Question

Parameterization

Answer 1

I cant figure out this one at all

Answer 2

I have the answer i think but like it doesnt show the process

Answer 3

ok i found the answer like the file i attached above

Answer 4

that is your answer, or /the/ answer?

Answer 5

no the answer lol

Answer 6

huh... I see\[0\le z\le48\]\[0\le\theta\le2\pi\]now the edge is a trig function\[A\sin(Bx+C)\]from the pic we can see that \(A=1\) and the period is \(T=6={2\pi\over|B|}\implies B=\frac\pi3\) so we have\[0\le r\le \sin(\frac\pi3z)\]now how to relate it to the rest of that stuff...

Answer 7

why there is a phase shift of 3 I cannot figure out

Answer 8

lol i def cant either figure that out

Answer 9

besides that though, it makes sense, right?
or did I lose you before that?

Answer 10

well umm i gotta reread it lol

Answer 11

sorry, that should be \[0\le r\le\cos(\frac\pi3z)\]in the last line above...

Answer 12

like y is it cos or sin like how wld u determine that?

Answer 13

look at z=0
the shape is at its widest there
\[\cos0=1\]so that is where it is the widest
if it were sin we would have the thinnest part of the shape at z=0, because \[\sin0=0\]

Answer 14

imagine if it were a straight cylinder with radius 3

Answer 15

okk i get that

Answer 16

the edge would be likebut it is wavy, so we add...