Question

The pressure exerted by a certain liquid at a given point varies directly as the depth of the point beneath the surface of the liquid. The pressure at 80 feet is 320 pounds per square inch. What is the pressure at 30 ​feet?

Find a polynomial of degree 3 with real coefficients and zeros of −​3, −​1, and​ 4, for which ​f(−​2)=18.

Answer 1

Solution:

Let the pressure exerted by a liquid be and the depth of the point beneath the surface of the liquid be .

Then .

, where is the constant of variation

When , then

is the equation of variation

When , then

So, the pressure at feet is pounds per square inch.

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Let   be the required polynomial.

Then

Also,