course MTH 272 05/08,1830 assignment #022022.
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21:42:45 Query problem 7.1.24 picture of sphere, diam from (-1,-2,1) to (0, 3, 3).
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RESPONSE --> Diameter =sqrt ( (0 - -1)^2 + (3 - -2)^2 + (3 - 1)^2) Diameter=sqrt(30) Diameter=Radius * 2 Radius= (sqrt(30))/2 MP of diameter equals center of sphere MP=( (-1 + 0)/2 , (-2 + 3)/2 , (1 + 3)/2 ) MP=( (-1/2), (1/2), 2) Equation of sphere: (x - (-1/2))^2 + (y - (1/2))^2 + (z - 2)^2= (30/4) confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:43:31 What is the standard form of the equation of the pictured sphere?
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RESPONSE --> (x - (-1/2))^2 + (y - (1/2))^2 + (z - 2)^2 = (30/4) confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:44:17 How did you find the center of the sphere?
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RESPONSE --> Center of the sphere was found by finding the midpoint of the diameter. Accompanying work found with first part of question. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:44:52 How did you find the radius of the sphere?
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RESPONSE --> Radius of the sphere was found by finding the distance of the diameter and then dividing this value by 2. confidence rating #$&* 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:53:37 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 --> x^2 + y^2 + z^2 - 6x - 10 y + 6 z + 30 = 0 (x^2 -6x + 9) + (y^2 -10y +25) + (z^2 + 6z + 9)= -30 (x-3)^2 + (y-5)^2 + (z +3)^2= -30+9+25+9 (x-3)^2 + (y-5)^2 + (z +3)^2=13 yz-trace (x=0) (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 confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:54:56 What is the equation of the yz-trace of the given sphere and what shape does this equation define in the y-z plane?
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RESPONSE --> Equation of the yz-trace: (y-5)^2 + (z +3)^2 =2^2 This defines a circular shape on the yz plane with a radius of 2. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:55:52 What is the center and what is the radius of the circle?
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RESPONSE --> Center (0,5,-3) Radius =2 confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:58:36 What is the standard form of the equation of the circle?
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RESPONSE --> (y - 5)^2 + (z - -3)^2=2^2 Standard form of equation of circle using y and z instead of the usual x and y since this is a yz-trace. confidence rating #$&* 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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