anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
https://gyazo.com/945c50dd03c9c13bfe58ff4bd2c269d8
Agl202
  • Agl202
Left Sum = 2 * (r(0) + r(2) + r(4) + r(6) + r(8)) = 2 * (10.7 + 8.6 + 6.6 + 5.2 + 5.0) = 72.2
anonymous
  • anonymous
@Agl202 could you write of out the Rieman Sum/ Sigma Notation?

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anonymous
  • anonymous
@jim_thompson5910 @zepdrix would any of you be willing to give me a hand? I'd really like to know the procedure not just the answer.
jim_thompson5910
  • jim_thompson5910
does this pic help?
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anonymous
  • anonymous
Yes but is there calculus way of solving this? Like writing out the Riemann sum?
jim_thompson5910
  • jim_thompson5910
@Agl202 wrote out the expanded form of the Riemann sum the step just before it would be something like this \[\Large \sum_{k=0}^{n-1}r(x_k)*\Delta x\]
jim_thompson5910
  • jim_thompson5910
Since delta x is constant, we can pull it out \[\Large \sum_{k=0}^{n-1}r(x_k)*\Delta x=\Delta x*\sum_{k=0}^{n-1}r(x_k)\]
anonymous
  • anonymous
How do I find Xk?
jim_thompson5910
  • jim_thompson5910
there are 5 rectangles, so n = 5 and n-1 = 5-1 = 4 the x_k is the general term for x_1, x_2, x_3, x_4
jim_thompson5910
  • jim_thompson5910
k starts at 0 and goes to 4 (k is a whole number)
jim_thompson5910
  • jim_thompson5910
each x_k value is found by looking at the first row of the table notice how @Agl202 plugged in x = 0, x = 2, etc etc
jim_thompson5910
  • jim_thompson5910
btw the answer isn't 72.2 but it's pretty close @Agl202 made a typo
anonymous
  • anonymous
I don't think I got it then. If he plugged in those values he wouldn't get those numbers.
anonymous
  • anonymous
Wait are you just adding what's in the table?
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
yeah he used the wrong numbers from the table
jim_thompson5910
  • jim_thompson5910
but the idea is still the same
anonymous
  • anonymous
So basically add then multiply by two?
jim_thompson5910
  • jim_thompson5910
yeah because delta x (or delta t) is equal to 2
jim_thompson5910
  • jim_thompson5910
keep in mind that the last value in the table is NOT used (look at how the rectangles are set up in my drawing to see why)
anonymous
  • anonymous
I got 70 for the final answer. @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
8.7+7.6+6.8+6.2+5.7 = 35 2*35 = 70 same here

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