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

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

trisarahtops · Answer

@mathmale

trisarahtops · Answer

@sleepyjess

trisarahtops · Answer

@Zarkon

xguardians · Answer

I should be able to help you with this, just give me a few.

trisarahtops · Answer

Np :)

xguardians · Answer

Would you prefer step by step or just the answer?

trisarahtops · Answer

step by step please

xguardians · Answer

Okay, so first off, the equation for Rectangular Riemann sum is Δx * (F(1) + F(2)...)

xguardians · Answer

In this scenario, Δx = 2, since the t = 2 for all of the intervals.

xguardians · Answer

Now, we must evaluate the equation for the left endpoints, meaning we will start with the leftmost value in r(t) and move our wave across until we have five values.

xguardians · Answer

Therefore, the equation will look like this: |dw:1461888778919:dw|, which equals 70 gallons.

trisarahtops · Answer

wow thank you so much! @xGuardians

xguardians · Answer

No problem, in AP calculus this year and AP test is next week. Practice like this helps not only you but also me. :)