The graph below shows the rate that water leaves a tank, in gallons per hour, where t is measured in hours. (Please give exact answers.)
y = f(t)
a How much water left the tank during the 6 hours shown?
10
gallons
b. How many hours did it take for 9 gallons to leave the tank?
hours

Part a) 10 gallons

Part b) 4.59 hours

Step-by-step explanation:

The picture of the question in the attached figure

Part a) How much water left the tank during the 6 hours shown?

To find out how much water left the tank during the 6 hours, determine the area of the graph in that interval

so

Calculate the area of the rectangle plus the area of the triangle

Part b) How many hours did it take for 9 gallons to leave the tank?

we know that

In the interval [0,4]

8 gallons of water leaves the tank in 4 hours (remember that the area in that interval is equal to 8 gallons)

so

Find out in the interval (4,6] how  many hours did it take for 1 gallon to leave the tank

First determine the equation of the line in the interval (4,6)

we have the points (4,2) and (6,0)

The slope is equal to

The equation of the line is

Determine the area of graph in the interval (4,x) (Is the area of trapezoid)

so

For A=1 gal

solve the quadratic equation by graphing

The solution is x=4.59 hours

see the attached figure N 2

d. vertex

step-by-step explanation:

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: