Question

how do I match slices of level surface

Answer 1

you are going to have to be less vague ....

Answer 2

\[2x ^{2}+5y ^{2}+z ^{2}=4\]
What is the graph when y=.75, z=1.5, y=0, and z=0

Answer 3

the function appears to be an elliptiod to start with; and we are allowing x to be any value

Answer 4

the plane slice are ellipses too arent they

Answer 5

They are, I am looking for exactly what each of them looks like

Answer 6

the intersects are when we let 2 variable be zero and we solve for the remaining;

2x^2=4 ; x= +- sqrt(2)
5y^2=4 ; y = +- sqrt(4/5)
z^2=4 ; z = +- sqrt(4)

at y=0; z=0, we have an ellipse in the xy plane

Answer 7

the intercepts give us the dimensions we need to determine the elliptic equation\[(\frac{x^2}{a^2})^2+(\frac{y^2}{b^2})^2=1\]

Answer 8

"at y=0; z=0, we have an ellipse in the xy plane"

Now I'm confused...

Answer 9

lol, well, I could be reading it askew ;)

since the sqrt(10/5) is greater than the sqrt(4/5); this thing widen along the x axis; and half the widths is the values of a and b; and ignoreing the typo above ....

\[\frac{x^2}{(\sqrt{2}/2)^2}+\frac{y^2}{(\sqrt{4/5}/2)^2}=1\]
\[\frac{x^2}{1/2}+\frac{y^2}{4/10}=1\]
\[2x^2+\frac 52 y^2=1\]
\[4x^2+5 y^2=2\]

Answer 10

I think letting z and y both = 0 would be bad...you'd get a line?

Answer 11

im kinda confused about what "y=.75, z=1.5, y=0, and z=0" might mean tho

Answer 12

It's asking about level curves on certain planes like z=1.5 and so on...
just plug in the value given and write it in standard form for an ellipse in the remaining variables...

Answer 13

so like on the plane z=1.5 you have an 'xy ellipse' to find the specific one, plug in z=1.5 and rearrange if necessary...

Answer 14

hmm, that does sound more cogent than the voices in my head :) thnx

Answer 15

:)

love you, don't b& me.

Answer 16

kiki .... is that making better sense now?

Answer 17

I think so