Old Mac D purchased a pool with a capacity of 100 gallons. One day at 1pm he placed a hose that filled it at 5g/h. After 10 hours, farm animals started drinking water at 2g/h.5 hours after that, farmer put in a 2nd hose that filled it at a rate if 4g/h. when did he have a pool full of water?

may i see the picture? it would a lot, xox

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.