Assignment 22

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11:29:40

Query problem 7.1.24 picture of sphere, diam from (-1,-2,1) to (0, 3, 3).

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RESPONSE -->

confidence assessment:

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11:29:49

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

confidence assessment: 3

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11:30:02

How did you find the center of the sphere?

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RESPONSE -->

(0-1)/2), (3-2)/2), (3+1)/2 = (-1/2, 1/2, 2)

confidence assessment: 3

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11:30:12

How did you find the radius of the sphere?

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RESPONSE -->

r = sqrt[(0+1)^2 + (3+2)^2 + (3-1)^2 = sqrt(30)

confidence assessment: 3

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11:30:16

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 -->

confidence assessment:

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11:30:33

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 -->

x^2 + y^2 + z^2 - 6x - 10y + 6z + 30 = 0

(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

(x-3)^2 + (y-5)^2 + (0+3)^2 = 13

(x-3)^2 + (y-5)^2 = 4

confidence assessment: 3

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11:30:42

What is the center and what is the radius of the circle?

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RESPONSE -->

center = (3,5,-3)

radius = 4

confidence assessment: 3

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11:30:52

What is the standard form of the equation of the circle?

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RESPONSE -->

(x-3)^2 + (y-5)^2 = 4

confidence assessment: 3

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11:30:55

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

confidence assessment:

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Your work looks very good. Let me know if you have any questions. &#