Homework Answers
such parametric equations show
plane because s×t represents the normal to the plane.
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D. Explain why the vectors in the following form describe a plane (where both t and s are parameters) t1,0,3 +s<1,1,-2 Then find an equation for the plane described by these vectors D. Exp...
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters): Then find an equation for the plane deeribed by these veetors. D. Explain why the vectors i...
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters): Then find an equation for the plane deeribed by these veetors.
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters): Then find an equation for the plane deeribed by these veetors.
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to...
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position ...
АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position vec- tor q = i + 3, and L3 is given by the equation r = (0, i, 2) + λ(1, 3,-1) (where λ is a real parameter). i) Write down two vectors representing two different directions which lie in the plane P. [2 marks i) By using the cross product or otherwise, find a direction perpendicular to the plane....
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...
The transport of pollution in an aquifer is described by advection-reaction equation an of the form...
The transport of pollution in an aquifer is described by advection-reaction equation an of the form Cxx 0< x < L t0 Ct+vc where c(x, t) is the concentration of pollutant v is a positive constant and L is the length of the aquifer. Suppose the boundary conditions are c(0, t) 0, cx(L, t) 0 t>0 and that the initial concentration is c(x, 0) f(x) 0< x< L (a) Find the associated eigenvalue problem. Is it a Explain (b) Show...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
Consider the differential equation: d y 6y--6 exp-2). d t 6.1 (1 mark) Find a solution of the form y(t) - Cp exp(-2t) f...
Consider the differential equation: d y 6y--6 exp-2). d t 6.1 (1 mark) Find a solution of the form y(t) - Cp exp(-2t) for this differential equation, and enter the value of Cp below. You have not attempted this yet 6.2 (1 mark Any solution yh of d yh d t is of the form C exp(r t) for an appropriate value of r. What r? Remark. The general solution of the differential equation labelled (1) above is y(t) ....
The motion of a body is described by the equation 4.15 sin (0.170πt) where t is...
The motion of a body is described by the equation 4.15 sin (0.170πt) where t is in s and y is in m. a. Find the amplitude b. Find the period c. Find the frequency d. Find the displacement at t= 5.50 s e. Find the displacement at t= 22.5 s
The motion of a body is described by the equation 1.40 sin (0.130πt) where t is...
The motion of a body is described by the equation 1.40 sin (0.130πt) where t is in s and y is in m. (a) Find the amplitude. (b) Find the period. (c) Find the frequency. (d) Find the displacement at t = 3.50 s. (e) Find the displacement at t = 29.0 s.
2. The electric field in a plane wave is described by the equation (k > 0):...
2. The electric field in a plane wave is described by the equation (k > 0): Ē(x,y,z,1)= E, sin(kz – mt)ị Answer the following questions about the wave. i. What direction is the wave traveling? Explain how you can tell from the equation for the electric field. ii. Write an expression for the magnitude of the magnetic field of the wave. iii. Calculate the average intensity of the wave if Eo = 3000 V/m. The MKS units of intensity are...
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters): Then find an equation for the plane deeribed by these veetors.
D. Explain why the vectors in the following form describe a plane (where both t and s are parameters): Then find an equation for the plane deeribed by these veetors.
Additional Problems: (HINT: It suffices to consider Just what happens (DX c A. Show by example that (a x b xc* a with i, j and k:) B. Find a vector which is perpendicular to every vector parallel to the plane z+y 0. C. Find the line which is the intersection of the planes x + y 0 and 3y-z = 0. D. Explain why the vectors in the following form describe a plane (where both t and s are...
АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position vec- tor q = i + 3, and L3 is given by the equation r = (0, i, 2) + λ(1, 3,-1) (where λ is a real parameter). i) Write down two vectors representing two different directions which lie in the plane P. [2 marks i) By using the cross product or otherwise, find a direction perpendicular to the plane....
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...
The transport of pollution in an aquifer is described by advection-reaction equation an of the form Cxx 0< x < L t0 Ct+vc where c(x, t) is the concentration of pollutant v is a positive constant and L is the length of the aquifer. Suppose the boundary conditions are c(0, t) 0, cx(L, t) 0 t>0 and that the initial concentration is c(x, 0) f(x) 0< x< L (a) Find the associated eigenvalue problem. Is it a Explain (b) Show...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
Consider the differential equation: d y 6y--6 exp-2). d t 6.1 (1 mark) Find a solution of the form y(t) - Cp exp(-2t) for this differential equation, and enter the value of Cp below. You have not attempted this yet 6.2 (1 mark Any solution yh of d yh d t is of the form C exp(r t) for an appropriate value of r. What r? Remark. The general solution of the differential equation labelled (1) above is y(t) ....
2. The electric field in a plane wave is described by the equation (k > 0): Ē(x,y,z,1)= E, sin(kz – mt)ị Answer the following questions about the wave. i. What direction is the wave traveling? Explain how you can tell from the equation for the electric field. ii. Write an expression for the magnitude of the magnetic field of the wave. iii. Calculate the average intensity of the wave if Eo = 3000 V/m. The MKS units of intensity are...
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