Matematicas

1. Your weight expressed in pounds is directly proportional to tour weight expressed in kilograms. Mary uses a scale to see her weight and weighs 50kg. , if she knows that she weighs 110 pounds.

• Write a particular equation that expresses her pounds in terms of kilograms.
• Write how many pounds would a person weighs if the scale reads:

1. 100 kilograms
2. 25 kilograms
3. 150 kilograms

• How many kilograms would Mary weigh if she weighs 165 pounds?
• How many pounds do you weigh?
• Sketch the function
• What is the constant of proportionality?

1. When you swim underwater your ears varies directly proportional with the depth. At 10ft., the pressure is near 4.3 per pound per square inch (psi).

• Write an equation that expresses the pressure in terms of depth.
• Predict the pressure at 50ft.
• For a rookie it is not safe to swim underwater beyond 65 psi, what depth is this?
• Sketch a graph of pressure verses depth.

1. The amount of strength used to tighten a screw depends on the length of the wrench. Suppose that for a certain screw, a 7 inches long wrench requires strength of  270 pounds and wrench of 21 inches long requires strength of 90 pounds.

• How the strength does vary with the length?
• Write a particular equation
• What is the unit of the proportionality constant?
• Find the strength for wrenches of 3,10,15,30, and 60 inches long.
• What would be the length of a wrench if it is applied 300 pounds of force?
• And for force of 50 pounds?
• Sketch the graph of force verses length with a domain of 3 to 69 inches.

1. The number of houses can be supplied by water pipes, it varies directly proportional to the square of the diameter of the pipes. Suppose the pipe with diameter of 10cm supplies 50 houses.

• Write a particular equation for this function.
• How many houses can be supplied by a pipe of 30,43 and on meter?
• In neighborhood with 1500 houses, what would be the diameter needed of the pipes?

e) When a boat is sailing at high speed, the main power of de motor goes to the trail on the wáter. The amount of power used to generate its trailis directyl proportional to the seventh power of the boat´s speed. Supposethet the boat travels at 10 knouts uses 0.1 horse power for itrs wake.

• .write a particular equation of this function
• . How mucho power is consumed in the trail when the boat travels at 30 and 40 knouts
• -Why is hard for boat is going very fast?

f) In Chemistry, Boyle´s Law states that the volumen of an amount of gas is inversely proportional to the preesure of the gas.

.Write  aparticular equation that expresses in terms of pressure, if a pressure of 40 compresses a gas with a volumen of 360 cubic feet

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