if u(x,y) = e sin (y) %3D show that: Uxx +Uyy =0
Q: 1. Show that (Aµ)* = X*µ* for all A, u E C.
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Q: If x = y2z2 and y= sin(y+ z), then is equal to: a) 2yz? - 2zy2 + 2yz tan(y + z) b) 2yz - y? + y…
A: Given: x=y2z ---(1)y=siny+z---(2)
Q: Show that if f(x) = Ac* where A and k are real constants, then f(x) satisfies: %3D d² f(x) + k° f(x)…
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Q: uonenba x(k + 2) + 3x(k + 1) + 2r(k) = e(k) %3D where k = 0 otherwise 1, e(k) = %3D 0, x(0) = 1 %3!…
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Q: 14 Find the eigenvalues of the matrix A = %3D 23
A: A=1423 So for eigenvalue, we have to calculate; DetA-λI=0…
Q: The ship O measures the positions of the ship A and the airplane B and obtains the coordinates…
A: Angle between the two vectors is given by the formula
Q: Q1: If (4, = 1/V2 (-i 0 1) and (42 = 1/V11(1 1 3). Find the outer product of: 1. |41)(42| 2. 142)(Y|…
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Q: Let E(r) : Calculate the line integral | E(r) - dr along the path a bc in the following two straight…
A: Let's solve the problem in Cartesian coordinate system. Given
Q: Q.3: Given the two vectors A = i+j and B =j+ k, find the following: (1) ЗА — 2B (2) Ax B (3) |Ãx B |
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Q: mw H.W.: If Pn(x) = An(a4)" e¯ ,then 2h (a) find A1, A2, a441, a_Þ½
A: Given: The wave function is
Q: Proove the follow commutators: (a) [L,x] = ihy (b) [L„,Þy] = -ihpx %3D
A: We know that the operator representing x component of the angular momentum is given by Lz=xpy-ypx…
Q: Radius is given by R(z) = 10,1 %3D 15 Using cylindrical polar coordinates, calculate the volume,…
A: here the volume required is in cylindrical co-ordinateswhere R(z)=10…
Q: For the plane shown in Figure 1, with respect to X and Y axes determine the location of the centroid
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Q: ), -G. ), a.) Total differentials: U(V,T) dU - C,dT + RydV S(V,T) ds ar + dv H(P,T) S(P,T) dH - C,dT…
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Q: For A = x āx + y āy + z āz and B = 2x āx + 3y āy + 4z āz Find the following a) C = Ā×B b) at (1,2,3)…
A: The cross product of two vectors is given by The dot product of two vectors is given by
Q: Given sin A = 13 5 for angle < A < n, determine tanA: O 13 5 O-5 13 12 12
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Q: A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m…
A: The mass of the bacterium is 0.100x10-18kg, velocity is 1.00x10-6m, and the percentage of…
Q: Find 2 fundamental (basic) solutions of the second order equation y" - 4y + 5y 0
A: The given differential equation is of second order and of the following form, It is linear with…
Q: Two forces, F₁ and F2, act at a point, as shown in (Figure 1). F₁ has a magnitude of 9.00 N and is…
A: Given:- The magnitude of the vector Force F1 and F2 as F→1= 9 N F→2=6.20 N The angle is α= 61.0°…
Q: prove that v.j = 0 V. Ả = B V²Ã = HoJ %3D with equation Ho Ã(r') = 4T %3D
A: The electric field is a vector quantity which means it has both magnitude and directions to it. The…
Q: 9. Show that the following functions are entire (see Definition 3.1). (a) S (2) = cosh z sin y-i…
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Q: Find the angle that is complementary to u.
A: Given, Angles to find out their Complementary angles
Q: Using simplified index notation, prove the following tensor identities: a) T:4 Y =y ·() b) и:(ухw)-…
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Q: Show that (a) [Jz, J+] = J+ = iJ₂
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Q: The maximum value of the expression sinθ+µcosθ, when θ can take any value.
A: Write the given expression, differentiate it with respect to theta and equate it to zero to get the…
Q: If A = (x²y)î + (2y z)j+ (xyz?)k, find the gradient of the divergence of A at the point (-1,1,-2)…
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Q: Plot the following a) x(n) = 2-u(n-1) for n ranging from -3 to 3 b) x(n) = (2)-n-¹u(-n-1) for n…
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Q: Cartesian to Cylindrical Coordinates.
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Q: If U(x,y)=In(x²-y³) then U,+Uy= O (2x-xy) /x^ 2+ y^2 O (2x + 2y) / x^2+y^2 O (2x-2y) / x^ 2+y^2
A: Given that Ux,y=lnx2-y2 The Uxx is given by the following expression Uxx=δUδx Substitute the known…
Q: Given that L* = L, ±iL, and L÷Ym (0, 6) = NYm±1 (0, 6), where N = h/(l+1±m) (t=m), show that, L* +L-…
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Q: A = 38+ 9 and B= 28- 59? What is the cross product of A and B given that
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Q: A person is standing at the edge of the water and looking out at the ocean (see figure). The height…
A: a) Apply the Pythagoras theorem in the triangle to calculate the distance of the person's eyes from…
Q: ) = Solve the IVP: xdy + (y – cos x)dx = 0, y %3D
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Q: 43) What will be the value of angle C? A. 27° B. 67° O C. 84° OD. 137° 44.) What is the measure of…
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