Variation And Proportion {Day 2}

My goal for the day is:

Find x:

Find the actual distance from New York to Mephis

A person's paycheck varies directly as the number of hours worked. Bill received $75 for 15 hours. How much would he receive for working 32 hours?

A person's weight on earth varies directly to his weight on the moon. A person weighing 168 pounds on Earth weighs 28 pounds on the moon. How much would an astronaut weighing 110 pounds on Earth weigh on the moon?

The frequency, f of a radio wave varies inversely as the length, w, of the wave. A wave 200 meters long has a frequency of 1400 kilocycles per second. A second wave has a length of 800 meters. What is the frequency of the second wave?

In sound and harmonics, the frequency of vibrating string is INVERSELY proportional to its length. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 7-inch string?

On a balance (or seesaw), the distance an object is from the fulcrum is inversely proportional to the weight of the object. Use this information to solve each problem. 

Aaron weighs 64 pounds and is 6 feet away from the fulcrum, how far would his 24 pound little sister have to sit from the fulcrum so that it would balance?

Charles' Law says that the volume of a gas is directly proportional to its temperature. If the volume of a gas is 2.5 cubic feet at 150° (absolute temperature), what is the volume of the same gas when the temperature is 200° (absolute temperature)?

The average number of words that can be printed on standard paper varies inversely with the font size. If 320 words can be printed with a 10-point font size, how many words can be printed with a 12-point font size?

 A company has found that the daily demand x for its product is inversely proportional to the price p. When the price is $5, the demand is 800 units. Approximate the demand if the price is increased to $6.

Leonardo da Vinci observed that a person's height varies directly as the width of their shoulders.

If a person is 70 [in] tall and has a shoulder width of 17.5 [in],

What is the height of a person whose shoulder width is 16 [in]?

When a person swims underwater the pressure in his or her ears varies directly with the depth at which he or she is swimming. At 10 feet, the pressure is about 4.3 pounds per square inch(psi).

What is the constant of variation (k)?

If it unsafe for amateur divers to swim where the water pressure is more that 65 psi. How deep can an amateur diver safely swim? (in other words, find the depth when the pressure is 65)

Find the pressure if the depth is 60 feet. (look up and find info to write a product or proportion)

A 2-foot-tall dog casts a 3-foot shadow at the same time a cat casts a one foot shadow. How tall is the cat?

The price, , that Eric pays for gas varies directly with the number of gallons, , he buys. It costs him $50 to buy 20

gallons of gas.

a. Write the equation that relates P and

b. How much would 33 gallons cost Eric?

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds getting 33

mpg on the highway.

a. Write the equation that relates the mpg to the car’s weight.

b. What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?