course mth 272 |XK܋ӂCm~Jцaݮ\wassignment #022 022. Applied Calculus II 07-27-2008
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09:33:44 Query problem 7.1.24 picture of sphere, diam from (-1,-2,1) to (0, 3, 3).
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RESPONSE --> ok, first you use the midpoint formula to find the center of the sphere... h, k, L, = ( (-1 + 0 / 2), (-2 + 3 / 2), (1 + 3 / 2) = ( -1/2, 1/2, 2) then, use the distance formula to find radius r = 'sqrt ( (-1 - 0)^2 + (-2 - 3)^2 + (1 - 3)^2 ) ='sqrt (1 + 25 + 30) ='sqrt(30) plug into standard equation form (x + 1/2)^2 + (y - 1/2)^2 + (z - 2)^2 = 30 confidence assessment: 2
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09:34:08 What is the standard form of the equation of the pictured sphere?
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RESPONSE --> previously answered confidence assessment: 2
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09:34:29 How did you find the center of the sphere?
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RESPONSE --> using the midpoint formula confidence assessment: 3
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09:34:41 How did you find the radius of the sphere?
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RESPONSE --> using the distance formula confidence assessment: 3
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09:54:47 Query problem 7.1.39 (was 7.1.38) yz-trace of x^2 + y^2 + z^2 - 6x - 10 y + 6 z + 30 = 0
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RESPONSE --> first you need to obtain the standard equation of the sphere by completing the square. which yields (x^2 -6x +9) + (y^2 - 10y +25) + (z^2 + 6z + 9) = -30 + 9 + 25 + 9 = (x-3)^2 + (y-5)^2 +(z+3)^2 = 13 center of the sphere is then (3,5,-3) radius = 'sqrt(13) now for that equation you want to let x=0 to find the yz-trace (0-3)^2 + (y-5)^2 +(z+3)^2 = 13 9 + (y-5)^2 +(z+3)^2 = 13 (y-5)^2 +(z+3)^2 = 4 (y-5)^2 +(z+3)^2 = 2^2 so, this is a circle of radius 2 confidence assessment: 2
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09:55:10 What is the equation of the yz-trace of the given sphere and what shape does this equation define in the y-z plane?
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RESPONSE --> just answered confidence assessment: 2
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09:55:37 What is the center and what is the radius of the circle?
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RESPONSE --> previously answered confidence assessment: 2
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09:55:49 What is the standard form of the equation of the circle?
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RESPONSE --> previoiusly answered confidence assessment: 2
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09:56:29 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I feel I have a good, solid understanding of the material in this section. confidence assessment: 3
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