Aconical tank has height 3 m and radius 2 m at the top. water level is rising at a rate of 1.8 m/min when it is 1.5 m from the bottom of the tank. at what rate is water flowing in? (round your answer to three decimal places.)

  5.655 m³/min

Step-by-step explanation:

Halfway from the bottom of the tank, the radius is half that at the top, so is 1 m. That means the surface area of the water at that point is ...

  A = πr² = π(1 m)² = π m²

The rate of flow of water into the tank is the product of this area and the rate of change of depth:

  flow rate = area × (depth rate of change)

  = (π m²) × (1.8 m/min) = 1.8π m³/min

  flow rate ≈ 5.655 m³/min

Step-by-step explanation:

The roots are x=-1 and x=-3, so (x+1) = 0 or (x+3) = 0.  As long as one is 0, the product is 0.

(x+1)(x+3) = 0

x^{2} +4x+3=0

So the numerator function is x^{2} +4x+3=0