Finn removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 12x2 −13x + 3, where x is the time in minutes. Choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty.

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

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.