Solve the system of first-order linear differential equations: x₂ - 6x₂-x₂+2x₂ x₂ = 3x₂-x₂ x₂ = x₂

Q: What is the definition of MATHEMATICS (science-related) pls elaborate in paragpraph

A: The group of sciences (including arithmetic, geometry, algebra, calculus, etc.) dealing with quantit...

Q: Find the inverse to the following matrices by using adjoint method. 1 31 A = 2 1 1 2 2.

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Q: Which of the following quadratics has imaginary roots? (1) x² +3x – 5 = 0 (3) 2x² – 3x+1=0 (2) x² +6...

A: For a quadratic equation: ax2+bx+c=0, the discriminant is calculated using the formula: D=b2-4ac. I...

Q: Solve the initial value problem " + y' – 56y = 0, y(0) = a, y'(0) = –56. Find a so that the solution...

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Q: (a) It, for f: AC R + R, at Xo, Ak > 0 for k odd, or Ag < 0 for k even, then show that f cannot have...

A: Local minimum is also known as relative minimum. A function f has local minimum at a  particular poi...

Q: (a) Find the solution to dy: dt dyz Y1 + 3y2 3y1 – V2 dt with the initial condition y1 (0) = 3, y2(0...

A: Solution a: Given system of differential equation is dy1dt=3y1-y2dy2dt=y1+3y2 with initial condition...

Q: (a) Create a graph with six vertices of degrees 2, 2, 2, 3, 4 and 5. Construct the matrix of the gra...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

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

Q: Use least squares technique find a curve of the form f(x)= a,e“:*4>* to fit the following data 1 2 3...

A: The main objective is to find the curve by using least square technique

Q: Find the Laplace transform of the following: 1) sinh3 4t

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Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

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

Q: Using ɛ-6 argument, prove that f(x) = x-[x] is continuous at all x ERexcept the integers. (Note: [x]...

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Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n...

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Q: Solve and evaluate problem involving Non- Bracketing Method. Use the Newton-Raphson method to obtain...

A: We want to find the value of 2. Let x=2 ⇒x2-2=fx  let ⇒f'x=2x By Newton-Rapson method the zero of th...

Q: Let C denote the unit circle centered at the origin in C. 1 1+ z +z*° dz, dz , Then 2ni where the in...

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Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (2, 4, 6), (6, 3, 2)}...

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Q: 2. Find F' (x) if F(x) = S VE² + Idt.

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Q: Find a value a > 0 so that the graph of the exponential function f(x) = a" contains the point (3, 1/...

A: Given:Exponential function f(x) = ax  

Q: Given -x--y =1 find the entire solution set 2

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Q: Convert the following symbolic statement into words if s=The sunroof is extra, r=The radial tires ar...

A: Introduction: Two simple statements can be joined together by logical connectivities. As a result, w...

Q: Use Simpson's rule with 2n = 10 subintervals to approximate the length of the curve. y = 2cosx, Roun...

A: Given y(x)=2cosx y'(x)=-2sin(x) And Arc Length =∫-π2π21+(y'(x))2dx                            =∫-π2π...

Q: QUESTION 1 Use least squares technique find a curve of the form f(x)= a,e“:* +a3x to fit the followi...

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Q: that specific answer by showing the complete solution set: 1. Find the derivative of the following f...

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Q: Solve the following recurrence: T(n) = 4T(n/2) + n²lgn

A: We wil use masters theorem.

Q: QUESTION 1 Use least squares technique find a curve of the form f(x)=a,e“**3* to fit the following d...

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Q: Determine if g is differentiable at r = 0 if 2 cos r, if -1<r<0 9(r) = %3D if r2 0. r+cos r

A: A function is differentiable at a point if left and right hand derivatives of the function at that p...

Q: Let G be a finite group and H1, H2,…., Hk be subgroups of G. .... (a) Show that N H; = Hị n H2 n..n ...

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Q: 2. Consider a square ABCD and an equilateral triangle BCE in its exterior. Let F be the midpoint of ...

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Q: The position vector of points A, B and C is OA=i+mj+2k,OB =-i+2j- OC = 2i +nj+3k where O is origin, ...

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Q: Dirt is sold by the cubic yard. The Vining family needs to purchase enough dirt to fill a hole that ...

A: Let us consider a cuboid of length L, breadth B , height H then the volume of the cuboid is Volume o...

Q: Solve the integral equation S" F(x) cos px dx = ' - P.01 4. .Hence prove that o sin?t -dt = %D

A: Given the integral equation is ∫0∞Fxcospxdx=1-p,0≤p≤10p&gt;1

Q: What is the value of x? Round to the nearest tenth. 8.45 cm 13.5 cm x = [ ? ] cm %3D

A: Here, we will find the value of x from the given figure.

Q: In a batch of 500 high school students, there are 252 students who own a laptop, 176 students who ow...

A: Here we can use the formula nU = nA+nB-nA∩B+nA∪B' 

Q: 3. Consider the following system of linear equations: x + 2y – z = -1 2.x + 2y + z = 1 3x + 5y – 2z ...

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

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Q: Let z, y, z be digits so that the 9-digit number 5z36y98z2 is divisible by 792. a Without calculatin...

A: Given 9 digit number 5x36y98z2 is divisible by 792. (a) Without calculating x,y explain what is the ...

Q: show that, The compactness of a subset vof fis Sufficient Condition for existness to a best approtio...

A: Best Approximation: An element h*∈V satisfying f-h*=infh∈Vf-h is called the best approximation of f ...

Q: Given the following: (x + 7)" 2n Vn2 – 1 n=2 Determine if the given series converges or diverges whe...

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Q: (a) Find the determinant of the matrix A = where z E R. (Hint: Use row reduction and factor the dete...

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Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the differe...

A: Solution:-

Q: A factory produces three models: copupe, ranchera, and economy. Each car needs the quantities of eac...

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Q: Solve the initial value problem y" + 5y- 36y = 0, y(0) = a, y'(0) = -63. Find a so that the solution...

A: Given differential equation is y'' + 5y' - 36y = 0 with y(0) = α, y'(0) = -63

Q: Prove Vr, y E Z, if ry is even and y is odd, then r + y is odd.

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Q: (a) Find the critical points, if any, of the following function on the given interval. (b) Use a gra...

A: Given: The function, fx=6x4-24x3-93x2+360x+28 and the interval -5,5   (a.) To find: The critical poi...

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0 ...

Q: e theolem Let f be acontinyous fanchion o interior Tand citfble on ay - Point XEI then O f )<o VxeIt...

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Q: test the following series. whether absolute convergence, conditionally convergent, or divergent! а) ...

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Q: Assume u solves the initial value problem Utt - Au = 0 in R" × (0, 0), u = 0, u = h on R" x {t = 0}....

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Q: A particle moves on a fixed surface in F.(0), which is defined by z = 2xy. During the motion, the x ...

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Q: he​ half-life of​ carbon-14

A: Given, the​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tr...