(4) a) Solve the initial value problem x'(t) = Ax(t), (i) 4 -5 8. A x(0) -2 1 1 Draw the phase portrait of this linear system of DE's emphasizing the par- ticular trajectory selected by the initial conditions.

Q: 1 -1 2 1 | -1 1 3 -1 1 Let, A = -1 3 -6 -2 1 4 3 -1 -5 1 a. Find a 5x5 matrix B such that AB = 0, wh...

A: Note :- You can cross check yourself to see that AB = 0.

Q: O ) Let -2 М— -16 Find formulas for the entries of M", where n is a positive integer. M" =

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Q: In order to make it very clear for her client, Jedda put together the following table for both optio...

A: First, we can fill all the data given and then we can find the unknown values in the table. 

Q: b) Approximate the value of the root of f(x)=-3x+5x+14x-16 near X3D3 to within 0.05 of its actual va...

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to calculate the root of the equation: f...

Q: 13. Determine the solution to the differential equation (y2+2xy) dx = 0. A. 2x / (c + x) B. x/(s x?d...

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Q: Using a method of this section or separating variables, find the general solution. If an initial con...

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Q: 5. Let A = {n E Z; n is odd} and B = {n € Z; 3n² +7 is even}. Prove that A = B.

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Q: r+ cimo - coso)drt r Cino + co-B ナ

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Q: t2 (sinh 2.75t – 5)

A: Laplace transform of a function of the form tn f(x) is given by the equation; L{tnf(t)}=(-1)ndndtnL{...

Q: 1. Prove that Si-2' = (n – 1) - 2"*+1 + 2 for any positive integer n.

A:

Q: 1 4. 1. L s+9 s- 5 20 1 7 2. s+3 5s-3 6s-5 3. 4s+7

A:

Q: 5. Prove that if a matrix A is invertible and diagonalizable, then matrix A-1 is also diago- nalizab...

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Q: The temperature T, at a point (x, y) in the xy-plane is given by T(x, y) = 4x^2y^3 degrees Celsius. ...

A: We have to find a unit vector in the direction in which the temperaturedecreases most rapidly at (2,...

Q: Question 6 The following function is homogenous of degree what? Vx++x²+y? x+y other/not possible 2 4...

A: For the detailed solution of the problem follow the next step.

Q: Locate all relative maxima, relative minima and saddle points of f(x, y) = xy − x^3 − y^3. Justify y...

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Q: Define a function S: Z+ → Z+ as follows: For each positive integer n, S(n) = the sum of the positive...

A:

Q: 1. For this question, use N as the universal set. Define f = {(X,Y) E P(N) × P(N) : XUY = N and XnY ...

A: Given that N(set of Natural numbers) is a Universal set. Also, given is a relation from P(N) to P(N)...

Q: Use the following matrices to compute the indicated expression if it is defined. 1. (С"В)A" 3 1 4 A ...

A: 1. (CTB)AT = 142315T4-10230-1211T              = 1341254-1023-11021              = 4516-2883-11021  ...

Q: If the sum of seven consecutive integers is zero, what is the biggest of the seven integers? x, x + ...

A: Let the consecutive integers be x, x+1, x+2, x+3, x+4, x+5, and x+6. Then,         x + (x+1) + (x+2)...

Q: Theorem (The Triangle Inequality) If A and B are vectors in R", then || A+ B|| < || A|| + || B||.

A:

Q: Two candidates are running for school president. The two choices are Emilio and Jose. The school's n...

A: What is the result of the vote after Paul entry.

Q: 7. Let z be a root of the polynomial p(z) = (z + 1)" + z". Show that %3D 1 Re z = - 2

A: For the solution follow the next step.

Q: Consider the points A(3, –3, 3), B(4, –5, 0), C(-3, –-4,0), and D(6, 2, –6). (a) Find the volume of ...

A:

Q: Let D be the set of all finite subsets of positive integers. Define a function T:Z+ → D as follows: ...

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Q: Test for exactness. If exact, solve. If not, use an integrating factor as given or obtained by inspe...

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Q: Part A: To the nearest tenth, approximately when will the flower’s height using fertilizer B exceed ...

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Q: enclosed by area find Ix, Ig and Io for the Y= 1+ CoSO

A: Use the following formulae, to determine the moment of inertia about the x-axis, the y-axis and the ...

Q: 10- A cosine function has a maximum value of 1, a minimum value of -5, a phase shift of t/4 to the r...

A: The general equation of a cosine function is given by the equation; y=Acos(Bx+C)+D Where A is the am...

Q: Find two power series solution of the given differential equation about ordinary point x = 0 y" - 3x...

A:

Q: 1 t3e0.035t 2

A: Use the following formulae, to obtain the solution. Laft=aLftLtkft=-1kdkdskLftLeat=1s-addxxn=nxn-1 W...

Q: 2. 3.

A:

Q: Integrals Involving Roots Evaluate each of the following integrals. 1. -4

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

Q: Writing logical notations to compound statements Let p: Man is rational. q: A century is 100 years. ...

A: The logical symbol "∧" is used to denote "AND". The logical symbol "∨" is used to denote "OR". The t...

Q: 1. Find the general solution of x =x2 – x1 + t, x, =x2. 1 2 3 2. Explain why we cannot aclculate the...

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Q: Number of 26 16 18 16 8 10 4 votes First B A M M Second M В Third A M Fourth A M B B Fifth A A A Pri...

A: Consider the case when Maria is included. No. of votes 26 16 18 16 8 10 4 First B B T A S M M ...

Q: 6. A company wants to buy 100 compressors with a capacity of 500 Hp. The compressors cost index was ...

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Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

A:

Q: a) Find the 4th approximation of the positive root of the function f(x)=x-7 using the bisection meth...

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Q: bu are given the data points (X¡, Yi) for l = 1,2, 3 : 2, 3), (1, –9), (2,9). = a + Bx is the equati...

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Q: Let E be the solid region bounded by the upper half-sphere x² + y? + z2 = 4 and the plane z = 0. Use...

A: Flux of a vector field F→ along surface S =∫∫SF→.dS Divergence theorem  ∫∫SF→.dS→=∫∫∫E divF→dV Where...

Q: 2. Let the rref of a matrix A be, 1 0 2 0 -2 0 1 -5 0 -3 0 0 1 6 Determine A if the first, second an...

A:

Q: Four candidates are running for mayor of Enterprise: • Cooper (C), • Vickers (V), • Brooks (B), • Sm...

A: Given: No. of votes 129 90 87 78 42 First S C V B B Second C B ...

Q: Let Q(3, 1,-6) and let l be the line passing through the point Q and perpendicular to the plane P1 d...

A:

Q: (b) The function f : R Ris defined as follows: -r, if r1 f(r) = {r. Plot the function, and say wheth...

A: Given f:Z →Za ) f(x) = n+1, if n is evenn-3, if n is oddTo check one-one or injective Case 1: x and ...

Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8+ 2 s, ...

A:

Q: Let p: Man is rational. q: A century is 100 years. r: Today is Monday. General Instructions: 1.) Wri...

A: Given statement p: Man is rationalq: A century is 100 yearsr: Today is Monday We have to write state...

Q: (a) Suppose that the squared matrix A is symmetric and all its eigenvalues are different. Show that ...

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

Q: 3s-2 2s2-4s+2

A: The given function is                                             3s-22s2-4s+2

Q: Question 3 Solve for the optimal x*, y*, z*, and 1* of the following problem: max(xy.z.à) 2x² + 3y² ...

A:

Q: L{e=u+3(sin(t) + cos(t))} = e*L{e=# sin(t)} + e°L{e=# cos(t)} –2t+3 O True O False

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as ∫0∞e-...