rates of change help (1 Viewer)

kr73114 · Apr 20, 2011

can someone please help me with some rates of change questions from fitzpatzrick
25a), pg. 100
qu. 9, 18, 24, 26
thanks

Drongoski · Apr 20, 2011

Q26

vol of cone (noting that in this question: r = h)

$V(h) = \frac {\pi r^2 h}{3} = \frac{\pi h^3}{3}$

V is also 0.1 x time ==> when t = 3, V = 0.1 x 3 = 0.3

corresp value of h is given by

$0.3 = \frac {\pi h^3}{3} \implies h^2 = (\frac {0.9}{\pi})^{\frac {2}{3}}$

$\frac {dV}{dt} = \frac {dV}{dh} \times \frac {dh}{dt}$

$\therefore 0.1 = \pi h^2 \times \frac {dh}{dt} = (\pi (\frac {0.9}{\pi})^{\frac {2}{3}}) \times \frac {dh}{dt}$

You'll end up with:

$\frac {dh}{dt} = 0.0732467 . . .$

hscishard · Apr 21, 2011

18 can be just a harder 2unit question
distance = speed x time
Let time be t and distance be c
Use the cosine rule and then find the rate of which c is changing

hscishard · Apr 21, 2011

for 9
find relationship between h and r
find tan(x/2) and then do it. I used the double angle formula and then realised I could've done I via calc.
Then use dV/dt=dV/dh x dh/dt

I can't picture 24 in my head. ???

kr73114 · Apr 21, 2011

Drongoski said:
Q26

vol of cone (noting that in this question: r = h)

. . .[/tex]

why is r=h?

rates of change help (1 Viewer)

kr73114

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