The points A, B and C have coordinates (3, -2, 4), (5, 4, 0) and (11, 6, -4) respectively. Find the vector BA ) (i) (b) (c) (ii) Show that the size of angle ABC is The line / has equation r = (i) Verify that C lies on 7. (ii) 8 -3+A 32 Show that AB is parallel to 1. 1 3 COS-¹ (-/-) The quadrilateral ABCD is a parallelogram. Find the coordinates of D.

Q: Q1: Find the Fourier series of the following functions form>t> 0 ₁. ƒ (0) = { ²/₁2 1 for 2n>t>n 2t…

A: According to our guidelines we can answer only one question and rest can be reposted.

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A: We must use row reduced Echolon form

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Q: 2. Determine whether the following vectors span the vector space P₂: P₁ = 1+ 3x + 2x², P2 = 3-x+3x²,…

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A: We will use Laplace transformation table  f't  = s Fs− f0f'' t= s2 Fs − s f0 − f0Lsinat=aa2+s2

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Q: 124x₁ + 245x₂ + 35x3 + 24x4 = 24 356x1 + 24x2 + 35x3 + 75x4 = 2 24x₁ +56x2 + 35x3 + 67x4 = 47 256x₁…

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Q: - f(x) = бе -чтх -3.5

A: The given problem is to find the inverse Laplace transform of the given function. Given function…

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Q: (i) (ii) Calculate (2 + i√5)(√5 - i). Hence verify that (√5 - i) is a root of the equa (2 + i√5)2 =…

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

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A: Sol:- y''' +y' =tantThe general solution to anxyn+...+a1xy'+a0xy=gx can be written asy=yc+ypyc is…

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Q: Verify that the given functions y₁(t) = t and y2(t) = te³t satisfy the corresponding homogeneous…

A: Given solutions are y1t=ty2t=te3t Given differential equation is t2y''-t3t+2y'+3t+2y=7t3…

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A: A mathematical method called a linear programming problem (LPP) is used to maximise or reduce the…

Q: Q2: Test the convergence of the following series 1. Σ=o cos(ηπ)· η 3η+1 2. Σñ=o(−1)n+1 (n!)2 (2η)!…

A: Note:- Our guidelines we are supposed to answer only one question. Kindly repost other question as…

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Q: 5. At a sunglass manufacturing company, the estimated average cost function for producing a new line…

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Q: Use the binomial series to expand the function as a power series. Find the radius of convergence. +…

A: We use binomial series to expand the function as power series.

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A: Here we have to find given questions of graph theory  using given graph.

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Q: Solve the heat equation ku əx² = u(0, t) = 0, u(L, t) = 0 u(x, 0) = x(L − x) ди 0 0 subject to the…

A: Use separation of variables to get a fourier series solution

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Q: 9. Given a recurrence relation a₁ = 8an-1- 16an-2, with a = 2 and a₁ = 6 Find explicit formula for…

A: The solution is given as

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A: Principal of Inclusion-Exclusion:                 A∪B∪C=A+B+C-A∩B-A∩C-B∩C+A∩B∩C Here A, B, C denote…

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Q: 21: Find Maclaurim expression for the following functions 1. f(x)= sinh(x). 2. f(x)=sin(x). 3.…

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Q: 7. Find the number of distinguishable permutations of the given letters. a) CHOCOLATE b)…

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Q: (a) The speed of waves in shallow water is given by the following equation. 6.3d v² = Aλ tanh 2 the…

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Q: Solve for x= 0.5 the initial value problem (I.v.p and Use: Euler method

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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A: we will find work done to pull a small portion of cable and then integrate it to find total work…

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Q: 1. Find the Laplace Transformation of the following function. First express the function in terms of…

A: What is your table? Use the formula and properties of laplace transform we solve the problem.

Q: 7. Let A- -2 4 70 % -4-2 N N 2 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

A: A)A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such that…

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Q: Find the general solution of the x²y" + xy' − y = 3x, x‡0;

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Consider finding the root of f(x) = e*(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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Q: While studying for Test 2, Miguel says to his classmates "Fermat's Theorem (page 5 in Lecture Notes…

A: According to Miguel's statement Fermat's theorem is " For a function f(x), if f'(x)=0, then f has…

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Q: Let Σ={a, b} 1- Find a CFG defining the language of all words that contain exactly two b's not more.…

A: Given: Let Σ=a,b.   To find / build: (1.) A CFG defining the language of all words that contain…

Q: A loan shark lends you $50 at 1% compound interest per week (this is a weekly, not an annual rate).…

A: The lent amount is $50. The compound rate of interest is 1% per week. We need to determine the…