Cartesian Equation: (x-2)^2 + y^2 = 1. This circle revolves about the y-axis, creating a torus. Consider this curve a pa...
Cartesian Equation: (x-2)^2 + y^2 = 1. This circle revolves about the y-axis, creating a torus. Consider this curve a parametric curve. Find the volume of the torus. (May use Simpson's Rule, n=10). Then find the area of the torus. (May use Simpson's Rule, n=10).
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Cartesian Equation: (x-2)^2 + y^2 = 1. This circle revolves about the y-axis, creating a torus. Consider this curve a pa...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use double integral to get the surface area of this torus. d) Let's say you have a circle on the xy-axis with the centre (a, a) and radius b as shown in the figure below, where a > b....
1. 2. 3. 4. (1 point) Eliminate the parametert to find a Cartesian equation for I=+2...
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(1 point) Eliminate the parametert to find a Cartesian equation for I=+2 y= 10 + 2t 2 = Ay? + By+C where A= and B = and C = (1 point) Consider the parametric curve: 2 = 8 sin 0, y = 8 cos 0, 0<<A The curve is (part of) a circle and the cartesian equation has the form 2? + y2 = R2 with R= The initial point has coordinates: 3 = !!! ,y=...
Consider the parametric equations below. x = 2 + 4t y = 1-t2
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
Theorem of Pappus: A torus is the object generated by revolving a circle about a line...
Theorem of Pappus: A torus is the object generated by revolving a circle about a line (the line should not pass through the circle but may be tangent to it). (a) Find the volume of the torus generated by revolving r?+ y =4 about the line r=5 . (b) A Different Approach: Let D be a closed bounded region in the plane with area A and centroid at 17.1). The volume generated by revolving D about the line L is...
number 9 9) Let C be the arc of the circle: x +y-9 from (3.0) to a) Find a parametric equation of a circle of radius r 3 that starts at (3,0) and has a counterclockwise orientation b) Find the int...
number 9
9) Let C be the arc of the circle: x +y-9 from (3.0) to a) Find a parametric equation of a circle of radius r 3 that starts at (3,0) and has a counterclockwise orientation b) Find the interval fort that sketches the arc from (3,0) to G. c) Use your limits from part(b) to calculate the area of the surface of revolution by revolving the curve C about the x-axis.
9) Let C be the arc of...
1. For the following equation, find the center, vertices, foci, transverse axis, and asymptotes, ...
1. For the following equation, find the center, vertices, foci, transverse axis, and asymptotes, and sketch the graph: 2. Consider the set of parametric equations (a) Graph in the following window: TMIN--3.74, TMAX- 3.74, TSTEP = 0.02, XMIN =-10, XMAX = 10, YMIN =-7, YMAX = 7, Sketch the graph. (b) At, find (x, y) and dy/dx. Write the equations of the lines tangent to and normal to the graph at (c) Find the length of the curve from to...
from Do Carmo. 5. Consider the torus of revolution generated by rotating the circle z2 r...
from Do Carmo.
5. Consider the torus of revolution generated by rotating the circle z2 r 2, y = 0, (x a)2 about the z axis (a > r> 0). The parallels generated by the points (a + r, 0), (a - r, 0), (a, r) are called the maximum parallel, the minimum parallel, and the upper parallel, respectively. Check which of these parallels is а. A geodesic. b. An asymptotic curve c. A line of curvature
5. Consider the...
4. The curve y = rs for 0 < | < 1 is rotated about the...
4. The curve y = rs for 0 < | < 1 is rotated about the z-axis to form a solid of revolution. (a) Find the volume of this solid of revolution 5 marks b) Calculate the surface area of this solid of revolution, leaving your answer in the form of a 5 marks definite integral. (c) Determine in the form of an integral the arc length of this curve from the points at which r0 and r 1, Use...
AMERICAN 1. Consider the curve represented by the parametric equations x=1-1 and y = 1° +1,...
AMERICAN 1. Consider the curve represented by the parametric equations x=1-1 and y = 1° +1, for -2 5732. a. (2) Sketch the parametric curve. b. (3) Eliminate the parameter to find a Cartesian representation of the curve.
Please help!! Thanks 1. Consider the function f(x) e a) Find the length of the curve given by the equation y - f(x), -1 3x<1. b) Let R be the region bounded by the graph of f(x) and the lines 1,1 a...
Please help!! Thanks
1. Consider the function f(x) e a) Find the length of the curve given by the equation y - f(x), -1 3x<1. b) Let R be the region bounded by the graph of f(x) and the lines 1,1 and y-0. Find the area of R. c) Find the coordinates of the center of mass of R. d) Consider the solid obtained by rotation of R about the r-axis. Find its volume and surface area.
1. Consider the...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use double integral to get the surface area of this torus. d) Let's say you have a circle on the xy-axis with the centre (a, a) and radius b as shown in the figure below, where a > b....
1.
2.
3.
4.
(1 point) Eliminate the parametert to find a Cartesian equation for I=+2 y= 10 + 2t 2 = Ay? + By+C where A= and B = and C = (1 point) Consider the parametric curve: 2 = 8 sin 0, y = 8 cos 0, 0<<A The curve is (part of) a circle and the cartesian equation has the form 2? + y2 = R2 with R= The initial point has coordinates: 3 = !!! ,y=...
Theorem of Pappus: A torus is the object generated by revolving a circle about a line (the line should not pass through the circle but may be tangent to it). (a) Find the volume of the torus generated by revolving r?+ y =4 about the line r=5 . (b) A Different Approach: Let D be a closed bounded region in the plane with area A and centroid at 17.1). The volume generated by revolving D about the line L is...
number 9
9) Let C be the arc of the circle: x +y-9 from (3.0) to a) Find a parametric equation of a circle of radius r 3 that starts at (3,0) and has a counterclockwise orientation b) Find the interval fort that sketches the arc from (3,0) to G. c) Use your limits from part(b) to calculate the area of the surface of revolution by revolving the curve C about the x-axis.
9) Let C be the arc of...
1. For the following equation, find the center, vertices, foci, transverse axis, and asymptotes, and sketch the graph: 2. Consider the set of parametric equations (a) Graph in the following window: TMIN--3.74, TMAX- 3.74, TSTEP = 0.02, XMIN =-10, XMAX = 10, YMIN =-7, YMAX = 7, Sketch the graph. (b) At, find (x, y) and dy/dx. Write the equations of the lines tangent to and normal to the graph at (c) Find the length of the curve from to...
from Do Carmo.
5. Consider the torus of revolution generated by rotating the circle z2 r 2, y = 0, (x a)2 about the z axis (a > r> 0). The parallels generated by the points (a + r, 0), (a - r, 0), (a, r) are called the maximum parallel, the minimum parallel, and the upper parallel, respectively. Check which of these parallels is а. A geodesic. b. An asymptotic curve c. A line of curvature
5. Consider the...
4. The curve y = rs for 0 < | < 1 is rotated about the z-axis to form a solid of revolution. (a) Find the volume of this solid of revolution 5 marks b) Calculate the surface area of this solid of revolution, leaving your answer in the form of a 5 marks definite integral. (c) Determine in the form of an integral the arc length of this curve from the points at which r0 and r 1, Use...
AMERICAN 1. Consider the curve represented by the parametric equations x=1-1 and y = 1° +1, for -2 5732. a. (2) Sketch the parametric curve. b. (3) Eliminate the parameter to find a Cartesian representation of the curve.
Please help!! Thanks
1. Consider the function f(x) e a) Find the length of the curve given by the equation y - f(x), -1 3x<1. b) Let R be the region bounded by the graph of f(x) and the lines 1,1 and y-0. Find the area of R. c) Find the coordinates of the center of mass of R. d) Consider the solid obtained by rotation of R about the r-axis. Find its volume and surface area.
1. Consider the...
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