4. Write the difference between the rational numbers and the irrational numbers, giving an example for each type

Q: Solve (D² + 4)y = 2 tan x ; x>0 , D= 4?

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Q: Consider the inner product space (P2, (,)) with the inner product (p(x), q(x)) = p(0)q(0) + p(1)q(1)…

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Q: 5 2 ; B = -2 -2B

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Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

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Q: Solve the following system of linear equations: 2x + 3y – 4z = 1, - 2w + x + y+ z = 0, w – x + y – z…

A: Given system of linear equations is w−2x+3y−4z=12w+x+y+z=0w−x+y−z=−1........1 We have to find the…

Q: Consider the following two matrices: -2 1 - C = 7 -1 D = 2 3 3 -2 Which of the following four…

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Q: Set up a system of linear equations and solve it to determine the general flow pattern for the…

A: Using Guass Eliminating method for solving the system.

Q: 3. Using the following table find f(x) as polynomial in x -103 6 7 f(x) | 3 -6 | 39 822 1611

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Q: An organization had 14 employees. There are 9 female employees and 5 male employees. How many teams…

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Q: 2-Solve the following logarithmic equations. a) Log, 2 – log 4 b) 2 + 5(3*) =3(3*) x +7/6=0 -

A: We have to solve the given logarithmic equations to find the value of the variable x. For this, we…

Q: Solve the system of linear equations 4y + 3z = 8 , 2x –z = 2, 3x + 2y = 5 by Gauss elimination…

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Q: Exercises 6.1 In Exercises 1-8, show that the given set of functions is orthogonal with respect to…

A: For first question using the results: sin(nπ)=0, cos(2nπ)=cos(0)=1 For second question:If the…

Q: Express 1+ cos a +i sin a in the modulus amplitude form.

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Q: (* if -<x<! (o if 플<x< Find the Fourier series expansion of f(x) = 2

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Q: The equations of three lines are given below. Line 1: y= -4x-6 Line 2: y= Line 3: 4x+ 16y=16 For…

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Q: ed on the

A: In this question, the concept of the Scale Factor is applied. Scale Factor A scale factor is a…

Q: 5 =A

A: Here we use the definition of eigen values to find this-

Q: latiolis • find general solutions; • solve the initial value problem with initial condition y(0) =…

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Q: Example 1.2.1 Here are two simple examples of set e you to verify. (i) U[0, n/(n + 1)) = [0, 1). %3D…

A: We have to verify given result.

Q: Use Green's theorem to find the area integral if V(x.y) = (x²+y®)į+ (x²=y®\j¸ where C is a solid…

A: The given vector is Vx,y=x2+y2i+x2-y2 j and  The given parabola is y=2-x2. We know the Green's…

Q: On our trip, diesel fuel cost averaged €1.80/l.  The currency conversion rate in April 2012 was…

A: Given that, the average fuel cost for one trip is  €1.80.

Q: 5- Graph the following function( Y=-1/4 log ,(3x-6)+1

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Q: 3 zdz =? 8/3 4 4/3 12

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Q: 9 Advantages of a Yector Space. Vector Space is set objects which soie Some properties, Once we get…

A: 1) What makes a set of objects a vector space? Let A is set of objects . It must satisfy following…

Q: Define the sequence {b, } as follows: bo 1 bn bn-1 +n for n > 1 Use induction to prove that an…

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Q: Use generating functions to solve the following recurrence relations with the corresponding initial…

A: Given the recurrence relation as (1)ak=4ak-1, ∀ k≥1, with initial condition a0=1 Therefore, the…

Q: f(t) = sin? 4t + cos? 4t 4+s А. s2+16 C. - С. s2+32 В. s(s?+16) D. s2 +16

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Q: f(t) = te3t cosh 4t s2-6s-7 А. (s2-6s+25)2 s2-6s+7 С. (s2-6s-25)2 s2-6s+25 3. (s2-6s-7)2 s2-6s-25 D.…

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Q: You have just sold your house for $1,100,000 in cash. Your mortgage was originally a​ 30-year…

A: Given: n = 360 FV = 0 PV = 750,000 rate = 5.25%/12 = 0.4375%

Q: Choose the best answer. Consider the following statements regarding the equilibrium points of the…

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Q: olve (2xy*e +

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: 3 4 f(x) 0 2 4 6 8 10 12 14

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Q: The height, h(t), of a baseball, in meters, t seconds after it is tossed out the window can be…

A: Given that, the functions are ht=-4.9t2+7t+15 and gt=4t+1.5. Find the point of intersection of the…

Q: One of the stationary points of the Uncuon Is this a maximum or minimum point of the graph?

A: Given: y=4x5-6x3+x2-2 The stationary point is (-1,1).

Q: A boat traveling with a velocity measured in meters per second is described by the vector 6 = (-2,…

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Q: f(t) = t? cos 6t 2s(108-s?) А. (s2 -36)3 2s(s? -108) C. (s2-36)3 2s(108-s2) В. (s2+36)3 2s(s?-108)…

A: Given function f(t)=t2cos6t. We have to find the Laplace Transform. Formula will use 1.…

Q: Let I = {(a, 0) | a e Z}. Show that I is a prime ideal, but not a maximal ideal of the ring Z×Z.

A: Ideal of a ring

Q: A stone is tossed into the air from ground level with an initial velocity of 35 m/s. Its height at…

A: Given- A stone is tossed into the air from grounded level with an initial velocity of 35 m/s. Its…

Q: D Derive Quadrahic lagrange Model Show Lagrange Model Quadratic Polynomial 2) as dy=axs bx tc ax*+…

A: 1. Lagranges quadratic model is the approximated second-degree function that passes through 3…

Q: Solve the following initial value problem using Laplace transformation d?y + 8y = cos 2t with y(0) =…

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Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: Define the sequence {b, } as follows: bo = 4 %3D b, = bn-1 +2n + 3 for n 2 1 %3D Use induction to…

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Q: [17] For each of the following equations, • find general solutions; • solve the initial value…

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Q: Prove that for every prime p, there exists an integer r, such that r = 16 mod p.

A: To prove: For every prime p, there exists an integer x, such that x8≡16 modp.

Q: A class is taking a multiple choice exam. There are 8 questions and 5 possible answers for each…

A: Given that, There are 8 questions and the possible answers for each question 5, in which one is…

Q: 2. Given U = 7i – j+ k and W = -2î – 5j + 6k, compute a) Proj w V and b) Proj v W

A: To find  The projection of given vectors.

Q: A brewery produces regular beer and a lower-carbohydrate "light* beer. Steady customers of the…

A: Let x represents the number of regular beers and y represents the number of light beer. Form the…

Q: Example 1.4.1 As an easy exercise, check that you believe that lim [0, 1- 1/n] = [0, 1) n-00 lim [0,…

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Q: Let S = {(x, y) : x and y rational numbers}. a. What is the interior of S? Justify your answer by…

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Q: = cot-" (2), a > 0 sin at Prove that L() = cot™

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