Amodel for the flow rate of water at a pumping station on a given day is given below, where 0 ≤ t ≤ 24. r(t) = 53 + 7 sin πt 6 + 3.6 + 9 cos πt 12 + 8.9 r is the flow rate in thousands of gallons per hour, and t is the time in hours..

a. find the maximum flow rate and the time at which it occurs?
b. what is the average rate of flow between the hours of 8: 00a. m. and 12: 00 p. m.?
c. what is the total volume of water pumped in 1 day?

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0