#Multivariable Calc Help Needed Asap
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dire stirrup
I mean... you know what rho and cos(phi) are in terms of x,y and z
smoky glacier
I mean... you know what rho and cos(phi) are in terms of x,y and z
wdym?
dire stirrup
I mean exactly what I wrote
rho is a function of x,y and z
phi and, subsequently, cos(phi) is a function of x,y and z
smoky glacier
oh rectilinear simply means of the form (x, y z) ?
dire stirrup
yes, like the bold text says
smoky glacier
How can an equation be converted to coordinates?
dire stirrup
x=ρsinφcosθ
y=ρsinφsinθ
z=ρcosφ
but anyway, you just solve for rho and cos(phi) from those equations
smoky glacier
but anyway, you just solve for rho and cos(phi) from those equations
is rho the p?
dire stirrup
yes
smoky glacier
aren't we given p?
dire stirrup
rho is the rho
dire stirrup
...
smoky glacier
I'm confused sorry
dire stirrup
you want to write rho=200cos(phi) as some equation in x y and z
that's known from reading the question
so... you want what rho is in terms of x, y and z
dire stirrup
rho is a function of x,y and z
said here
and what cos(phi) is in terms of x, y and z
dire stirrup
phi and, subsequently, cos(phi) is a function of x,y and z
said here.
dire stirrup
x=ρsinφcosθ
y=ρsinφsinθ
z=ρcosφ
write rho as a function of x, y and z.
then
write cos(phi) as a function of x, y and z
then
replace rho and cos(phi) in rho=200cos(phi) with the functions you just found
then idk, put a bow on it
smoky glacier
write rho as a function of x, y and z.
is that not just p = sqrt(x^2 + y^2 + z^2) ?
dire stirrup
yep, it is
smoky glacier
ok
smoky glacier
write cos(phi) as a function of x, y and z
is that not just cos(phi) = z /( sqrt(x^2 + y^2 + z^2) )
dire stirrup
yep
smoky glacier
replace rho and cos(phi) in rho=200cos(phi) with the functions you just found
how does this give me a coordinate of the form (x, y, z)?
dire stirrup
...
plug those into rho=200cos(phi)
and, wow shock, it'll magically be in terms of x,y and z
who could've seen that coming
smoky glacier
umm
well plugging those into rho=200cos(phi)
gives this:
sqrt(x^2 + y^2 + z^2) = 200(z /( sqrt(x^2 + y^2 + z^2) ))
dire stirrup
there you go
you write rho=200cos(phi) in terms of x, y and z
give yourself a pat on the back
smoky glacier
isn't the answer supposed to be of the form (x, y, z) tho?
smoky glacier
yeah but they want me to have a final answer of the form (x, y, z) like exaclty that
smoky glacier
oh ok ok
but just out of curiousity
if i were to solve for each variable in sqrt(x^2 + y^2 + z^2) = 200(z /( sqrt(x^2 + y^2 + z^2) ))
I would always get
a negative answer and a positive answer
so which one would we choose in that case?
dire stirrup
whichever one makes sense
you have the level set of some function of (x,y,z,w)
$w=\sqrt{x^2+y^2+z^2}-\frac{200z}{\sqrt{x^2+y^2+z^2}}$ is a function from punctured 3d space to the real line
craggy edgeBOT
Omegabet_
dire stirrup
rho=200cos(phi) is the w=0 level set
smoky glacier
sqrt(x^2 + y^2 + z^2) = 200(z /( sqrt(x^2 + y^2 + z^2) ))
could I even rewrite this as x^2 + y^2 + z^2 = 200z ?
smoky glacier
+close