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Case wTIEle u - D. 3.53. Show that the Frenet-Serret formulas can be written dT =...
The 1st Law of Thermodynamics can be written in the differential form dQ dUPdV. i) By expressing dU in terms of dT and...
The 1st Law of Thermodynamics can be written in the differential form dQ dUPdV. i) By expressing dU in terms of dT and dV, show that dQ dV +P аT . dT (15 marks) Hence show that for one mole of an ideal gas, the heat capacities Cp and Cv differ by the Gas Constant, R (10 marks) TV B2 av Show that Cp-C can be also be expressed as Cp-C, -T| ӘР ат av к (15 marks)
The 1st...
Surface area. Consider a Surface written in the vector form where u and v are parameters (a) Justify or motivate the su...
Surface area. Consider a Surface written in the vector form where u and v are parameters (a) Justify or motivate the surface-area formula du dv 1. CiU . (b) Show that the above surface-area formula can also be written as 1.64 where E. F, and G are the coefficients of the first fundamental form. c) Write the surface 1.65 in vector form and show that the above formulas for area imply that S-2
Surface area. Consider a Surface written in...
Slove 4.3.8 please axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
The general water budget for a watershed can be written as dS dt Where I represents...
The general water budget for a watershed can be written as dS dt Where I represents inputs to the watershed and Q represents outflows. The watershed can be approximated as a "linear reservoir", in which outflow and storage are related via a linear relationship: Q= KS where K is a constant called the "reservoir coefficient" A precipitation event of constant intensity Po and duration τ as shown in Figure 1 (a) is the only inflow to the watershed. Assume that...
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv...
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes 9E+VxB- Iv. E) /c 1 v
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes...
energy U 8.10 Show that in LC corent, the total can be written as [ 0...
energy U 8.10 Show that in LC corent, the total can be written as [ 0 = 1 W²222 where LC, do and w are the inductance Capantanis, maximum change on capacitor and freparing respectively. (Use Ue = 1 of 16 and US 5 272) Hint
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute...
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.
a) Show that x-component of the Lorentz force, when written in terms of vector potentials as...
a) Show that x-component of the Lorentz force, when written in
terms of vector potentials as we did in class, can be expanded and
then recast as
where
Thus show that Lagrange’s equations still hold so long as U is
taken to have this form, and that the Lagrangian for a
non-relativistic particle in an electric and magnetic field can be
written as equation (7.104) in the text:
b) Show from this Lagrangian and the analysis in Section 7.8
that...
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t...
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint: (-1)" as ds (b) Use the above formula to compute L[t? cost].
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint:...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
The 1st Law of Thermodynamics can be written in the differential form dQ dUPdV. i) By expressing dU in terms of dT and dV, show that dQ dV +P аT . dT (15 marks) Hence show that for one mole of an ideal gas, the heat capacities Cp and Cv differ by the Gas Constant, R (10 marks) TV B2 av Show that Cp-C can be also be expressed as Cp-C, -T| ӘР ат av к (15 marks)
The 1st...
Surface area. Consider a Surface written in the vector form where u and v are parameters (a) Justify or motivate the surface-area formula du dv 1. CiU . (b) Show that the above surface-area formula can also be written as 1.64 where E. F, and G are the coefficients of the first fundamental form. c) Write the surface 1.65 in vector form and show that the above formulas for area imply that S-2
Surface area. Consider a Surface written in...
Slove 4.3.8
please
axbycz d be the equation of a plane with normal Exercise 4.3.16 a. Show that w- (u x v) = u (vxw) = v x (w x u) holds for all vectors w, u, and v. n= C w and (u x v) + (vxw) +(wxu) b. Show that v- a. Show that the point on the plane closest to Po has vector p given by are orthogonal Exercise 4.3.17 Show u x (vxw) = (u w)v-...
The general water budget for a watershed can be written as dS dt Where I represents inputs to the watershed and Q represents outflows. The watershed can be approximated as a "linear reservoir", in which outflow and storage are related via a linear relationship: Q= KS where K is a constant called the "reservoir coefficient" A precipitation event of constant intensity Po and duration τ as shown in Figure 1 (a) is the only inflow to the watershed. Assume that...
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes 9E+VxB- Iv. E) /c 1 v
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes...
energy U 8.10 Show that in LC corent, the total can be written as [ 0 = 1 W²222 where LC, do and w are the inductance Capantanis, maximum change on capacitor and freparing respectively. (Use Ue = 1 of 16 and US 5 272) Hint
a) Show that x-component of the Lorentz force, when written in
terms of vector potentials as we did in class, can be expanded and
then recast as
where
Thus show that Lagrange’s equations still hold so long as U is
taken to have this form, and that the Lagrangian for a
non-relativistic particle in an electric and magnetic field can be
written as equation (7.104) in the text:
b) Show from this Lagrangian and the analysis in Section 7.8
that...
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint: (-1)" as ds (b) Use the above formula to compute L[t? cost].
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint:...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
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