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course Mth 277
2/8 2
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:
Elliptic paraboloid that has a center of mass that runs along y-axis for pos y values. Tip of paraboloid begins at (0, 0, 0) pt
confidence rating #$&*:
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Given Solution:
@& If x = constant then the equation is
4 y = z^2 / 4 - c
or
y = z^2 / 16 - c
which is the equation of a parabola in a y vs. z plane having its axis of symmetry in the y direction.
If z = constant then a similar argument shows that the equation is a parabola in a y vs. x plane, axis of symmetry parallel to the y axis.
If y is constant then the equation is of the form
z^2 / 4 - x^2 / 9 = c,
which is a hyperbola.
c = 4 y, so c is positive or negative if y is, respectively, positive or negative.
The hyperbola opens in the z direction if c is positive, and in the x direction of c is negative.
This equation therefore yields a hyperbolic paraboloid.
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Self-critique (if necessary):
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Question: Identify the quadric surface given by the equation 8z^2 = (1/8) + (x^2)/9 + (y^2). Describe the traces in planes parallel to the coordinate planes (and sketch the graph).
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Your solution:
Hyperboloid of one sheet
xy-plane is ellipse
xz and yz-planes, traces are hyperbolas
confidence rating #$&*:
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Given Solution:
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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:
confidence rating #$&*:
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Given Solution:
@& If z = constant then we have a hyperbola in x and y, opening in the x direction. The hyperbola is centered at (x, y) point (3, 1) and its axes of symmetry are the lines y = +- sqrt(2) x. The constant value of z determines the vertices of the hyperbola, which move further from the center as (z - 2) increases.
If y = constant then we have a hyperbola in x and z, opening in the x direction. Its detailed behavior is analogous to that of the y vs. x hyperbola described above, with its center at the (x, z) point (3, 2).
if x = constant then, provided (x-3)^2 / 2 > 4, we have an ellipse centered at the (y, z) coordinate (1, 2). The ellipse gets larger as (x - 3) increases. If (x-3)^2 / 2 < 4, there are no solutions.
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Self-critique (if necessary):
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Question: Describe the curve intersection of the two quadric surfaces 4z = (y^2)/9 - (x^2)/16 and (x^2)/4 + 2(y^2) - 4(z^2)/3 = 1.
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Your solution:
Elliptic Cone
trace in xy plane is a point
planes parallel to the xy-plane it is an ellipse
confidence rating #$&*:
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Given Solution:
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Self-critique (if necessary):
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