1. A group of 5 men and 3 women is randomly splittes into two groups of four people. What is the proba- bility that one of the groups is composed by only men? A B D U 27

Q: :Prove that the function f(x₁, x,)=- X₂ X₂ purpose, compute the Hessian matrix for f(x). defined on…

A:

Q: 43 Compute for the sum. Answer directly. 2 3 ΣΣ11;3 i=0j=0

A:

Q: A car drived 50 km on a bearing of 125°. If its position is defined in terms of Cartesian…

A:

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

A: Using cylindrical shell method

Q: Find the principal value of [in (1-j)]^ A) 4.71+2.08j B) -4.71-2.08j C) -4.71+2.08j D) 4.71-2.08j E)…

A:

Q: GIVEN: f(x) = 2x³ − 2x¹ +10x² -2=0 Using NEWTON'S METHOD, determine new estimate after 2nd…

A: We have to determine the new estimate after second iteration by Newton’s Method. Newton's  Method…

Q: Calculate the direction of P₁P2 and the midpoint of line segment P1P2- P 1(3, 4, 6) and P 2(6, 0, 1)…

A:

Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

A:

Q: 6. Find the general solution to the system of equations dx dy + dt dt 2t + +x+y=0 d²x dx dt² dt

A:

Q: Let f(x) = x. Use L16 (x) to approximate 16.3 to exactly 6 decimal places. You will be required to…

A: Solution

Q: Determine y(t) y" - 13y' + 40y = 0, where y(0) = 0, y'(0) = -2

A:

Q: 2. Show that the following functions are harmonic, that is, that they satisfy Laplace's equation,…

A:

Q: The differential equation formed by eliminating a and b from y = ae* + be* is

A:

Q: Consider a force field F = yi+zj+k that acts along a path from foothill A to the top B as in the…

A:

Q: Example: Test the following series converges. a. { In ( n + 12 ) n+2 M=1 or not

A:

Q: in fuzzy graph What is the connectivity in fuzzy graph And give an examples

A:

Q: Solve step by step in digital format 2x - 6 b) lím X-00 x²-9

A: Solution

Q: Transportation Model (Optimal Feasible Solution) Minimize: C = 15x₁a + 24xıb + 12xic + 19x1D + 10x2A…

A: The following steps are used to obtain the optimal solution of the given transportation problem.…

Q: An airplane is travelling at 620 km/h on a heading of 305°. The wind of 80 km/h is flowing from a…

A:

Q: TASK Double Ferris Wheel Some amusement parks have a double Ferris wheel, which consists of two…

A: Given, Each wheel has 6m diameter and revolve in every 12sec. Rotating bar is 9m long. Height is 8m…

Q: 9. Show that is a two-dimensional vector. Ai = -x2 X1

A:

Q: (a) Define a metric space (X, p). (b) Let p: R+ → R+ be a function defined by ln (2). Prove that p…

A:

Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: Q2- By using Chain Rule, find au/ax, du/dy, du/əz at (x, y, z) = (√√3, 2, 1) P-q u= p=x+y+z q=x-y+z,…

A:

Q: PROBLEM NO. 6 GIVEN: f(x) = cos(x)-√√9-x² Using NEWTON'S METHOD, determine new estimate after 2nd…

A:

Q: hat is the limit as n goes to infinity of the power series (log n)2/nxn ?

A:

Q: Q2/ solve Simultaneous Differential Equations: Find X(t) only dx dy 2 +x+ = t ... (1) dt dt dy dx 3…

A:

Q: What is the anticlockwise moment acting on this crane? 25 m 5m load 4000 N O 120000 Nm O 100000 Nm O…

A: To find the anticlockwise momentum acting on the body :-

Q: X"-1 Prove that the function f(x)= a concave function. For this purpose, compute the Hessian matrix…

A: This is a question from optimization and real-valued function.

Q: CQ 13 A hot metal bar has temperature 260°C. The metal bar is placed in a 20°C room where it cools…

A: Given that a hot metal has a temperature of 260°C. It is placed in a room where it is cooled down…

Q: Find the volume of the solid bounded by the paraboloid z= 32-8x²-8y² and the plane z=0

A:

Q: Find the differential equation whose general equation is y = C₁x + c₂ex. A. (x-1)y" - xy' + y = 0 B.…

A:

Q: Which one is a correct symbolization of the following sentence in FOL? "Only happy poets like all…

A:

Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

A:

Q: Consider the following 2 planes: ?1: 2? − ? − 4? − 4 = 0                   ?2: 4? − 2? − 3? = 3…

A:

Q: 9. Show that is a two-dimensional vector Ai = -x2 X1

A:

Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

A:

Q: c) Develop an M-file function for the trapezoidal rule. Use it to estimate the integral of f(x) =…

A:

Q: Find the Volume: Rotate the region bounded by y = 7 - x², x = -2 and x = 2 and the x-axis about the…

A:

Q: 4- 3 C

A:

Q: B.) Convert the following function to standared form Min Z = 2x₂ + 5x3 S.t: x1 - x₂ ≥ 2 2x₁ + x₂ +…

A: Given  Min z= 2x2+5x3 x1-x2&gt;=2 2x1+x2+6x3&lt;=6 x1-x2+3x3=4 x1,x2,x3&gt;=0

Q: Consider

A: We find the general solution by finding roots of equation.

Q: 1. Factor the given matrix into LU decomposition (= 1 for all i) 2.1756 4.0231 -2.1732 5.1967…

A: ⌈ 1 0 0 0 ⌉ L = | -2 1 0 0 ｜   | -0.5 -0.214 1 0 ｜   ⌊ 3 -0.357 -5.34 1 ⌋

Q: 1. Use the Cauchy-Riemann conditions to find out whether the following functions are analytic. b.…

A: Cauchy-Riemann conditions:  The complex valued function  f(z)=u(x,y)+iv(x,y) is analytic if it…

Q: Q4) Find the result of the following: 1. i¹ = ? 2. B (125/50, 1) =? (Beta function) 3. Given z/= (4…

A:

Q: Q2) a steel plate of dimensions 4 cm x 4 cm and negligible thickness is in steady state conditions.…

A:

Q: Use the Cauchy-Riemann conditions to find out whether the following functions are analytic. b.…

A:

Q: For the function z = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

A: given function z=fx,y=x2-xy2+y3 find the equations of tangent lines in both the x-direction and the…

Q: 24- Solve the following differential equation: (1+x²)dy + (y-tan-¹(x)) dx = 0

A: Solution to the differential equation

Q: 1 : Prove that the function f(x,x)= defined on the domain , is a convex function. For this purpose,…

A: Here we find  determinant of the hessian matrix. Which is positive on its Domain.