Question

Newton method:
Volume of tank -> V = (4/3)(pi)(r^3) + (pi)(r^2)(h)
V = 50, h = 4, so
50 = 4/3(pi)(r^3) + 4(pi)r^2
or
50/(pi) = 4/3(r^3) + 4(r^2)

Take r1 = 1.5 as initial guess, find f(r) and f'(r)

Answer 1

@Zarkon can u help?

Answer 2

okay i'll try myself.

Answer 3

The f(r), is that just the equation in standard form, or should I also sub in the value 1.5 to get an actual number?

Answer 4

no not yet:
x_(n+1) = x_n - f(x_n)/f'(x_n)

Answer 5

f(r) = (4/3)(pi)(1.5^3) + (pi)(1.5^2)(4)

Answer 6

f'(r) = [ (4/3)(pi)(r^3) + 4(pi)(r^2) ] ' = 4pi*r^2 + 8pi*r

Answer 7

f ' (r) = 4pi*(1.5)^2 + 8pi*(1.5)

Answer 8

So am I just writing out the equation for f(r) and subbing in 1.5, and then for f'(r) I find the derivative of the first equation and THEN sub in 1.5?

Answer 9

yes

Answer 10

but first sub in h for both

Answer 11

do u need more help?

Answer 12

Umm, give me a moment to look it over I got distracted by something.

Answer 13

I don't understand this:
x_(n+1) = x_n - f(x_n)/f'(x_n)
Where is the n variable coming from?

Answer 14

it's x sub n

Answer 15

x sub n is the first guess which is your r
x sub n+1 is the next guess.