Question

Two rate of change problems: Would really appreciate step by step help as I am nowhere with these kinds of problems

Answer 1

@TuringTest @Hero @Zarkon @Algebraic! @mahmit2012 @cwrw238

Answer 2

how fast is "s" changeing?

can you write up an equation the we can use to relate s with how fast the rope is moving??

Answer 3

something along the lines of a^2 + b^2 = c^2 perhaps?

Answer 4

Okay, so if H is the hypotenuse then,\[\large 8^{2} + s^{2} = H^{2}\]

Answer 5

then,\[\Large s' = \frac{1}{2}(H^{2}-64)^{-\frac{1}{2}}2H\]

Answer 6

but i don't know where to go?

Answer 7

@amistre64

Answer 8

Okay so I got an answer of 5 which is one of the answers there so I'm gonna go ahead and assume it's right. Anyone willing to help with the second question?

Answer 9

dQ/dt = 2p*dp/dt + 4*dp/dt

Answer 10

remember p is thousands of people...

Answer 11

Oh, got it, 156

Answer 12

btw, for the 1st problem, you should be taking the derivative with respect to time

(in other words you should have a dh/dt in there...)

one way:
start with
8^2+s^2= h^2
\[ 2s\frac{ds}{dt}= 2h \frac{dh}{dt} \]
evaluate when s= 6, and dh/dt = 3 meters/min
h= sqrt(8^2+6^2) = sqrt(100)= 10
plug in h=10, dh/dt = 3 m/min, s=6 into
\[ s\frac{ds}{dt}= h \frac{dh}{dt} \]
\[ 6 \frac{ds}{dt}= 10\cdot 3 m/min \]
and
\[ \frac{ds}{dt}= 30/6 = 5 m/min\]

Answer 13

Thanks for the help @Algebraic! @amistre64 @phi