8,520 gallons of water begins to drain at a rate of 12 gallons per minute. which equation can be used to find the number of minutes, m, it will take for the pool to be half full?

The time taken to drain water to be half full is 5 hours 55 min .

Step-by-step explanation:

Given as :

The total quantity of water pool = 8520 gallons

The rate of water drain = 12 gallons per min

The time taken to drain water to be half full = t min

Now, According to question

Time of water drain =

Or, time =

Or, time = 710 minutes

So, The time taken to full empty the pool = 710 minutes

Again, time taken to ran water to half full =

Or, t = 355 minutes

So, time taken to drain water to be half full = t = 355 min = 5 hours 55 minutes

Hence, The time taken to drain water to be half full is 5 hours 55 min . Answer

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.