dh and simplify it. Use this equation to explain why the drain rate h' (t) cannot be a dt (c) Solve the related rate equation from (b) for constant function unless the filter is completely clogged (that is, unless k = 0.) [Hint: You may use h" (t) to be able to answer this. There h (t)] and about are other ways, too.] Suppose the water is completely drained at a time t = to . Talk about the limits lim,, lim,¬to [h' (t)]. To answer these, make an assumption that h (t) is a monotonically decreasing continuous function (i.e. water doesn't climb back up!), and that h (to) = 0. Verify your findings analytically by using the related rate equation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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First image is the word problem context. Please answer PART C from second image. Please show all steps and explain with clear handwriting. No cursive if possible. 

dh
and simplify it. Use this equation to explain why the drain rate h' (t) cannot be a
dt
(c) Solve the related rate equation from (b) for
constant function unless the filter is completely clogged (that is, unless k = 0.) [Hint: You may use h" (t) to be able to answer this. There
h (t)] and about
are other ways, too.] Suppose the water is completely drained at a time t = to . Talk about the limits lim,,
lim,¬to
[h' (t)]. To answer these, make an assumption that h (t) is a monotonically decreasing continuous function (i.e. water doesn't
climb back up!), and that h (to) = 0. Verify your findings analytically by using the related rate equation.
Transcribed Image Text:dh and simplify it. Use this equation to explain why the drain rate h' (t) cannot be a dt (c) Solve the related rate equation from (b) for constant function unless the filter is completely clogged (that is, unless k = 0.) [Hint: You may use h" (t) to be able to answer this. There h (t)] and about are other ways, too.] Suppose the water is completely drained at a time t = to . Talk about the limits lim,, lim,¬to [h' (t)]. To answer these, make an assumption that h (t) is a monotonically decreasing continuous function (i.e. water doesn't climb back up!), and that h (to) = 0. Verify your findings analytically by using the related rate equation.
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