#$&* course 272 11/30 7:45pm If your solution to a stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `a The midpoint between (-1, -2, 1) and (0, 3, 3) is (-1/2, 1/2, 2). Thus the sphere will have the form (x - (-1/2) )^2 + (y - 1/2)^2 + (z-2)^2 = r^2. r is half the diameter, which is half of `sqrt( (0 - -1)^2 + (3 - -2)^2 + (3 - 1)^2 ) = `sqrt(1+25+4) = `sqrt(30). The radius is therefore `sqrt(30) / 2 and r^2 = 30 / 4 = 15/2. The equation is therefore (x - (-1/2) )^2 + (y - 1/2)^2 + (z-2)^2 = 15/2. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `qQuery problem 7.1.39 (was 7.1.38) yz-trace of x^2 + y^2 + z^2 - 6x - 10 y + 6 z + 30 = 0 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: x^2 + y^2 + z^2 - 6x - 10 y + 6 z + 30 = 0 0^2 + y^2 + z^2 - 6(0) - 10 y + 6(0) + 30 = 0 y^2 + z^2 -10y+6z+30 = 0 complete the squares: (y^2 - 10y +25-25 )+(z^2 + 6z+9-9) + 30 = 0 (y-5)^2 + (z+3)^2 = 4 (y-5)^2 + (z+3)^2 = 2^2 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a The yz trace is characterized by x = 0. The equation of the y-z trace is therefore y^2 - 10 y + z^2 + 6z + 30 = 0. This is the equation of a circle in the y-z plane. Completing the square we get (y^2 - 10 y + 25 - 25) + (z^2 + 6 z + 9 - 9) + 30 = 0 or (y-5)^2 + (z+3)^2 = 4 or (y-5)^2 + (z+3)^2 = 2^2. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `qWhat is the equation of the yz-trace of the given sphere and what shape does this equation define in the y-z plane? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Equation of yz trace is: y^2-10y+z^2+6z+30=0 The shape this equations defines is a circle. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a `a The yz trace is characterized by x = 0. The equation of the y-z trace is therefore y^2 - 10 y + z^2 + 6z + 30 = 0. This is the equation of a circle in the y-z plane. Completing the square we get (y^2 - 10 y + 25 - 25) + (z^2 + 6 z + 9 - 9) + 30 = 0 or (y-5)^2 + (z+3)^2 = 4 or (y-5)^2 + (z+3)^2 = 2^2. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `qWhat is the center and what is the radius of the circle? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I completed the square earlier so know: (y-5)^2 + (z+3)^2 = 2^2 therefore the center is (0, 5 , -3) and radius is 2 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a `a The yz trace is characterized by x = 0. The equation of the y-z trace is therefore y^2 - 10 y + z^2 + 6z + 30 = 0. This is the equation of a circle in the y-z plane. Completing the square we get (y^2 - 10 y + 25 - 25) + (z^2 + 6 z + 9 - 9) + 30 = 0 or (y-5)^2 + (z+3)^2 = 4 or (y-5)^2 + (z+3)^2 = 2^2. We thus have a circle of radius 2, in the y-z plane, centered at (0, 5, -3). &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `qQuery Add comments on any surprises or insights you experienced as a result of this assignment. I enjoy tying concepts together, so far the three dimensional coordinate system is making sense. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: