Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z2 + (z)? = 2

Q: Find the centroid of the solid of constrant density p using cylindrical coordinates bounded by the…

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Q: Evaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by…

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Q: For each of the following vector fields F, decide whether it is conservative or not by computing the…

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Q: If k is any positive number, what is the size of the angle between the vectors a = (k, k) and b =…

A: The angle between the vector a→ and b→ is define by the following formula. cosθ=a→·b→a→b→

Q: Find the Miller Indices of a plane whose intercepts are (2,1,3).

A: Given intercepts are (p,q,r)= (2,1,3) The Miller indices of a plane is    h,k,l=1p,1q,1r…

Q: Show a[1 2 1] direction on a simple cubic unit cell and give the location (in correct notation) for…

A: The required direction vector for [1 2 1] is shown in the figure below.

Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: Suppose Vf(x, y) = 6y sin(xy)i + 6x sin(xy)j, F = V f(x, y), and C y = 5x? from the point (1, 5) to…

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Q: as

A: Obtain the miller indices    a1 a2 z Intercept -a -a c2 Intercepts in terms of lattice…

Q: Calculate the areas of the following surfaces using the differential surface area dS p=2,0 ≤z≤ 5,…

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Q: Prove the Jacobi identity: A × (B × C) + B × (C × A) + C × (A × B) = 0. Hint:Expand each triple…

A: A × (B × C) + B × (C × A) + C × (A × B) = 0

Q: Given the following matrix 3 3 1 5 Find its two eigenvectors. (A 3 and H2 0. B 3 and A, !! R -3 and…

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Q: Let S be the ellipsoid ()´ + (%)´ + () with upward-pointing normal. = 1. Calculate the flux of F =…

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Q: Evaluate the surface integral /| (2xzdydz + ydzdx + z?dxdy) where S is a closed surface, given by S:…

A: Given:I = ∯S 2 xz dy dz + y x dx dz+…

Q: Let P:(-1,2,3), Pa(2,-1,1) and Pa(1,1,1) area of the triangle equal..

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Q: a Anguarm om entum of a partice, reative b the orig in ofa certain coordinate system is defined as…

A: Given: Angular momentum of a particle, relative to the origin of a certain coordinate system is…

Q: lands at the point having the coordinates (1.84, 1.18) m, determine tne polar coordinates or the…

A: x= 1.84m    and y= 1.18m

Q: Match each of the spherical coordinates r, 0, and ø with each of the following descriptions and give…

A: The spherical coordinates are r,θ and ϕ

Q: 1 A) L= zmit – mgRcos0 What are the Lagrange equations for the particle in the given figure B)…

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Q: Evaluate the commutator L,, L, L,- (a) h'L, (b) 0 (c) h'L, (d) h°L.

A: In rotational mechanics, Angular momentum holds a similar place as linear momentum. If Net torque on…

Q: Compute and sketch the vector assigned to the points P (0, 6, –1) and Q = (4, 1,0) by the vector…

A: Given, P =(0, 6, -1)Q = (4, 1, 0)Vector field, F = xy, z2, x

Q: Consider a vector field of A = (2x-z) i + xyj - x ²k taken over the region (a cube) bounded be x =…

A: Vectors are physical quantities that have both magnitude and direction. Scalars on the other hand…

Q: In the graph given below, at the point B, the second derivative (d'y/dx?) is B O a. infinite O b.…

A: The second derivative tell us whether the curve is Concave Up or Concave Down. If the second…

Q: Set up the triple integral of an arbitrary continuous function f(x, y, z) in spherical coordinates…

A: Please see the answer below

Q: Get the expression for the divergent of a vector field in spherical coordinates.

A: Given : Divergence :                           Divergence of a vector field is a measure of the “…

Q: nates of point N. 2) Write the vector KM in terms o

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Q: Use the Euler's Lagrange equationto prove clearly that the shortest distance between two points in…

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Q: 1 2 3 y 8 4 7 6.

A: The vector r from 1 to O is given by:

Q: Consider a cube with one corner at origin and the other corner along the body diagonal at (1,1,1).…

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Q: P-1 Show the given set of function is orthogonal and find the Norm of the function in given set {cos…

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Q: unction D çâp in spherical polar coordinates is

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Q: If we have two vectors, A and B, vector A extends from the origin to P1=(2,3,3) and vector B points…

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Q: 1. Compute the divergence and curl of the given vector function: xy2 ,4x² – 3z) 2z F(x, y, z) = (7x…

A: Bartleby's guidelines allowing answer only the first question

Q: 1. Let C denote the positively oriented boundary of the square whose sides lie along the lines x =…

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Q: Given vectors ū = [-2,3,1] i = [1,2, –2] and w = [4, –2, –1] find: b) ü w b) the angle between i and…

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Q: Consider the following scalar and vectors: Ã = 41+ 3) + 7k T = 3x+8yz + 2zx 1. Calculate for the…

A: REQUIRED  LAPLACIAN. DIVERGENCE.

Q: Can two vectors, of unequal magnitude, add up to give the zerovector? Can three unequal vectors?…

A: If two vectors have equal magnitude but different directions then only their sum will be zero.

Q: Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 22.

A: Given that  and we have to solve for

Q: 4. Find the gradient of the following scalar fields: (a) U = 4xz + 3yz (b) W = 2 p (z + 1) cos

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Q: The distance of the plane 2x – 2y – z = 27 from the origin is A 9 B 3 C 27 D 6

A: The distance between any point x1,y1,z1 and a plane with the equation ax+by+cz+d=0 is given…

Q: If A = (x²y)î+ (2y z)j+ (xyz2)k, find the curl of the curl of A at the point (-1,1, –2)

A: Write the given values. A→=x2yi^+2y3zj^+xyz2k^x,y,z=-1,1,-2

Q: Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 21. z +1

A: z = 2 - 3 i

Q: . Using the differential length dl, find the length of each of the following segments/curves: a) 2 <…

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Q: In the graph given below, at the point C, the second derivative (d'y/dx) is. C O a. zero O b.…

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