4) Given that z= 3 + 2i and w= √3 - 5i. Find zw and (z/w).

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: 3) If A = 2x²i – 3yzj + xz?k and ¢ = 2z – x³y, find A - Vo and A x V¢ at the point (1,-1,1). ww. 4)…

A: A=2x2 i-3yz j+xz2 kA(1,-1, 1)=(2, 3, 1)ϕ=2z-x3y∂ϕ∂x=-3x2y∂ϕ∂y=-x3∂ϕ∂z=2∇ϕ =∂ϕ∂x i +∂ϕ∂y j+∂ϕ∂z k∇ϕ…

Q: 17. If mzp = 6x + 12 and mzg = 7x - 1, find the value of x so that p is perpendicular co 18. If mz1…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: a. My =n xyy

A:

Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0,…

A:

Q: af 7. Compute and дхду a²f : f(x, y)=x'y² – sin 2 + xe" - əx' əy

A:

Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

A:

Q: for w = ze(zy²+2:). Do not include =" in your answer.

A:

Q: Use Gauss- Jordan to solve the values of x,y and z for this problem: 2x – y+z =-3 x+y-z = 6 3x - y-…

A:

Q: AISO is isosceles with IS = IO. 22 = 2x+24, mZ3 = 6x– 52, %3D %3D nd mZ1. 1/ 3 bX 2 bx -52-180 S x-…

A: We have to solve the problem

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

A:

Q: If (x, y) = (-V3, 1) , then find r and 0.

A:

Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

A:

Q: ди ди + 2y ду ди ди 2x³y Əx az ax

A:

Q: Solve the following IVP by the method of Undetermined Coefficients: y′′−3y′+ 2y= exsin(x); y(0) =…

A:

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

A:

Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: use the jacobi method to ding approximate solution for x+6y-8z=-6.6 10x-3y+6z=8.6 x+15y-9z=0.8

A: Given x+6y-8z=-6.6           10x-3y+6z=8.6            x+15y-92=0.8 To find: The solution of system…

Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

A:

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

A:

Q: Using Cramer's Rule to solve 3x + y + 4z = 2x + 3y – 2z х — — -8 11 = Зу — 2г 4 for y, we obtain y =

A: Given: 3x+y+4z=-82x+3y-2z=11x-3y-2z=4

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

A:

Q: Using Cramer's rule to solve Зх + у + 42 - 2х + Зу - 2z x - 3y – 27 = -8 %3D 11 %3D 4 for y, we…

A: Consider the given information. 3x+y+4z=-82x+3y-2z=11x-3y-2z=4 Now, make the matrix D, according to…

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

A:

Q: Verify that z 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2+ 41 also a solution?

A:

Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

A:

Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: the following DE are Bernouli type and solve: 1. y’ – x = y 2. y’ + 5y/x = x 7 y 4

A:

Q: 11T 60. Given that sec 12 13T V2 - V6, determine the value of sec 12

A:

Q: If i = xi+yi+zk then grad (r") is equal to

A:

Q: If z = (2x + 3y)³ and x = r2 - 2s and y = 2s - r, then when r = 2 and s = 1 is as %3D %3D

A: To find the partial derivative when r=2, s=1.

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: •1-i Evaluate 4z dz . J3i

A:

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

A:

Q: If In(ax)dx = 2, then a = %3D 1

A:

Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

A:

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: 10. f(x) =-x2 +3x+ m, y 4-IOBI = 10CI %3D A(ABC) = ? B.

A: As per guidelines, we will solve first question poste. 10) Given fx=-x2+3x+m 4OB=OC

Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

A:

Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

A:

Q: We have the following DFT results for two 1D signals x and y of length two as x' = [4 - 3i 0], y' =…

A: Given: DFT findings for two 1D signals x and y of length two are as follows: x'= [4 - 3i  0], y' =…

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

A:

Q: Solve the following IVPS using LT method. 3) y" + 16y = 1, y(0) = 1, y(0) = 2;

A:

Q: GIVEN: TV || WÝ with transversal RS W MZRUV (x + 4)(x – 3) R U 2 MZWXS 3 3/X %3D FIND: X

A: Consider the given diagram, m∠RUV=m∠TUX       ⋯⋯1 because both are vertically opposite angles.…

Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

A:

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Function as, y (x) = (x² – 2) (3x + 2) %3D

A: Given,          yx=x2-23x+2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.