edugen wileyplus.com GCll-Lab-9 CHE-1131-0A1-Spring-2017-General Chem... WileyPL
ID: 2883495 • Letter: E
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edugen wileyplus.com GCll-Lab-9 CHE-1131-0A1-Spring-2017-General Chem... WileyPLUS Chapter 5, Section 5.4, Question 005 oil leaks out of a tanker at a rate of r- (t) gallons per minute, where t is in minutes. Write a definite s semisns4, integral expressing the total quantity of oil (in gallons) which leaks out of the tanker in the first five hours. Sedan 4. The total quantity of oil which leaks out of the tanker in the first five hours is Review Results by Study Question Attempts: o of 3 used obiecthe MapleNet 2000 2017 by John Wiley & Sons, In or related companies. Al rights reserved.Explanation / Answer
Solution:(003)
The total cost C(x) is the fixed cost plus the "sum" of marginal costs from 0 to x.
The quotation marks are because "sum" in this context is really an integral since x is a continuous real variable.
By the Fundamental Theorem of Calculus
x
C'(t) dt = C(x) - C(0).
0
C(0) is the fixed cost---the amount of cost incurred independent of drilling. This was given as 1,000,000
x
(5000 + 18t) dt = 5000t + 9t2 {evaluate at x and 0} = 5000x + 9x2
0
So
C(x) - C(0) = 5000x + 9x2
==> C(x) = 5000x + 9x2 + 1000000
cost at x = 700 meter
=> C(x) = 5000(700) + 9(700)2 + 1000000
=> C(x) = 3500000 + 4410000 + 1000000 = 8910000 riyals
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