Oil is leaking from a tank. For 0 ≤ t ≤ 24, the number of gallons G in the tank at time t is given by G(t) = 6,000 - 5t2, where t is measured in hours past midnight. (a) Use the definition of the derivative to find G'(9). G'(9) = (b) Interpret the meaning of G'(9) in the context of this problem. Indicate the units of measure. At 9:00 a.m. the oil is leaking from the tank at a rate of G'(9) gallons per hour. At 9:00 a.m. the oil is leaking from the tank at a rate of G'(9) hours per gallon. At 9:00 a.m. G'(9) gallons of oil have leaked from the tank. Between 9:00 a.m. and 10:00 a.m. exactly G'(9) gallons of oil will leak from the tank. At 9:00 a.m. G'(9) gallons of oil are left in the tank.
Oil is leaking from a tank. For 0 ≤ t ≤ 24, the number of gallons G in the tank at time t is given by G(t) = 6,000 - 5t2, where t is measured in hours past midnight. (a) Use the definition of the derivative to find G'(9). G'(9) = (b) Interpret the meaning of G'(9) in the context of this problem. Indicate the units of measure. At 9:00 a.m. the oil is leaking from the tank at a rate of G'(9) gallons per hour. At 9:00 a.m. the oil is leaking from the tank at a rate of G'(9) hours per gallon. At 9:00 a.m. G'(9) gallons of oil have leaked from the tank. Between 9:00 a.m. and 10:00 a.m. exactly G'(9) gallons of oil will leak from the tank. At 9:00 a.m. G'(9) gallons of oil are left in the tank.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Oil is leaking from a tank. For 0 ≤ t ≤ 24, the number of gallons G in the tank at time t is given by G(t) = 6,000 - 5t², where t is measured in hours past midnight.
(a) Use the definition of the derivative to find G'(9).
G'(9) =
(b) Interpret the meaning of G'(9) in the context of this problem. Indicate the units of measure.
At 9:00 a.m. the oil is leaking from the tank at a rate of G'(9) gallons per hour.
At 9:00 a.m. the oil is leaking from the tank at a rate of G'(9) hours per gallon.
At 9:00 a.m. G'(9) gallons of oil have leaked from the tank.
Between 9:00 a.m. and 10:00 a.m. exactly G'(9) gallons of oil will leak from the tank.
At 9:00 a.m. G'(9) gallons of oil are left in the tank.
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