Find Dy, Dx and the value of x, y,z    x + y + z = 2   6x -4y+5z=31   5x +2y+2z=13

Q: 9 10 12 13 5) Using Rational Root Theorem and Descartes' Rule of signs. Find all roots of f(x)=3x°…

A: Descartes's rule of signs, in algebra, rule for determining the maximum number of positive real…

Q: Let S be the set of all 2 x 2 matrices A = (a;) such that a1 = an. Determine whether or not S is a…

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Q: 2. If the product of matrices cos² 0 cos e sin 0 A = cos 0 sin 0 sin 0 cos² cos o sin sin? cos ó B =…

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Q: 2. Find the Fourier series expansion of: | 0, f(x) = -1<x < 0 sin TX, 0 < x < 1 and then use it to…

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Q: J(s) = s(s +2s +2)

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Q: Exercise 2 Let 1 B = 3 C = These are bases for R? (no need to prove this). Find the change of…

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Q: 6. Find the intersection of the line I and the plane . 1:7 = (4,-1,4) + t(5,-2,3) T: 2x+5y+z+2=0

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Q: 1. Prove that if f(x) is bounded and measurable on E, and c is any constant, OMNIA then S, [f(x) +…

A: Given, f(x) is bounded and measurable on ETo prove: ∫Ef(x)+c=∫Ef(x) dx+c m(E)

Q: Let E be the surface with equation (y – 4/2)? 1. 32 42 8/2, and (a) Give equations of the traces of…

A: The given equation is x232+z252=(y-42)242-1. (a) To sketch: Traces on all coordinate planes and on…

Q: ĐUse the imProved wmethod Solve the: Sayt an x=Sinzt, yl0)=1 ,h20.

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Q: Minimize: Z = x + 3y Subject to: x + 2y > 6 х — у <3 X, y 2 0

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Q: Problem 19. Let g(z) - | S(t)dt, where f(t) is the function graphed below. %3D 3. -4 -2 -1 -3 3 -2…

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Q: a linear system in matrix form. 2. Rewrite the specified linear system in component form. dx dr = 2x…

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Q: y - 2 -1, 3 z - 1 2. Suppose the symmetric equations of lines l1 and l2 are 2 2 - y = z and a = 2…

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Q: Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES: y co) = し h=o.2…

A: Given the ODE y'+5x4y2=0 and  y0=1⇒x0=0, y0=1   Step size h=0.2 Solve using Euler's Method at a…

Q: 1. What does the Fundamental Theorem of Arithmetic tell us about natural numbers?

A: Fundamental theorem of arithmetic : Any natural number can be decomposed uniquely into the product…

Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan 349 630 19 - 45 등 - 공 + 음프…

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Q: 1.) s 10e-35 2.) s² +4 se 3.) s² +1

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Q: linear operator on the finite – dimensional space V. Let c1,...,Cg be the distinct characteristic…

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Q: Solve

A: We use Mathematical Induction method to prove given example.

Q: 4. Determine wether. the semies.Converyes.cor... diverges. K.. CeJ Cn) 3n +1 ... n4 13n-2

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Q: easured the dimensions of the three perpendicular sides of a r 02 cm Y = 7.25 ± 0.03 cm Z = 9.14…

A: In this question, the concept of the differential is applied to find out the uncertainty in the…

Q: 3" + 27+1 (c) Evaluate 5" n=1

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Q: 2. (i) Let A be an invertible matrix. Assume that A = A-1, What are the possible values for det(A)?…

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Q: Use the above formula to write each of the following limits as an integral (a) (b) m%3D0 nm- lim n2…

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Q: Use Gauss-Jordan Elimination to find the inverse of -1 4 2 2 4 2 0 2

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Q: Predicate Logic 1. Suppose that predicates and individuals are defined as follows: S: should be…

A: Answers are written below. Hope this is useful.

Q: Which of the following is not linear in the variable x and y? O 2x-3y =4 %3D O a? + y? = 4 %3D +2…

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Q: Determine d?g/aydx.

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Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, mEn m-nis even. Is this an…

A: The given relation is defined as For all m,n, m E n⇔m-n is even. To Prove or disprove:  whether the…

Q: 2. (i) Let A be an invertible matrix. Assume that A = A-1. What are the possible values for det(A)?…

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Q: 10. (. A is the relation defined on Z as follows: for all x, y € Z, x Ay = x=y (mod 3). Describe the…

A: Given : A is the relation defined on ℤ as-               xAy ⇔ x=y mod 3  for all x, y ∈ ℤ. To find…

Q: , How many ways are there to distribute r+s identical balls among five different children such that…

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Q: dY 1. The system in Section 3.2 - Exercise 1 (previous page): dt Y dt -5 2. The system in Section…

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Q: 1.37] Consider the following problem: Мaximize subject to 3x1 -X1 -2x1 + 6x2 + 2x2 < 2 + X1 X1, 2x2…

A: 1st we will draw graphs for constraints and then use corner points method to find optimal solution…

Q: Q2: Find a root of x - 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that…

A: Solution :-

Q: f(x) = (x² + + 6) cos(4x) 3 х

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Q: Consider the function defned by fCX, y) - y-ex (a) Find the domain and ran ge of f. (b) Draw a conto…

A: Given data  f is a function x&amp;y  f(x,y)=y-ex  (a) find the domain and range of f=? (b) draw a…

Q: In urban gardens, box hill planters need to fence the garden so that other livestock will not…

A: #considering the garden is rectangular length of the garden is x-7 fencing material required is 4x-4…

Q: (a) 으-2y %3D3,y(0) %=D 0 dt

A: Solve the differential equation using Laplace transferoms

Q: Utt = 8uxx for 0 < x < ™ u(x, 0) = x² u(x, 0) = 1/2cos(8x) Uz(0, t) = u„(T, t) = 0 %3D II

A: The given P.D.E is                            utt=8uxx for…

Q: 25. (i) Calculate the determinant of thenxn matrix 1 1 1 0 1 1 0 1 ... ... I 1 1 1 A = 1 1 ... 1 1 1…

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Q: Use the Cayley-Hamilton theorem to find A1, A°, and A“ for the given matrix A. 1 5 1 A = 0 2 1 0 0 2

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Q: 2. If the product of matrices cos² 0 cos e sin 0 A = cos O sin 0 sin² 0 cos² cos o sin sin? ó B =…

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Q: Solve the initial value problem (3+x*)y" + 4y = 0, y(0) = 0, y(0) = 12. If the solution is y = co +…

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Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

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Q: Definition: The area A of the region S that lies under the graph of the continuous function f is the…

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Q: Let U={a,b,c,d,e,f.g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

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Q: For Items (b), label all important points such as intercepts, vertices of parabolas and hyperbolas,…

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Q: 5. (i) Let A be an nxn matrix over C. Show that the eigenvectors corresponding to distinct…

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