Consider a 2-space with the following metric ds² = rdr² + ydy? (a) Calculate the nonvanishing connection coefficients I'1 and r2. (b) Hence, use your result from part (a) to determine the geodesic for this metric. Do not integrate these equations.

Q: 2. If the product of matrices cos² 0 cos e sin 0 A = cos 0 sin 0 sin 0 cos² cos o sin sin? cos ó B =…

A: Solution :-

Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = eV1--, y(0) = 0…

A: Existence of solution If f is continuous on an open rectangular interval R{a<x<b,c<y<d}…

Q: Solve the following linear equations using the 5 methods: (Gaussian Elimination, Ga Inverse Matrix…

A: Gauss elimination: Given system of linear equation is…

Q: shve SEGMENT for x. Circles may not be drawn to scake. Directions: 3. 5. 6. 4 10

A: Introduction: If 2 secant segments square measure drawn to a circle from AN exterior purpose, the…

Q: 1. Suppose that ACX is connected. Show that A is connected. Hint: Suppose we could write A = FUG,…

A:

Q: If k >= 2 and x in R^ k prove that there exists y in R^ k such that y ne0 but xy = 0 Is this also…

A: If x has any components equal to 0, then y can be taken to have the corresponding components. equal…

Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan I - 3y + 2z = 18 %3D 5x -…

A: Since there are two equations and 3 unknown i.e. 2 Rows and 4 columns but For the method to solve…

Q: (a) Find the exact length of the curve (i) r = 1+ sin 0, 0<0< 2ñ, (ii) r= 2(1+ sin 0), 0<0< 27. (b)…

A: If f is continuous and non negative on the interval α≤θ≤β with 0&lt;β−α≤2π. Then  Arc length of…

Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: 1/2 :Evaluate e sinx dx by using trapezoidal rule so that er < 0.025

A: Solution :-

Q: Let M be the surface with the equation r+y+z 9 that is above the right triangular region with…

A: Note : The unit normal to the surface f(x,y,z)=c is taken as            ±gradfgradf .

Q: a) Is the series sin(n) Σ is – 7n + 1 n³ + 3n² n=1 absolutely convergent or divergent? justify your…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: dz IV. Suppose z is a function of x and y, and a? – y? = 2"e©y. Solve for %3D dx

A:

Q: A rectangular tent is made to have a square base with two partitions inside that divide the tent…

A:

Q: Given an 8-inch wafer costing $2200 each, with Y, 80%, Y = 98% and die area of 4 x 4 mm², estimate…

A: Solution :-

Q: What is the area of the region in the first quadrant enclosed by y= e 4. and the line y0.5. 0.516 sq…

A:

Q: LDE with Constant Coefficients dªy dx4 + 2y = e-* + xe-* dx dx2

A:

Q: Find the following for the vectors u = 10i – 8j + V5 k and v = - 10i + 8j - V5k. a. v•u, |v|, and…

A:

Q: Exercise 1.9 Suppose z = a + bi, w = c + di. Define z < w if a < c, and also if a = c but b < d.…

A: Suppose z=a+ a+bi and 2 = c+d2 are distinct complex numbers either If a not equaal to c then either…

Q: d*y Section A: Solve the boundary value problem = x+ 2y, with the boundary conditions %3D Y(0)=0 and…

A: Section A: Given boundary value problem is d2ydx2=x+2y with boundary condition y(0)=0, y(1)=0 We van…

Q: n* In n ,4 b) Is the series is absolutely n8 – 2 n=1 convergent or divergent? justify your answers.

A: Test for converges of the series, using limit comparison test

Q: Find the work done by F over the curve in the direction of increasing t. F = -4z i + 6x j + 7y k;…

A:

Q: d - 1 Use -f'(x) = to find the derivative of the inverse at the indicated point. dx - 1 Let f(x) = -…

A:

Q: Mr. Farmer planted tomatoes on the ground garden beds as seen below. Suppose the garden bed row for…

A: Given, Garden bed row for tomato plants is modeled by polynomial (y2 -17y+16) in2 Then, Area of…

Q: f If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

A:

Q: Q4) The state space representation of a dynamical system is given as: *(t) = [ ) x(t) + [LLO %3D…

A:

Q: Express the vector - 14i + 8j - 8k as a product of its length and direction. - 14i + 8j- 8k =TOi+…

A:

Q: 19. lim 1– 3 = -2 3. 20. lim = 7 2 x- 2)

A: ε-δ definition of limit: Let f be a function defined on an open interval I. Let x0∈I. Then the limit…

Q: easured the dimensions of the three perpendicular sides of a r 02 cm Y = 7.25 ± 0.03 cm Z = 9.14…

A: In this question, the concept of the differential is applied to find out the uncertainty in the…

Q: 5. A rectangular tent is made to have a square base with two partitions inside that divide the tent…

A: The total surface area of an object refers to the two-dimensional space the object's surfaces…

Q: 10. (. A is the relation defined on Z as follows: for all x, y € Z, x Ay = x=y (mod 3). Describe the…

A: Given : A is the relation defined on ℤ as-               xAy ⇔ x=y mod 3  for all x, y ∈ ℤ. To find…

Q: 4x2 Let S be the surface with equation y = + 2². 9 (a) Write the equation of the traces of S on the…

A: (a) The equation of the surface given is as follows: y=4x29+z2 The equation of the trace of the…

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

A:

Q: Suppose that X and Y are topological spaces and f: X- Y. Show that f is continuous iff for each…

A: Definition: Let X and Y are topological spaces and f : X→Y be a function. We say that the function f…

Q: how that , Oi – y)² = , &i – y)? + E, Vi - ŷa %3D1 =D1

A:

Q: 1 Find the L s(s²+1) O 1-cos x O 1+sin x O 1-sin x O 1-cos x

A:

Q: P.. 5 21 ....... .... 3" n²+3

A:

Q: Q3 By using the derivatives transformation find the transfer of the function a" (t) + æ(t) =…

A:

Q: 4) Consider the fun ction g defined by gx, y) = car (7x Jy )+ log3(x-y) does 9 have the maximum (c)…

A: The maximum directional derivatives of a function F at a given point P is obtained in the same…

Q: Determine whether the Fourier series of the following functions converge uniformly or not. a) f(x)…

A: We have to determine whether the Fourier series of the following functions converge uniformly or…

Q: dz IV. Suppose z is a function of æ and y, and a? – y? = 2"e®y. Solve for dx

A:

Q: The Cookie Jar bakes 80 dozen cookies at a cost of $1.08 per dozen. If a markup of 60% on selling…

A:

Q: do i prove this

A: Introduction: A triangle could be a 3-edged polygonal shape with three vertices. it's an elementary…

Q: Test the convergence and divergence of the following series. find the sum of Fonvergent series. 2)…

A: Here we have to test the convergence and divergence of given series.

Q: Let fnf, where if 0<a < (2 a) if< <1 In (x) n-2 2- 0. if 0<<1 if x 0 and f(x) Then lim sup fn (x)…

A:

Q: , then A'(V) is a free K – module of rank

A:

Q: Let. f be q into medric Captinyous. marping of a medric rpare %.

A: Matric space

Q: Let P(x1, y1) be a point on the parabola r? = 4py, p> 0, with focus F(0, p). Let a be the angle…

A: