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 2 years ago
can someone answer this quadric surface using completing the square ?thank you :)
x^2 + 4y^2  z^2  6x + 8y + 4z = 0
 2 years ago
can someone answer this quadric surface using completing the square ?thank you :) x^2 + 4y^2  z^2  6x + 8y + 4z = 0

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amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1get your like variables together and complete the squares .... which part is giving you pause?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1you can pull it apart into 3 quads if you like .... that might be less data to cull thru.

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0i don't know how to solve this..i'm sorry

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1do you know how to complete a square?

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0it means that it will have a two factors in each variables..all in all it has a 6 factors?

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0it is x^2  6x , 4y^2 + 8y and z^2 + 4z?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1lets go ahead and split this up into 3 different parts: x^2 + 4y^2  z^2  6x + 8y + 4z = 0 x^2 6x 4y^2 +8y z^2 + 4z now that its organized better, you just work each one in its own right .... complete the square for each part

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1the key is, do you know how to complete a square? :)

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0i'm sorry i forgot how to complete a square..

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1basically, you add and subtract a useful form of zero. square half the "x" term ..... for example: x^2 6x ; the x term is 6, 6/2 = 3, (3)^2 = 9. Lets add and subtract 9 x^2 6x + 9  9; and condense the square (x3)^2  9

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1z will be trick only in that you have to account for the 

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0x^2 6x ; the x term is 6, how it become 6/2?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1we are trying to make a complete square, a perfect square. numbers of the form (a+b)^2 are perfect squares: (2+5)^2 = 49, (3+1)^2 = 16, ... we want to condense this thing back into some (a + b)^2 form, thats all. In order to do that we have to modify its form, but not its value. Since adding zero changes nothing ... its useful to us. BUT what form of zero? lets expand (a+b)^2 = a^2 +2ab + b^2 ; let a=x (x+b)^2 = x^2 +2bx + b^2 notice that the b^2 is missing above. and we know that the "x" term in the middle is equal to 2b. 2b = 6 b = 6/2 = 3 b^2 = 9

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1so, adding and subtract 9; 99 = 0 right? will allow us to "complete" the square and alter its form ... not its value

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.14y^2 +8y 2b = 8 b = 8/2 = 4 b^2 = 16, +1616 = 0 4y^2 +8y + (1616) therefore 4y^2 +8y = (2y +4)^2  16

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0oh..i see. thanks i will solve this..

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0btw do you know about contour plotting?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1i would need a little more information to see if i have contour plotting rolling around in my head someplace :)

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0do you know what kind of contour plot is this if f(x,y) = \[\sqrt{x^2 + y^2}\] ?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1so the height, or z, is dependent on x and y inputs if we hold one input constant, we can generate a cross section plot and such, are some ideas ive got z = sqrt(x^2+y^2) z^2 = x^2 + y^2 is a circle, and so im gonna extrapolate that this is a sphere or hemisphere as a guess

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1http://web.monroecc.edu/manila/webfiles/calcnsf/javacode/calcplot3d.htm might be useful :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1well it use to work fine, i guess they changed some stuff about

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=sqrt%28x%5E2%2By%5E2%29 hmmm, its conic not spherical. it comes to a point at the origin and makes bigger circles as z gets bigger and bigger

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0our topic to this is about contour plotting..

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1361892976311:dw

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1im not up to date on what contour plotting is, this is mostly from an old, decripid memory :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1for your private message z = k z = x^2 + y for what values of x^2 + y does k = the stated set of values

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1x^2 + y = 2 when y=x^2 2dw:1361893200001:dw

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1in other words, the contour follows its reflection in the xy plane if that makes sense

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1for any value of k, the reflected graph in the xy plane changes its y intercept so it will float up and down the y axis as needed

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0what kind of contour plot is that?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1it looks like a repeition of a parabola to me, so its a type of cylindar right?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1361894575970:dw

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0i don't know..but i heard that there is a graph named paraboloid, elliptical paraboloid etc..

jedai17
 2 years ago
Best ResponseYou've already chosen the best response.0but i think it is elliptical paraboliod because you said that it is cylindar..
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