Question

A tank has an intake valve and a release valve. The rate of follow through each valve is inversely proportional to the area of its cross-section. The cross-section area of the input can be described by the equation, f(x)= x^2+2x+1; The cross-section area of the release can be described by the equation, f(x)= x^2+4x+3. If the proportion constant is equal for the input and output, find x such that the volume of material in the tank remains constant.

Answer 1

• x = - 1

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The volume will remain constant if both input and output cross - sections are equal:

• x² + 2x + 1 = x²+ 4x + 3
• 4x - 2x = 1 - 3
• 2x = - 2
• x = - 1