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5s , y s-t to compute the (1 pt) In this problem we use the change...
14) Consider the parallelepiped D determined by the vectors (2,-1,2), (1,3, 1), and (2,-1,1). Let...
14) Consider the parallelepiped D determined by the vectors (2,-1,2), (1,3, 1), and (2,-1,1). Let T(z, y, 2)a-ytz. Consider the integral I - JSsD TdV. Using the Change of Variables Theorem, write I as an integral of the form T(r(r, s,t), v(r, s, t), z(r, s,t))lJ(r,s, t) dr ds dt for a suitable linear change of variables (r, s, t) (, y,z). The Jacobian J(r,s,t) you get here should be a constant function.
14) Consider the parallelepiped D determined by...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F(x, y, z) - 2ri + 5y + 3-k across the boundary of the right rectangular prism: -3 <<6, -15y<3,-425 oriented outwards using a surface integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism to be...
(1 point) Consider the transformation T : x = sau - Sov, y = ou +...
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square...
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
To evaluate the following integrals carry out these steps. a. Sketch the original region of integration...
To evaluate the following integrals carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. х x,y): 0 5x57, 7 sys 6 - -x}; use x=7u, y = 6v - u. S5x25x+7y da,...
1/3 x + y 7. Consider dA where R is the region bounded by the triangle...
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F= <2y, y, z2> and S the closed surface formed by the paraboloid z = x2 + y2 and the disk x2 + y2 ≤ 4 at z = 4. Use divergence theorem...
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F=
<2y, y, z2> and S the closed surface
formed by the paraboloid z = x2 + y2 and the
disk x2 + y2 ≤ 4 at z = 4. Use divergence
theorem to solve one way, and use SSs F * N ds to solve the other
way. (This is a Calculus 3 problem.)
* 36.3. Compute in two ways the fux integral ф...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are s...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
с 1. Determine the work done by force F along the path C, that is, compute...
с 1. Determine the work done by force F along the path C, that is, compute the line integral F.dr from point A to point B. You need to find the parameterization of the curve C and use it to find the line integral: Work = ff.dr =[F(F(t)). 7"(t)dt с с Use F = (-y)ỉ +(x)ì in Newtons. and use a = 4 and b = 5 meters in the figure. Parameterization of a straight line: Remember that for any...
Score: 0 of 1 pt 6 of 10 (5 complete) 15.1.3-T Use the accompanying set of...
Score: 0 of 1 pt 6 of 10 (5 complete) 15.1.3-T Use the accompanying set of dependent and independent variables to complete parts a through d below. Click the icon to view the data set. a) Construct a 95% confidence interval for the dependent variable when xy = 9 and X2 = 11. The 95% confidence interval is from a lower limit of to an upper limit of (Round to two decimal places as needed.) 0 Set of dependent and...
14) Consider the parallelepiped D determined by the vectors (2,-1,2), (1,3, 1), and (2,-1,1). Let T(z, y, 2)a-ytz. Consider the integral I - JSsD TdV. Using the Change of Variables Theorem, write I as an integral of the form T(r(r, s,t), v(r, s, t), z(r, s,t))lJ(r,s, t) dr ds dt for a suitable linear change of variables (r, s, t) (, y,z). The Jacobian J(r,s,t) you get here should be a constant function.
14) Consider the parallelepiped D determined by...
(1 point) This problem will illustrate the divergence theorem by computing the outward flux of the vector field F(x, y, z) - 2ri + 5y + 3-k across the boundary of the right rectangular prism: -3 <<6, -15y<3,-425 oriented outwards using a surface integral and a triple integral over the solid bounded by rectangular prism. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the prism to be...
(1 point) Consider the transformation T : x = sau - Sov, y = ou + A. Compute the Jacobian: d(xy) d(u,v) = B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S :-50 su < 50, -50 SV < 50 into a square T(S) with vertices: T(50, 50) =( T(-50, 50) =( T(-50, -50) =( T(50, -50) =( C. Use the transformation T to evaluate the integral Stor? + y2...
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
To evaluate the following integrals carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. х x,y): 0 5x57, 7 sys 6 - -x}; use x=7u, y = 6v - u. S5x25x+7y da,...
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F=
<2y, y, z2> and S the closed surface
formed by the paraboloid z = x2 + y2 and the
disk x2 + y2 ≤ 4 at z = 4. Use divergence
theorem to solve one way, and use SSs F * N ds to solve the other
way. (This is a Calculus 3 problem.)
* 36.3. Compute in two ways the fux integral ф...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
с 1. Determine the work done by force F along the path C, that is, compute the line integral F.dr from point A to point B. You need to find the parameterization of the curve C and use it to find the line integral: Work = ff.dr =[F(F(t)). 7"(t)dt с с Use F = (-y)ỉ +(x)ì in Newtons. and use a = 4 and b = 5 meters in the figure. Parameterization of a straight line: Remember that for any...
Score: 0 of 1 pt 6 of 10 (5 complete) 15.1.3-T Use the accompanying set of dependent and independent variables to complete parts a through d below. Click the icon to view the data set. a) Construct a 95% confidence interval for the dependent variable when xy = 9 and X2 = 11. The 95% confidence interval is from a lower limit of to an upper limit of (Round to two decimal places as needed.) 0 Set of dependent and...
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