Answer:
Step-by-step explanation:
The expression used to model the volume, in gallons, is 12x^2-13x+3
When the through is empty it means that there is no water in it wich means that the expression used equals 0
● 12x^2-13x+3 = 0
The expression is quadratic equation so to solve it we will use the discriminant method
The discriminant is b^2-4ac
● b= -13
● a= 12
● c= 3
b^2-4ac = (-13)^2+4×12×3 = 25
25 > 0 so the discriminant is positive
We have two solutions
Let x and x' be the solutions
x = (-b-5)/2×a =(13-5)/24 = 8/24 = 1/3
5 is the root square of 25 (the discriminant)
x' = (-b+5)/2a = (13+5)/25 = 18/24 = 3/4
The solutions are 1/3 and 3/4
1/3 = 0.34
3÷4 = 0.75
The through can't be empty from water in two different times
So it will be empty when reaching one of the 2 solutions first
0.34 < 0.75
Then at 0.34 min the through is epty from water
