Consider points A = (1,0, -1), B = (4, -4, -2) and O = (0,0,0). Determine...
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Consider points A = (1,0, -1), B = (4, -4, -2) and O = (0,0,0).
Determine...
Consider the region bounded by y = (1 - 2)2 and y = 4 - r....
Consider the region bounded by y = (1 - 2)2 and y = 4 - r. For each of the following, set up (but do not compute) integrals that determine the volume of the solid obtained by rotating the region around the specified axis: (a) The y-axis. (b) The line r = 5. (c) The line y = -1.
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.)...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
consider the region bounded by y= (x-2)^2 and y = 4-x.. set up integral that determines...
consider the region bounded by y= (x-2)^2 and y = 4-x.. set up integral that determines the volume of the solid obtained by rotating the region around the specified axis a) the y-axis b) the line x=5
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined...
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
Consider the points P(2, 1, 1) and Q(3, 0, 0). (a) Write the equation of the...
Consider the points P(2, 1, 1) and Q(3, 0, 0). (a) Write the equation of the line that passes through the points P and Q. Express your answer with both parametric equations and symmetric equations. (b) Write the equation of the plane (in terms of x, y, z) that passes through the point P and is perpendicular to the line from part (a).
10. Express the following in vector form: a. Line IcR that passes through the points A-(-1,-1,0)...
10. Express the following in vector form: a. Line IcR that passes through the points A-(-1,-1,0) and B = (2, 3, 5) b. Plane P Rwhich passes through the appoints A = (1, 1,-1,-1), B = (1,-1, 1,-1) and whose coordinates satisfy the equation x + y + 2z - W=3.
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a pot...
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
problem 3 pls Problem 3. Consider the curve {> 1, y = 1/x}. Compute the length...
problem 3 pls
Problem 3. Consider the curve {> 1, y = 1/x}. Compute the length of the part of this curve lying to the left of the line x = a for any a > 1. Show that the length of the whole curve is thus infinite. Compute the area of the surface obtained by rotating this curve about about the x axis by computing the corresponding improper integral; it should be infinite. What is the area of the...
3 Jiguull A line segment with the end points: A[1, 1, 0] and B[6, 2, O]...
3 Jiguull A line segment with the end points: A[1, 1, 0] and B[6, 2, O] lying in the xy-plane. Rotating the line about the x-axis yields a surface. Determine the point on this ?surface at t = 1 and = 30° [1.5 ,1.8 ,1].a O [3,3.5 ,1.2). O (4 3,2].CO [1 ,1.732,6].d O
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point...
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
Consider the region bounded by y = (1 - 2)2 and y = 4 - r. For each of the following, set up (but do not compute) integrals that determine the volume of the solid obtained by rotating the region around the specified axis: (a) The y-axis. (b) The line r = 5. (c) The line y = -1.
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
Assignment 4: (Arc Length and Surface Area - 7.3) 1. Consider the plane curve C defined by y=e" between y-1 and y-e. (a.) Set up, but do NOT evaluate, an integral with respect to y for the arc length of C. (b.) Set up, but do NOT evaluate, an integral with respect to x for the arc length of C. Set up, but do NOT evaluate, an integral for the area of the surface obtained by rotating C about the...
10. Express the following in vector form: a. Line IcR that passes through the points A-(-1,-1,0) and B = (2, 3, 5) b. Plane P Rwhich passes through the appoints A = (1, 1,-1,-1), B = (1,-1, 1,-1) and whose coordinates satisfy the equation x + y + 2z - W=3.
(1) Integrate f(x, y,z)+Vy - z2 over the straight line segment path from (0,0,0) to (1,1,1) (2) Consider the field F (2xyz+2,x2z, x2y), (a) (b) (c) Show that the field is conservative. Find a potential function for the field. Find the work the field does on an object that follows the path consisting of the line segment from (0,0,0) to (1,2,2), followed by the line segment from (1,2,2) to (2,4,3) Find the work done by the field ß-(x, 3y,-5z) along...
problem 3 pls
Problem 3. Consider the curve {> 1, y = 1/x}. Compute the length of the part of this curve lying to the left of the line x = a for any a > 1. Show that the length of the whole curve is thus infinite. Compute the area of the surface obtained by rotating this curve about about the x axis by computing the corresponding improper integral; it should be infinite. What is the area of the...
3 Jiguull A line segment with the end points: A[1, 1, 0] and B[6, 2, O] lying in the xy-plane. Rotating the line about the x-axis yields a surface. Determine the point on this ?surface at t = 1 and = 30° [1.5 ,1.8 ,1].a O [3,3.5 ,1.2). O (4 3,2].CO [1 ,1.732,6].d O
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
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