If Aj is a covariant tensor of the second order and Bi, Ci are contravariant vectors; prove that AB'C' is an invariant.

Q: 2. d²y dy +5 − 3y=0, given that when x =0, dx2 dx dy y=4 and =9. d.x

A:

Q: Show that the following equation has a solution on (4,8). 2x-5= -3 sin() + Drag and drop an image or…

A:

Q: Given the Taylor polynomial for f(x) at x = 3, find ƒ(³) (3) T₁(x) = 1 + x −3+2(x − 3)² + 2(x-3)³ -…

A:

Q: Classify each statement as true or false. If the statement is false, give a counterexample. Part 1…

A:

Q: The following table shows the daily receipts in millions of dollars of the movie "Avatar" for…

A: Instantaneous rate of change is the slope of the given data . So, basically we have to find the…

Q: Determine the singular and ordinary points of the given differential equations. Classify each…

A: Note :  Please repost remaining parts as your all parts are not too small.

Q: Find the mass of a thin funnel in the shape of a cone z = √√√x² + y², 1 ≤ z ≤ 2 if its density…

A:

Q: Find the residues of f(z) = z²-2z (z+1)²(z²+4) at all its poles in the finite plane

A:

Q: Find the local maxima, local minima, and saddle points of the function, f(x, y) = x³ + 3xy + y³

A:

Q: show that the following function analytic f(z) = 4e²+ Sin Z arp

A:

Q: Write Fourier series for the function y=4n-k T≥X≥0

A:

Q: Find the divergence of the vector field At the point (2,4,1). F(x, y, z)=x²2√√yi + -j + zk

A:

Q: Consider the vectors x(¹) (t) = ( ) and x(²) (t) = ( 6 ). 6t (a) Compute the Wronskian of x(¹) and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find laplacian f = (sec(z) - tan(x))i + (sin(z))j + (xy)k

A: The given problem is to find the laplacian of the given vector field. Given vector field…

Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor…

A:

Q: A national chain of clothing goods stores recently sent shipments to the following stores. The…

A: We have to find the cost of jeans and jackets  So we write it matrix form  But here we have 3 stores…

Q: Find Q for the QR factorization of A Ex: 1.23 02 0.given the orthogonal vectors 4 ------ 0.83 1.67…

A:

Q: (3) If M is integers ring module n, then M is a field if n=...... O (i) 9 O (ii) 5 O (iii) 12

A:

Q: Solve the following problem. If answers are not whole numbers round off to the nearest hundredths.…

A:

Q: . The general solution of the equation A. sin(x+y)+x² + 2y² = c D. sin(x+y)+2x+4y=c…

A:

Q: :y= x,y = 2x2 − 3x

A: To find centroid we need to find area bounded A between curves  then centroid x =∫abx×fxdxAy…

Q: Use the Divergence Theorem to calculate the surface integral 11. F F. ds; that is, calculate the…

A:

Q: The particular integral of the difference equation Yn+3 - 6yn+2 + 12Yn+18Yn = 3n is

A: We have to find Particular Solution of given difference equation yn+3 - 6yn+2  +12yn+1 - 8yn  = 3n.

Q: Q3: Approximate the integral using Taylor series method: TU 2 S x. cos²x dx

A:

Q: 10. Consider the differential equation x" + 16x = f(t) where f(t) = 2- |t| for -2 < t < 2 which is…

A:

Q: 1. Write the solution of the system of equations: P₁ = 5p₁ - 4p₂ + e²t; p2 = P₁; P₁(0)=P₂ (0) = -11

A: Given system of equations are p1'=5p1-4p2+e2t,    p2'=p1   Also given p1(0)=32,   p2(0)=-11   To…

Q: Show that the following equation has a solution on (4,8). 2-53 sin()

A: To Show: The equation 2x-5=3 sinπ x8 has a solution on (4, 8).

Q: Q2: a group of 6 boys and 4 girls, in how many way four children can be selected such that at least…

A: Given is a group of 6 boys and 4 girls.   To Find: Number of ways four children can be selected such…

Q: Q1. Use reduction of order to find the second solution y₂ (x), if the indicated function is a…

A:

Q: Let CR be the space of all continuous and bounded functions x(t) on R with norm ||x|| = supR |x(t)|.…

A: As per the question we are given a normed space over the field CR and an operator A such that :…

Q: Consider M(x, y) + N(x, y) = 0. (a) Suppose we can find a function F = F(x, y) so that Fa = M and Fy…

A: see my solution

Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: 3. Find the function M(x, y) such that M(x, 0) = e¯ª and the differential equation M(x,y) dx + (sin…

A:

Q: The complex numbers an, n > 0, are defined by the condition that Σan (z-2i)" = 1+ 2z+3z² + Σ(n+1)z"…

A:

Q: [4 1 01 5. Find the eigenvalues and eigenvectors the system X'= 0 4 1 [x]. 1x. Lo 0 11 Use the…

A: First we will find eigenvalues and associated eigenvectors of the coefficient matrix off system then…

Q: sin x cos x) (2 -

A:

Q: Let K be integer ring module 12 and let I=([4]) and J-([6]) be ideals of K. Then ([0])

A:

Q: Find the angle between the two vectors A=i+j+k and B = 2i+j-k

A:

Q: Solve by the Lapace Transform: y(t) + 4 y(T) (t - 7)dt = 2t [₁

A:

Q: (1) Let I be ideal and a does not exist in I, then I is a subset of (a, I). T O F

A:

Q: solve the system. Y₁ The initial value problem Y₂ Y₂ Y""(t) + 3Y"(t) + 3Y!(t) + Y(t) = -4 sin(t),…

A:

Q: Theorem 3. The covariant derivative of the product (outer or inner) of two tensors is equal to the…

A:

Q: A is an m x p matrix, B is a p x k matrix, and C is a k x n matrix. Show that A or (B or C) = (A or…

A: The product of two matrices is possible when the number of column of first matrix is equal to the…

Q: 3. Find all integer solutions to the pair of congruences (if any) x = 1 (mod 2) x = 2 (mod3) x = 3…

A: To Find: Integer solutions to the pair of congruences(if any) x≡1(mod 2), x≡2(mod 3), x≡3(mod 5)…

Q: Let K be integer ring module 12 and let 1=([4]) and J=([6]) be ideals of K. Then ([0])

A: We have given a integer ring module 12 which have given two ideals I and J  so first we find the…

Q: Consider the initial value problem 1 (x + 2) y" + y' + e²y = x³ X - with initial condition y (0) = 7…

A:

Q: show that a bounded Lineart on a complex Hilbert spase H is normal (i-eTT* = T*T) if and only if 11+…

A: We have to show that T  is normal if and only if ||T* x || = || Tx|| for all x € H. Using this, to…

Q: A Let (A, +,.) be a subgroup of (M₂ (Z), +,.), Then A is ideal of M₂ (Z), where = {(ab) a, b, c €…

A: Let I be a non-empty subset of a ring (R,+,·). Then I is an ideal of (R,+,·) if and only if the…

Q: A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the…

A:

Q: Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric…

A: