(D³ – D² + 4D – 4)y = 2e* sin(2x) – 3e*

Q: 3. A cellphone company has 1000 employees, 615 are male, 682 are single, and 345 are union members…

A: Given: A cellphone company has 1000 employees, 615 are male, 682 are single, and 345 are union…

Q: 5. Find the following limits. (a) lim,0 EE. 22-iz-1-i (b) limz→1+i z2–22+2 °

A: Apply the limits.

Q: The approximation of , xln (x +) dx using two points Gaussian quadrature formula is: 4.08176 3.0323…

A:

Q: 3. There are 12 fishermen. In order to fish, each fisherman who decides to do so has to rent a boat…

A: (a) If all of the fishermen decided to fish then there are 12 fishermen, so all 12 will go for…

Q: Problem 1 Let Z denote the integers. Let S = {0 a,b e z} (a) Prove that S is a subring of M2 (Z) (b)…

A:

Q: Q2 The following graph shows the position function r(t) of a mass attached to a spring. Note that…

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

Q: Prove that if a and b are rational then a – b is rationa If n = 4k+3 does 8 divide ² _ 1? Eplain…

A: Introduction: In mathematics, a rational number is any number that can be represented in the form…

Q: 10. The organizers of an essay competition decide that a winner in the competition gets a prize of…

A: Let x be the number of winners . Then, 100x + 25(63-x)= 3000 Or, 75x = 3000-25*63 = 1425 Or, x =…

Q: Q) Consider The system 1- a/ Find a fundamental matrix for thisgls tem ) Find the solution o f the…

A:

Q: (B) Let I be a maximal proper ideal of commutative ring with identity R. Prove that R/I is a field.

A:

Q: Answer the following questions.   A. Complete the square to show that f(x) can be rearranged in…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Given the angle equals n/6 where. Calculate the combined circumference of the two circles minus the…

A: Q.38 Given the two circles with radius of one circle r1=10 and the distance between their centers is…

Q: 8. Find all values of (a) 212i.

A: Use the given information.

Q: Q15: Define the concept of ideal and then show that the set I = is not an ideal of the ring of all 2…

A:

Q: is a vector v1, can be expressed as a linear combination of v2 and v3? b) Do the three vectors…

A:

Q: Q24: What's mean by a nilpotent element of a ring R? Find all nilpotent elements of Z6-

A:

Q: Qs: (A) Let R be a ring with identity. Define g: Z→ Z by g(x) = x. 1, Vx E Z. Is ga homorphism?…

A: We show that the given map is a homomorphism using the definitions. The detailed solution is…

Q: A cycle (i iz is ... in) is called an n-cycle. If n 2 then the n-cycle is called transposition. Note…

A:

Q: (a) Find the general solution to y" + 2y' + 2y = 0. (b) Write down a linear, homogenenous 2nd order…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (B) Define the triangle group. Then 1. Find all subgroups of it. 2. Is it abelian? Why?

A:

Q: Ex: Use a double in tegral to Pind the volume of the tetrahedron" bonnded by the coordinate lanes…

A:

Q: x = 2+5 cost Consider the parametric equations for 0<tsa. y = 8 sin t (a) Eliminate the parameter to…

A:

Q: (B) Let G be a set of all real numbers except , Define on G by a * b = la|b, where Ja| is the…

A: Solution

Q: 4. Find all the values of z for which each equation holds. (a) Log(z – 1) = -i. (b) exp(z+1) =…

A:

Q: [8]. Consider the series (-1)" – n+4 n(n + 3) * Is this series conditionally convergent, absolutely…

A:

Q: 9. I= set of all positive even integers, (a*b) = (a-b)/2 10. J= set of all positive odd integers,…

A: If the set does not satisfy any condition then we will not check the next conditions...

Q: 1 Brandt r at an ans monthly within a • Deter order b Find

A: Introduction: The formula for a monthly payment of loan amount is given by, A=Pr1+rn1+rn-1 Where P…

Q: The following table shows the number of candidates who scored 0, 1, . . . , 10 marks for a…

A:

Q: Find the saddle point and solve the game Player B B, B2 B3 A, 15 3 Player A A, 6. 5 A3 -7 4 3 70 2.

A: We need to find the saddle point and solve the game              Player B Player A B1 B2 B\3…

Q: (B) Explain the relationship between each of th. a) Field and integral domain. b)

A:

Q: 2 p"(5) is: The degree of precision of a quadrature formula whose error term is 5 2 This option O…

A:

Q: Question A formula of order 4 for approximating the first derivative of a function f gives: f'(0) -…

A:

Q: swer no. 1 and

A: 1. Given,           A=R, (a*b)=a+b

Q: If an n-cycle o e S, is a product of an even number of transpositions then o is called an even…

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

Q: 1. Consider the function g(x, y) = cos(xy) + sin(x - 2y)

A: INTRODUCTION: The formula of directional derivative of a function f(x,y) at a point (a,b) is given…

Q: 4. (D2 - 5D + 4)y = 2x2 - 6x – 5 フェ

A:

Q: Let T : P2 → P2 be the linear transformation such that T(1) = 4+ 2x + x², T(x) = 3x, T(x²) = 1+2x +…

A: The matrix is diagonalizable if and only if the algebraic and geometric multiplicity of each…

Q: Solve the system of equations S below in R³. x + 2y + 5z = 2 %3| (S) : 3x + y + 4z = 1 2.x – 7y + z…

A:

Q: d) 1, x, e-2x Q.3) The radius of convergence of (x-1)y" + 4y' + 6xy = 0 about xo = 2, is: a)+o Q.4)…

A:

Q: A Beverton-Holt model for a fish population is described by the DDS 3.07Pn Pn+1 1+ 0.003Pr with Po…

A: We are given an equation which represents Beverton - fish model for fish population.

Q: A planet P in the xy-plane orbits a star S counterclockwise in a circle with radius 10 units,…

A: To find parametric equations for the x- and y- coordinates of the planet P at time t.

Q: ohow by example if I, and Iz are ideals an of R then IUI is not ideal

A:

Q: 16. Find the area of the region. -2,4 f2,4) 2- y=x-3x -2

A:

Q: ABC is a right-angled triangle at A and AB > AC. Bisect BC in D draw DE perpendicular to the…

A:

Q: Q30: Define nilpotent element. Are 1 and 3 nilpotent elements of Z11?

A: An element x∈R (where R is a ring) called nilpotent element if xk=0, where k is a positive integer.

Q: The population size of Batangas in 2015 is 2,600,000. This increased to 2,908,494 based on the last…

A: 7. Change of population from 2015 to 2020,i.e, in 5 years = 2,908,494 - 2,600,000…

Q: Let consider the following table that gives the values of a function f at some specific points: 0 25…

A:

Q: Q4) Solve the boundary value problem y 3y' + 2y 0 with y'(1) = 1 , y(3) = 2e* – e? h = 0.5

A:

Q: (c) What is the real part of ein/4?

A:

Q: Prove that the only homomorphisms from Z to Z (Z being the ring of integers) are the identity and…

A: