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 with explanation:

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

t (hr)             0      2       4        6810

r(t) (gal/hr)8.7   7.6   6.8     6.2     5.75.3

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

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.

51-50

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.