Query Assignment 97

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course Mth 277

9/20 9

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it.

This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

At the end of this document, after the qa problems (which provide you with questions and solutions), there is a series of Questions, Problems and Exercises.

query_09_7

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Question: Identify the quadric surface 4y = (z^2)/4 - (x^2)/9.

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Your solution:

for the xy plane, sub z=0 and get

y= -x^2/36

for the xz plane, sub y=0 and get

x=(3/2)z

for yz plane, sub x = 0 and get

z = 4y

we can make the equation 0 = z^2 / 4^2 - x^2 / 6^2 - y

there, all the planes are given, if we were to substitute 1,2,3 etc for each value of x,y, and z we would see either intersections of planes or empty spaces. I'm not sure how far you want me to go with this problem

I think this is a hyperboloid of one sheet

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Given Solution:

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Self-critique (if necessary):

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Question: Identify the quadric surface given by the equation 8z^2 = (1/8) + (x^2)/9 + (y^2). Describe the traces in planes parallel to the coordinate planes (and sketch the graph).

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Your solution:

the general plane x = c, are just vertical planes parallel to the y-z plane. or the x-z plane.

setting the function equal to 1 we get 1= -8x^2/9 - 8y^2 + 64z^2. all of the planes are ^2 which would mean this is an elipse.

with the plane yz, x is parralell. so for the yz plane, we sub x=0 in and we have 1= -8y^2 +64z^2.

hyperboloid of two sheets

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Question: Describe the quadric surface given by the equation ((x-3)^2)/2 - ((y-1)^2)/4 - (z^2-2)/9 = 4.

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Your solution:

I'm hoping you meant to put the square in the (z^2-2)/9 on the outside of the parenthasis, i'm going to work the problem like that.

if so we can manipulate the equation to say ((y-1)^2)/4^2 + (z^2-2)/6^2 - ((x-3)^2)/sqrt(8) ^2 = -1 which is a hyperboid of two sheets

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

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Question: Describe the curve intersection of the two quadric surfaces 4z = (y^2)/9 - (x^2)/16 and (x^2)/4 + 2(y^2) - 4(z^2)/3 = 1.

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Your solution:

first solution can be written as z = y^2/6^2 - x^2/8^2 which is a hyperbolic paraboloid or ""saddle surface""

second solution is already written as a hyperboloid of one sheet.

the positive z x and y direction of the second equation will ""fill in"" the blank emptiness of the saddle surface..making the positive z direction with both + and - y and x direction filled in.

however the -z and both +- x and y direction will be doubly filled in because they will overlap throughout eachother indefinetely.

confidence rating #$&*:

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Given Solution:

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Self-critique (if necessary):

???????????? the only problem i have is graphing these equations. I will come to you later for some tips and ways to get started.

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Self-critique rating:

@& Hopefully we covered that in class today, at least as far as getting you a start.

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&#Good responses. Let me know if you have questions. &#