3 when x = 33

Find the variation constant and an equation of variation for the given situation.y varies directly as x, and y = 3 4 when x = 2

Find the variation constant and an equation of variation for the given situation.y varies inversely as x, and y = 1 5 when x = 35

Find the variation constant and an equation of variation for the given situation.y varies inversely as x, and y = 1.8 when x = 0.3

Find the variation constant and an equation of variation for the given situation.y varies directly as x, and y = 0.9 when x = 0.4

Sales Tax. The amount of sales tax paid on a product is directly proportional to its purchase price. In Indiana, the sales tax on a Sony Reader that sells for $260 is $17.50. What is the sales tax on an e-book that sells for $21?

Childs Allowance. The Gemmers decide to give their children a weekly allowance that is directly proportional to each childs age. Their 6-year-old daughter receives an allowance of $4.50. What is their 11-year-old sons allowance?

Beam Weight. The weight W that a horizontal beam can support varies inversely as the length L of the beam. Suppose an 8-m beam can support

Rate of Travel. The time t required to drive a fixed distance varies inversely as the speed r. It takes 5 hr at a speed of 80 km>h to drive a fixed distance. How long will it take to drive the same distance at a speed of 70 km>h?

Fat Intake. The maximum number of grams of fat that should be in a diet varies directly as a persons weight. A person weighing 120 lb should have no more than 60 g of fat per day. What is the maximum daily fat intake for a person weighing 180 lb?

U.S. House of Representatives. The number of representatives N that each state has varies directly as the number of people P living in the state. If New York, with 19,254,630 residents, has 29 representatives, how many representatives does Colorado, with a population of 4,665,177, have?

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

Pumping Rate. The time t required to empty a tank varies inversely as the rate r of pumping. If a pump can empty a tank in 45 min at the rate of 600 kL>min, how long will it take the pump to empty the same tank at the rate of 1000 kL>min?

Hookes Law. Hookes law states that the distance d that a spring will stretch varies directly as the mass m of an object hanging from the spring. If a 3-kg mass stretches a spring 40 cm, how far will a 5-kg mass stretch the spring? Spring at rest m d

Relative Aperture. The relative aperture, or f-stop, of a 23.5-mm diameter lens is directly proportional to the focal length F of the lens. If a 150-mm focal length has an f-stop of 6.3, find the f-stop of a 23.5-mm diameter lens with a focal length of 80 mm.

Musical Pitch. The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 330 vibrations per second and a wavelength of 3.2 ft. Find the wavelength of another tone that has a pitch of 550 vibrations per second.

Weight on Mars. The weight M of an object on Mars varies directly as its weight E on Earth. A person who weighs 95 lb on Earth weighs 38 lb on Mars. How much would a 100-lb person weigh on Mars?

Find an equation of variation for the given situation.y varies inversely as the square of x, and y = 0.15 when x = 0.1

Find an equation of variation for the given situation.y varies inversely as the square of x, and y = 6 when x = 3

Find an equation of variation for the given situation.y varies directly as the square of x, and y = 0.15 when x = 0.1

Find an equation of variation for the given situation.y varies directly as the square of x, and y = 6 when x = 3

Find an equation of variation for the given situation.y varies jointly as x and z, and y = 56 when x = 7 and z = 8

Find an equation of variation for the given situation.y varies directly as x and inversely as z, and y = 4 when x = 12 and z = 15

Find an equation of variation for the given situation.y varies jointly as x and the square of z, and y = 105 when x = 14 and z = 5

Find an equation of variation for the given situation.y varies jointly as x and z and inversely as w, and y = 3 2 when x = 2, z = 3, and w = 4

Find an equation of variation for the given situation.y varies jointly as x and z and inversely as the product of w and p, and y = 3 28 when x = 3, z = 10, w = 7, and p = 8

Find an equation of variation for the given situation.y varies jointly as x and z and inversely as the square of w, and y = 12 5 when x = 16, z = 3, and w = 5

Intensity of Light. The intensity I of light from a light bulb varies inversely as the square of the distance d from the bulb. Suppose that I is 90 W>m2 (watts per square meter) when the distance is 5 m. How much farther would it be to a point where the intensity is 40 W>m2 ?

Atmospheric Drag. Wind resistance, or atmospheric drag, tends to slow down moving objects.

Stopping Distance of a Car. The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car traveling 60 mph can stop in 200 ft, how fast can a car travel and still stop in 72 ft?

Weight of an Astronaut. The weight W of an object varies inversely as the square of the distance d from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find his weight when he is 200 mi above the surface of the earth.

Earned-Run Average. A pitchers earned-run average E varies directly as the number R of earned runs allowed and inversely as the number I of innings pitched. In 2010, Bronson Arroyo of the Cincinnati Reds had an earned-run average of 3.89. He gave up 93 earned runs in 215.2 innings. How many earned runs would he have given up had he pitched 238 innings with the same average? Round to the nearest whole number.

Boyles Law. The volume V of a given mass of a gas varies directly as the temperature T and inversely as the pressure P. If V = 231 cm3 when T = 42 and P = 20 kg>cm2 , what is the volume when T = 30 and P = 15 kg>cm2 ?

In each of Exercises 4145, fill in the blank with the correct term. Some of the given choices will not be used. even function relative maximum odd function relative minimum constant function solution composite function zero direct variation perpendicular inverse variation parallelNonvertical lines are if and only if they have the same slope and different y-intercepts.

In each of Exercises 4145, fill in the blank with the correct term. Some of the given choices will not be used. even function relative maximum odd function relative minimum constant function solution composite function zero direct variation perpendicular inverse variation parallel An input c of a function f is a(n) of the function if f 1c2 = 0.

In each of Exercises 4145, fill in the blank with the correct term. Some of the given choices will not be used. even function relative maximum odd function relative minimum constant function solution composite function zero direct variation perpendicular inverse variation parallelFor a function f for which f 1c2 exists, f 1c2 is a(n) if f 1c2 is the lowest point in some open interval.

In each of Exercises 4145, fill in the blank with the correct term. Some of the given choices will not be used. even function relative maximum odd function relative minimum constant function solution composite function zero direct variation perpendicular inverse variation parallelIf the graph of a function is symmetric with respect to the origin, then f is a(n) .

In each of Exercises 4145, fill in the blank with the correct term. Some of the given choices will not be used. even function relative maximum odd function relative minimum constant function solution composite function zero direct variation perpendicular inverse variation parallelAn equation y = k>x is an equation of .

In each of the following equations, state whether y varies directly as x, inversely as x, or neither directly nor inversely as x. a) 7xy = 14 b) x - 2y = 12 c) -2x + 3y = 0 d) x = 3 4 y e) x y = 2

Volume and Cost. An 18-oz jar of peanut butter in the shape of a right circular cylinder is 5 in. high and 3 in. in diameter and sells for $2.89. In the same store, a 28-oz jar of the same brand is 51 2 in. high and 31 4 in. in diameter. If the cost is directly proportional to volume, what should the price of the larger jar be? If the cost is directly proportional to weight, what should the price of the larger jar be?

Describe in words the variation given by the equation Q = kp2 q3 .

Area of a Circle. The area of a circle varies directly as the square of the length of a diameter. What is the variation constant?