When you stand on snow, the average pressure P (in pounds per square inch) that you exert on the snow varies inversely with the total area A (in square inches) of the soles of your footwear. Suppose the pressure is 0.43 pound per square inch when you wear the snowshoes shown. Write an equation that gives P as a function of A. Then find the pressure if you wear the boots shown. (A=400in^2)

Find the pressure if you wear the boots shown below. (A=60in^2)

Answer:

0.43*0.43

Step-by-step explanation:

The pressure on the snow if the area of the footwear is 400 in² is 0.0645 pounds per square inch.

The force applied perpendicular to an object's surface per unit area across which that force is spread is known as pressure.

[tex]P= \dfrac{W}{A}[/tex]

As it is given that the pressure is inversely proportional to the area of the footwear. Therefore, the relation can be written as,

[tex]P\propto \dfrac{1}{A}\\[/tex]

Now, introducing a constant to remove the proportionality symbol, w that is the weight of the person, therefore,

[tex]P= \dfrac{W}{A}[/tex]

Now, as the area of the shoe is 60in²,  the pressure on the snow is  0.43 pounds per square inch. Therefore, the value of w can be written as,

[tex]0.43= \dfrac{W}{60}\\\\W = 25.8\rm\ pounds[/tex]

Now, the pressure on the snow if the area of the footwear is 400 in².

[tex]P= \dfrac{W}{A}\\\\P= \dfrac{25.8}{400}\\\\P = 0.0645 \rm\ pounds\ per\ inch^2[/tex]

Hence, the pressure on the snow if the area of the footwear is 400 in² is 0.0645 pounds per square inch.

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