Find the change of variable x = Py that transforms the quadratic form x Ax into y Dy as shown. - 20x19x2 - 18x3 +24x₁x2 − 24x2x3 = -2y³ - 19y/2 - 36y3 P=

Q: Prove that fo f = Idom f iff f-¹ is a function from ran f to dom f.

A: Prove That : f-1of=Idom iff f-1is a function from ran f to dom f.

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Q: Set up the iterated double integral equivalent to (refer to the photo) bounded by the points (0,0),…

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Q: . ACB iff P(A) CP(B). . ACB if and only if AUB = B . (A x B) U (C x D) C (AUC) x (BUD)

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Q: 8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p…

A: Given that in ∆ABC AD and BE are altitudes intersecting at P.       The position vectors of…

Q: 17 The diagram shows objects of mass 3 kg and m kg attached to the ends of a light inextensible…

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Q: K Solve the initial value problem for r as a vector function of t. dr Differential equation: Initial…

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Q: 1 15 12 3 -12 -15 (a) Find the expansion factor, X₁, that keeps the direction of the vectors in one…

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Q: Find the equation of osculating sphere and osculating circle at the point (1, 2, 3) on the curve x =…

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Q: 2x² 2 c + xy – y/2 xy + 3y x2 + 3xy + 2y 2 कर = = = 1 = 13 = 0 = = =

A: System of linear equations

Q: 20. Let g(t)= cos(31) +2. (a) Write the parent function and draw one cycle here: (b) Find the…

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Q: How do you know that sup R is a lower bound for S? How do you know that it is greater than or equal…

A: Given: S⊂ℝ is a non-empty set which is bounded below. A set R is defined as R=b∈ℝ|b is a lower bound…

Q: PROBLEM 2: Solve for the optimal solution of the following OR Model: Minimize z = 80x + 60y…

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Q: 6) A homeowner is painting one coat on the side of their home which is 975 square feet, at a speed…

A: Total area to be painted is 975 square feet and speed of painting is 200 square feet per hour.

Q: 2. (a) Let S= A 0 I B A, B & GL (R), B = B, A = (B n ¸ Check whether or not S SP2n(R). Also give an…

A: Here , I use latex to write the answer.

Q: Let y = 3 1 [] [-] and u = 4 -7 Write y as the sum of two orthogonal vectors, one in Span {u} and…

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Q: 5) Find the divergence of (√x² + + z 5) kî + yj vj + zk)

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A: To find the arc length parameter along a curve, we need to first evaluate the integral of the…

Q: Consider a servomechanism that models an automatic pilot. Such a mechanism applies a torque to the…

A: Servomechanism can be modeled by the given initial value problem and is given by Iy''(t)=-ke(t)…

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Q: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1),…

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Q: -2 0-1 -6 -1 0

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Q: 3. Solve (2 + 3x)² + 3(2 + 3x) -36y= ax² + bx + 1 + 2 sin ln(2 + 3x). dx²

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Q: w that : The degree of Q(√√2, √√5) ove least 35. The degree of (√√2, V5) ove most 35. The polynomial…

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Q: Given that A = is used. 1.01 0.991 10.099 1.011 ] and b = [2]. If || 4-1¹||. and an approximation =…

A: We are given the following information. A=1.010.990.0991.01, b=22, and an approximation x~=2,0t. For…

Q: The inductive step of an inductive proof shows that for k > 0, if Στo 2 = 2k+1 – 1, then Σ± 20 =…

A: Mathematical induction proof consists of two steps: 1. The base case : prove that the statement…

Q: 2X Solve the following ODE: (D²- 3D²+4) y = 3 ² ² find yh Using inverse Operator Method e

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Q: For two finite sets A and B. prove that AUB ≤Ã+B. Prove that U [Qn (n, n+1)] is countable.

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Q: Let H be the subset of C consisting of the nth roots of unity. Prove that H is a group under…

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Q: Consider the solid bounded by the planes x = 0, y = 0, and x + y = 2 along with z = 4 - (a) Write…

A: Solution

Q: b) Determine the type of the given equation: xxx +(x-2)2xy + y

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Q: Solve the initial value problem below using the method of Laplace transforms. w" - 6w' +9w=18t+ 78,…

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Q: Find the volume of the solid that is below z = 6-x, above inside the cylinder x² + y² = 3 -√4x²+4y²…

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Q: Find the range and domain @ f(x,y) = x 1Ⓒ fcx, y) = √x== y X-J x+y 3 f(x, y) = y (XI 1@ f(x, y, z) =…

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Q: Let A = a b c d and let k be a scalar. Find a formula that relates det(kA) to k and det(A). Find…

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Q: Σ1 (3)* (?)² i=1 ►Give a combinatorial proof of the following identity (3η) = (²n) HINT: Remember…

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Q: Evaluate the following integral by first converting to an integral in cylindrical coordinates √5…

A: Given, ∫05∫-5-x20∫x2+y2-119-3x2-3y2 (2x-3y) dz dy dx We have to convert an integral in cylindrical…

Q: A. Show that any sequence of positive real numbers either has a subsequence that converges, or else…

A: Construct a new sequence which is easier to study.

Q: Let f(x) = x - x² for 0 ≤ x ≤ 1. What is the Fourier series of the odd component of f(x) on the…

A: Fourier series is the expansion of the periodic function it is a combination of the sine and the…

Q: Let z₁ = 10 + 6i and z₂ = 4 + 6i. Then prove that all the Z- Z1 T complex numbers satisfying arg =…

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Q: Suppose G is a semigroup with the property that for each a∈G, there is a unique a*∈G such that aa*a…

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Q: Consider the following state space representation of a first order systern. x=-3x + 2u y = 2x Which…

A: answer is 5. 4/(s+3)

Q: From the list below select the domain and range of the function that assigns to each pair of…

A: As described, the function f is given as       f(x, y) = max{x, y} Where x and y are positive…

Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

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Q: PROBLEM 2: Solve for the optimal solution of the following OR Model: Minimize z = 80x + 60y…

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Q: Show that the tangent to the locus of centre of curvature P nd makes an angle tan lies in norma…

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Q: Use the definition of the Laplace Transform and the properties of the Dirac Delta generalized…

A: As per guidelines ,I will give solution for first three problems only.

Q: Prove Wilson's theorem that, for any prime p, (p — 1)!= -1 (mod p).

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Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. A…

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Q: 8) Consider the following set of data: 13 7 19 4 46 25 45 14 b) Construct a Frequency Table. c)…

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