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course MTH 272 12/14 about 3 pm 024..............................................
Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:OK ********************************************* Question: `qWhat is the name of this quadric surface, and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 0=x^2/(1^2) + y^2/(sqrt(2))^2 – z^2/(1^2) This is an elliptic cone because in this form it equals zero and there is one negative variable. When z=1 you get 1=x^2/(1^2) + y^2/(sqrt(2))^2 which is an ellipse. When y and x are 0, you get the following linear functions z=+/-x and y=+/-z*sqrt(2) respectively. This would accurately depict an elliptic cone. confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a f z = c, a constant, then x^2 + y^2/2 = c^2, or x^2 / c^2 + y^2 / (`sqrt(2) * c)^2 = 1. This gives you ellipse with major axis c and minor axis `sqrt(2) * c. Thus for any plane parallel to the x-y plane and lying at distance c from the x-y plane, the trace of the surface is an ellipse. In the x-z plane the trace is x^2 - z^2 = 0, or x^2 = z^2, or x = +- z. Thus the trace in the x-z plane is two straight lines. In the y-z plane the trace is y^2 - z^2/2 = 0, or y^2 = z^2/2, or y = +- z * `sqrt(2) / 2. Thus the trace in the y-z plane is two straight lines. The x-z and y-z traces show you that the ellipses in the 'horizontal' planes change linearly with their distance from the x-y plane. This is the way cones grow, with straight lines running up and down from the apex. Thus the surface is an elliptical cone. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:OK ********************************************* Question: `qGive the equation of the xz trace of this surface and describe its shape, including a justification for your answer. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: For the xz trace, y=0 so: Z^2=x^2 so z=+/-x which is two linear functions showing the outer edges of the cones crossing at the origin. confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a The xz trace consists of the y = 0 points, which for z^2 = x^2 + y^2/2 is z^2 = x^2 + 0^2/2 or just z^2 = x^2. The graph of z^2 = x^2 consists of the two lines z = x and z = -x in the yz plane. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:OK ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. "
Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ________________________________________ `gr91 #$&*#$&* course MTH 272 12/14 about 3 pm 024.
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:OK ********************************************* Question: `qWhat is the name of this quadric surface, and why? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 0=x^2/(1^2) + y^2/(sqrt(2))^2 - z^2/(1^2) This is an elliptic cone because in this form it equals zero and there is one negative variable. When z=1 you get 1=x^2/(1^2) + y^2/(sqrt(2))^2 which is an ellipse. When y and x are 0, you get the following linear functions z=+/-x and y=+/-z*sqrt(2) respectively. This would accurately depict an elliptic cone. confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a f z = c, a constant, then x^2 + y^2/2 = c^2, or x^2 / c^2 + y^2 / (`sqrt(2) * c)^2 = 1. This gives you ellipse with major axis c and minor axis `sqrt(2) * c. Thus for any plane parallel to the x-y plane and lying at distance c from the x-y plane, the trace of the surface is an ellipse. In the x-z plane the trace is x^2 - z^2 = 0, or x^2 = z^2, or x = +- z. Thus the trace in the x-z plane is two straight lines. In the y-z plane the trace is y^2 - z^2/2 = 0, or y^2 = z^2/2, or y = +- z * `sqrt(2) / 2. Thus the trace in the y-z plane is two straight lines. The x-z and y-z traces show you that the ellipses in the 'horizontal' planes change linearly with their distance from the x-y plane. This is the way cones grow, with straight lines running up and down from the apex. Thus the surface is an elliptical cone. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:OK ********************************************* Question: `qGive the equation of the xz trace of this surface and describe its shape, including a justification for your answer. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: For the xz trace, y=0 so: Z^2=x^2 so z=+/-x which is two linear functions showing the outer edges of the cones crossing at the origin. confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a The xz trace consists of the y = 0 points, which for z^2 = x^2 + y^2/2 is z^2 = x^2 + 0^2/2 or just z^2 = x^2. The graph of z^2 = x^2 consists of the two lines z = x and z = -x in the yz plane. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:OK ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!#*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!#*&!#*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!#*&!#*&!#*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!#*&!#*&!#*&!#*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!#*&!#*&!#*&!#*&!#*&! ********************************************* Question: `qDescribe in detail the z = 2 trace of this surface. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2^2=x^2+(y^2)/2 1=(x^2)/(2^2) + (y^2)/(2*sqrt(2))^2 This is the standard form for an ellipse with the major axis y and minor axis x. points on the x axis are +/-2 and points on the y axis are +/-(2*sqrt(2)) confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4. This is an ellipse. If we divide both sides by 4 we can get the standard form: x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1. This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!