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Calculus/related rates


duckboy81 wrote at 2009-10-30 05:57:45
From the last post:

dV   3 pi r^2 dr

-- = -------- --          <--------- 4 IN DENOMINATOR

dt       4    dt

At the instant in question:  h = 4, so r = 4h/3 = 16/3.  Substituting:

10 = 3 pi (16/3)^2 dr/dt

   3 pi 256 dr

10 = -------- --          <--------- 4  NOT IN DENOMINATOR

      9     dt      

---During the implicit diff, the 4 in the denominator was dropped somehow...

Billy wrote at 2012-12-13 19:26:08
The answer above is incorrect.  The author forgot to add the 4 on the bottom when he plugged 16/3 into the equation.  In actuality, it should be:


         4          dt

10=64pi dr

        3   dt

30  =dr

64pi  dt


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Paul Klarreich


All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.


I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

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