c. The differential equation 1.25 u" + 20 u = 25 sin (t) +5 cos (t) describes a mass-on-a-spring system with no damping and external forcing. O TRUE O FALSE d. For the forced mass-on-a-spring system, the forcing frequency at which the amplitude of oscillations is largest equals the natural frequency of the unforced system. TRUE O FALSE e. The solution of the initial value problem mu" + yu' + ku и (to) %3D ио, и' (to) %3D u'о can be expressed as the sum u = v+ w, where v satisfies the initial conditions v (to) = 0, v (to) = u,, and w satisfies the initial conditions w (to) = uo, w' (to) = 0, and both v and w satisfy the same differential equation as u. O TRUE O FALSE

Q: Question 5. Prove that O- subgroup of itself. (the set of positive rational numbers) under multiplic...

A:

Q: x+6 The solution of - 63 is 3 x = -6 x = -9 x = 3

A:

Q: Newton Raphson Method Assignment 1 1. Determine the positive root'of f(x) = x³ + 2x - 2 = 0 using th...

A: Since you have posted a multiple question according to guildlines I will solve first question for yo...

Q: Solve for x that satisfy the equation x2 + 36 = 9 – 2x2 A. +6i В. +3і С. 9i D. -9i

A: Given expression is x2 + 36 = 9 - 2x2

Q: 2ni If A = 40e 3 , B = 202 - 40°, C = 26.46 + 0i, solve for A + B + C. A. 27.7445° B. 35.1445° C. 30...

A:

Q: Theron wants to save $5,550. If he has $3,000 and invests it at 5% simple interest, how long will it...

A: It is the given that Theron invested 3000 dollars at an interest rate of 5%. We have to calculate th...

Q: The figure shows the flow of traffic (in vehicles per hour) through a network of streets. 400 - -600...

A: The following steps are used to find the solution of the system of equations AX=B, where A, X and B ...

Q: A marketing class did a survey of the number of fast food outlets near campus. The results of the su...

A: This is a problem of Set Theory.

Q: D1 D2 D3 D4 demand 2- S00 Q.2//This table is the solution of the problem $1 500 Find the optimal sol...

A: Using given table we will find the initial feasible solution and then by stepping stone method we'll...

Q: How many basic variables are needed to solve a transportation problem with M sources and N destinati...

A: We find number of basic variables needed to solve a transportation problem with M sources and N dest...

Q: Let U = {0, 1, 2, 3, ..., 12}. A = {1, R - S1 2 5 7 o C - SO 2 4

A: # we are entitled to solve three subparts at a time, please resubmit the other parts if you wish to ...

Q: Find the minimum and maximum values of z= 2x + 9y, if possible, for the following set of constraints...

A:

Q: 9. Which ordered pair lies on the graph of y = 3(2)*1? (-1,0) B (0, 9) © (1, 12) D (3, 24)

A: The given function is:  y=32x+1 Find the value of y at x=-1: y=32-1+1=320=31=3 The graph of the give...

Q: Parametrize the following two curves in R³ and find their arclength. (1) the intersection of the cyl...

A: Question 1:Given:The intersection of the cylinder x2 + y2 =1 and the plane x+y+z = 1  

Q: If (G,X) be the group of all real 2 x 2 matrices (“ ") such that ad - be + 0 with matrix multiplicat...

A: First we have to show that f:G→G' is homomorphism or not. To show homomorphism, we have to show fAB=...

Q: (a) Identifying whether a function is a convex function is useful because a convex function's local ...

A:

Q: Write a recursive formula for each sequence. 3,-6, 12, -24, ... 2, 6, 10, 14, ... %3D for n 2 2 for ...

A:

Q: If x and x are independent coordinates of a point, show that

A:

Q: Consider the following graph of f(x) and g(x). State the interval where f(x) > g(x 8- f(x) 4- -6 -5 ...

A: If y=f(x), then the variable x is called the input of the function, and the variable y is called the...

Q: A. Each week, Gavriel buys cheese (C) and sausage (S) which provides her a utility of U- 5th root of...

A: We will use  method of lagranges multiplier . To maximize f(x,y) subject to g(x,y)=k  Solve system o...

Q: [2 31 Given A =1 1, B = [4 2) [1 21 1.D = [3 1 2), find 14 (a) A+2B (b) ВС (c) AC (d) DD' (e) D'D

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

Q: Check the DE if it is exact or not. Solve it (if it is not exact use the method by using the integra...

A:

Q: The graph shows a region of feasible solutions. Use this region to find maximum and minimum values o...

A: Given a graph which shows a region of feasible  solutions. We have to find maximum and minimum value...

Q: (x – 6)" 1. f(x) = %3D 4n n=1

A:

Q: Question 2. Suppose that G is a group that has exactly one non-trivial proper subgroup. Prove that G...

A: Given: G is a group that has exactly one non-trivial proper subgroup. To prove: G is cyclic and |G|=...

Q: Find the general solution of the differential equation 14y^(4)+57y''+25y=0

A:

Q: Find a unitary matrix U such that UH AU is diagonal, where (: 4 A = -3 2i 0 -2i

A:

Q: - Solving for the expected return: 537.06 612.25 697.86 795.67 907.07 15446 =- (1+r) (1+r) (1+r)' (1...

A: We can solve this using given information

Q: dy x fan x

A: Introduction: The variable is separated when the differential equation can be written as dydx = f(y)...

Q: -41 Find the adjoint matrix of 01 21 01 -2 C. 4 A. [-2 B. 4 D. 01 -1

A:

Q: Consider the following planes. x + y + z = 3, x + 7y + 7z = 3 (a) Find parametric equations for the ...

A: The given questions are related with planes. Given two planes x +y + z = 3 and x + 7y + 7z = 3 . We ...

Q: By using Gauss-Jordan method, the solution of set following above equations will be 2x1 – 4x2 + 6x3 ...

A:  Here A=2-4613-7759,b=524 The argumented matrix is A:b=2-46:513-7:2759:4

Q: • Find f(22) using Gregory-Newton method: 5 10 15 20 25 f(x) 8.720 17.36 25.88 34.20 42.26

A: Introduction: The formula of Newton-Gregory method is given by, y(x)=y0+p∆y0+p(p-1)2!∆2y0+p(p-1)(p-2...

Q: 6. Use the fact that every odd degree polynomial with real coefficients has a real root to show that...

A: Show that the function f:ℝ→ℝ defined as fx=x5-2x2+x is onto for all x∈ℝ. Definition:  A function f:A...

Q: 5. Let E be a set that bounded and c > 0. Prove that sup(cE) = -c inf(-E) %3D

A: This is a problem of Real topology, metric topology.

Q: Ços e cot & 12.) 1 = Csc e sin &

A:

Q: Prove the following statement by mathematical induction. n+ 1 For every integer n2 0, i I.2' = n- 2"...

A: Right Hand side of P(k) can be evaluated just by substituting n=k in given mathematical statement. I...

Q: Evaluate log(1+i) (1+ v3i) A. 1.442 – 0.246i C. 0.151 + 0.341i - B. 1.198 – 0.215i D. 0.301 + 0.455i

A: Use following formula to find out result  log(z) = log(r) + i θ 

Q: points-2 Decide which of the following statements are true. Select one: O a. If æn does not converge...

A:

Q: Suppose {u, v, w} is an orthonormal set in R". Prove that u +v is not orthogonal to v + w.

A: The set {u, v, w} is an orthonormal set. Therefore, the modulus of each vector is 1. The vectors u, ...

Q: secx - I 10.) sin*x = 11.) 1- CSC X =- 2tan x sec x %3D sec?x I+ CsC X

A:

Q: 1. Let R be a relation defined on the set of rational numbers Q where for a, b E Q, a R b if and onl...

A:

Q: Two airplanes, at points A and B, have elevations of 23,000 feet and 18,000 feet, respectively. Both...

A:

Q: Find the eigenvalues and the correspþnding eigenvectors of the matrix A 8.

A: Given the matrix A=4-28-4 We will find the eigenvalues and the corresponding eigenvectors of A. Eige...

Q: 5. If log, x = 0.3 and loga Y = 1.24, then the value of log, x²y? = %3D

A:

Q: We solve the problem of determining the production of two products (x1, X2), unless their market pri...

A: 1st we will find total profit then will use  Method of lagranges multiplier to maximize it . To maxi...

Q: For the initisl value problem z"+4z' +13z =t, z(0) = -1,z'(0) = 1, the Laplace transform X(s) of the...

A: Properties of Laplace transform  L[y'']=s2Y(s)-sy(0)-y'(0) Ly'=sY(s)-y(0) Ltn=n!sn+1

Q: 7. L {f(t)} where f(t) = t sin 2t sin 5t %3D

A: Use the trigonometric identity sin Asin B=12cosA-B-cosA+B to simplify the given function.  

Q: Solve by the addition method. (If there is no solution, enter NO SOLUTION. Use the parameters x and ...

A:

Q: Show that if a|b and b|a then a=±b.

A: