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In a chemical reaction, one unit of compound Y and one unit of compound Z are...
Problem 1 Let gi(x, y, z)-y, 92(x, y, z)z and f(x, y, z) is a differential function We introduce ...
Problem 1 Let gi(x, y, z)-y, 92(x, y, z)z and f(x, y, z) is a differential function We introduce F(x, y, z, A, )-f(x, y, z) - Xgi(x, y, z) - Hg2(x, y, 2). ·Show that the Lagrange system for the critical points off with constraints gi (x, y, z) = 92(x,y, z)0: F(zo, yo, 20, λο, μο)-(0, 0, 0, 0, 0) is equivalent to the one-dimensional critical point equation: df dr(ro, 0, 0) = 0, 30 = 20 =...
a) Show that the equation 23 : 1 f(z, Y, z) := +y+ defines a smooth...
a) Show that the equation 23 : 1 f(z, Y, z) := +y+ defines a smooth surface S. b) Show that for any (r, y, z) E S, the gradient vector (fz(x, y, z), fy(, y, z), f:(x, y, z)) of f is a normal vector to S. (Hint: let a = x(t), y = y(t), z = z(t) be a curve in the surface passing through a point (o, Yo, 2o) in S, where ro = r(0), yo: y(0),...
Extra Credit Prove that the V fo at each point Po (xo. yo, zo) on the surface f(x(t),y(t),z(r)) =...
Extra Credit Prove that the V fo at each point Po (xo. yo, zo) on the surface f(x(t),y(t),z(r)) = K for some constant K is orthogonal to the tangent vector T() of each curve C described by the vector function on the surface passing through Po (xo,yo, zo). Hint, remember that the tangent vector T(o) R'(), so prove that Vfo R'O) 0
Extra Credit Prove that the V fo at each point Po (xo. yo, zo) on the surface f(x(t),y(t),z(r))...
3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where soluti...
just (A) (B) (C)
3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where solutions must travel vertically. Identify the regions (b) On a separate set of axes, sketch the y-nullcline, where solutions must travel horizon in the plane where solutions will move toward the right, and where solutions move toward the right tally. Identify the regions in the plane where solutions will move upward, and where solutions move downward. (c) On a third set of...
Differential Equations Need Help! Will Rate! Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt...
Differential Equations Need Help! Will Rate!
Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt2. (15) 2. Verify that the two solutions are linearly independent. (5) 3. Build the general solution to the DE as a linear combination of these two solutions. (5) 4. Using the general solution, calculate the solution for the same DE with the initial conditions z(0) 5, x(0) 3. (10) Question...
3. (a) (6 points) Expand S(x, y, z) around (20,40, zo) to the second order in...
3. (a) (6 points) Expand S(x, y, z) around (20,40, zo) to the second order in Az = 1 - TO, Ay=y - Yo, and Az = 2-20. Detailed derivation is required. (b) (3 points) Find the extremum of f(x, y, z) = xyz subject to the constraint g(x, y, z) = I+y+z-e= 0, where x, y, z are positive variables and c is a positive constant. (c) (6 points) Show explicitly the nature of the extremum found in (b).
please show a detailed mechanism from X-Y, X-Z, Z-W. 2. Compound X, with chemical formula C...
please show a detailed mechanism from X-Y, X-Z, Z-W.
2. Compound X, with chemical formula C Ho, gives 1,3-dimethylcyclopentane when treated with Hz Over Pt. That same compound, when treated with hot and concentrated KMnO, produces carbon dioxide and Y. Compound X reacts with two equivalents of HBr in the presence of a peroxyether to form compound Z, with chemical formula C H2Br2. When pound Z is heated in methanol it yields compound W, among others. (a) (6 pts., 3...
Find out if y = Sa sin Vedt. de = sin V 28 – 24 =...
Find out if y = Sa sin Vedt. de = sin V 28 – 24 = sin 24 – sin 22 = 2 (sin 28 – sin æ4) O D.de = 22 (2ą? sin 24 – sin x2) O E. de = 423 (22^ sin 24 – sin z) _, sin (5ck) 4.x, where ck is chosen arbitrarily in the kth Which integral can be represented by lim subinterval and Ac = *°? O A. So sin (z)dx O B....
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) =...
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evalu...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
Problem 1 Let gi(x, y, z)-y, 92(x, y, z)z and f(x, y, z) is a differential function We introduce F(x, y, z, A, )-f(x, y, z) - Xgi(x, y, z) - Hg2(x, y, 2). ·Show that the Lagrange system for the critical points off with constraints gi (x, y, z) = 92(x,y, z)0: F(zo, yo, 20, λο, μο)-(0, 0, 0, 0, 0) is equivalent to the one-dimensional critical point equation: df dr(ro, 0, 0) = 0, 30 = 20 =...
a) Show that the equation 23 : 1 f(z, Y, z) := +y+ defines a smooth surface S. b) Show that for any (r, y, z) E S, the gradient vector (fz(x, y, z), fy(, y, z), f:(x, y, z)) of f is a normal vector to S. (Hint: let a = x(t), y = y(t), z = z(t) be a curve in the surface passing through a point (o, Yo, 2o) in S, where ro = r(0), yo: y(0),...
Extra Credit Prove that the V fo at each point Po (xo. yo, zo) on the surface f(x(t),y(t),z(r)) = K for some constant K is orthogonal to the tangent vector T() of each curve C described by the vector function on the surface passing through Po (xo,yo, zo). Hint, remember that the tangent vector T(o) R'(), so prove that Vfo R'O) 0
Extra Credit Prove that the V fo at each point Po (xo. yo, zo) on the surface f(x(t),y(t),z(r))...
just (A) (B) (C)
3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where solutions must travel vertically. Identify the regions (b) On a separate set of axes, sketch the y-nullcline, where solutions must travel horizon in the plane where solutions will move toward the right, and where solutions move toward the right tally. Identify the regions in the plane where solutions will move upward, and where solutions move downward. (c) On a third set of...
Differential Equations Need Help! Will Rate!
Question 1 (35) 1. Build the characteristic polynomial for the DE z',-4x,-52-0 and find two particular solutions. Here, x' = dx/dt, x" = d2x/dt2. (15) 2. Verify that the two solutions are linearly independent. (5) 3. Build the general solution to the DE as a linear combination of these two solutions. (5) 4. Using the general solution, calculate the solution for the same DE with the initial conditions z(0) 5, x(0) 3. (10) Question...
3. (a) (6 points) Expand S(x, y, z) around (20,40, zo) to the second order in Az = 1 - TO, Ay=y - Yo, and Az = 2-20. Detailed derivation is required. (b) (3 points) Find the extremum of f(x, y, z) = xyz subject to the constraint g(x, y, z) = I+y+z-e= 0, where x, y, z are positive variables and c is a positive constant. (c) (6 points) Show explicitly the nature of the extremum found in (b).
please show a detailed mechanism from X-Y, X-Z, Z-W.
2. Compound X, with chemical formula C Ho, gives 1,3-dimethylcyclopentane when treated with Hz Over Pt. That same compound, when treated with hot and concentrated KMnO, produces carbon dioxide and Y. Compound X reacts with two equivalents of HBr in the presence of a peroxyether to form compound Z, with chemical formula C H2Br2. When pound Z is heated in methanol it yields compound W, among others. (a) (6 pts., 3...
Find out if y = Sa sin Vedt. de = sin V 28 – 24 = sin 24 – sin 22 = 2 (sin 28 – sin æ4) O D.de = 22 (2ą? sin 24 – sin x2) O E. de = 423 (22^ sin 24 – sin z) _, sin (5ck) 4.x, where ck is chosen arbitrarily in the kth Which integral can be represented by lim subinterval and Ac = *°? O A. So sin (z)dx O B....
At least one of the answers above is NOT correct. (1 point) Suppose f(x, t) = e 3t sin(x + 2t). (a) At any point (x, t), the differential is df = e^(-3t)cos(x+2t)dx+(e^(-3t))(2cos(x+2t)-2sin(x+2t))dt (b) At the point (-1,0), the differential is df = cos(-1)dx+(2cos(-1))+3sin(-1)dt (c) At the point (-1,0) with dx = -0.5 and dt = 0.3, the differential is df = 0.97344 Note. You can earn partial credit on this nrohlem (1 point) Consider the surface xyz = 20....
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
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