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Calculus/Instantaneous rate of change problem

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Expert: Alon Mandes - 11/8/2008


Question
1)  A water bucket containing 10 gallons of water develops a leak.  The volume v of water in the bucket t seconds later is given by v(t)=10(1-(t/100))^2 until the bucket is empty 100 seconds later.



a) At what rate is the water leaking after exactly 1  minute?



b) When is the instantaneous rate of change of volume equal to the average rate of change of volume from t=0 to t=10?



c) At the instant described in part "b", how much water is in the tank?



Thanks for you help, I really appreciate it.

Answer
Ok, so we know the following :
V(t)=10(1-t/100)^2 (" The volume of water remaing in the tank").
L(t)=10-10(1-(t/100))^2 (" The volume of water Leaked out so far") .

a)L'(t)=-10*2(1-t/100)*(-1/100)=(1/50)(1-t/100)
L'(60sec)=(1/50)(1-60/100)=0.008

b) According to the mean value theorem : There excists a point
to in which V'(to)=[V(10)-V(0)]/10.

C)calculate V(to)

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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M.A in Mathematics & Bs.c in Electronics.

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