Question

Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.
Give your answer with one decimal place.


t (hr) 0 2 4 6 8 10
r(t) (gal/hr) 8.7 7.6 6.8 6.2 5.7 5.3

I believe it's 70.0 because 10-0/5=2 and 2*(8.7+7.6+6.8+6.2+5.7). is this correct or is it 8-0/5 and then the rest?

Answer 1

Answer: Correct, 2[8.7+7.6+6.8+6.2+5.7] = 70.0 gallons

Step-by-step explanation:

Answer 2

Answer with explanation:

The rate of leak of water from a tank per hour is shown:

t (hr)             0      2       4        6 8 10

r(t) (gal/hr) 8.7   7.6   6.8     6.2     5.7 5.3

Total amount of water that leaked out by using five rectangles is given as:

$\int\limits^0_2 {f(x)} \, dx + \int\limits^4_2 {f(x)} \, dx +\int\limits^6_4 {f(x)} \, dx +\int\limits^8_6 {f(x)} \, dx +\int\limits^{10}_8 {f(x)} \, dx$

where f(x) is the curve ,which shows the rate at which water is leaking out from the rectangle.It is continuously decreasing function.

Total amount of water leaked in 2 hours =r(t) (gal/hr)* t (hr)

=(8.7+7.6+6.8+6.2+5.7)×2

= 35*2

=70 liter

So, it's 70.0 because 10-0/5=2 and 2*(8.7+7.6+6.8+6.2+5.7)=70 , is correct for five rectangles.