Find the unknowns using Gauss-Jordan Method (express all coefficients in fractions). Apply S-I-N-E. x+y+z-w=-2 x-y-z+w=4 2x+y+z+2w = 5.5 3x +y + 2z-w = 3.5

Q: Example 7.16. Given the table x: 310 320 330 log x: 2.49136 2.50515 2.51851 find the value of log…

A: Taking the origin at x0 =330 and h = 10, we have p = (x-330)/10.

Q: The half-life of a substance is found by using the equation A(t) = A0e−kt   where A(t) is the…

A: GIven: Half life of a substance is given by equation: A(t) = A0e−kt   where A(t) is the amount…

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Q: 1. Find the root of f(x)=x²+2x²-5x-6, using the initial guesses of x₁ = -4.5 x=-1.0 and a…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given f(x)=√x-5;x#5 and g(x)=x+3. Find the domain of (gof)(x)? All real numbers greater than 5. All…

A:

Q: Example 7.1. The table gives the distance in nautical miles of the visible horizon for the given…

A: Here we need to find y at x = 218 ft and x = 410 ft.

Q: (d) on {1,2,3} given by R₁ = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}

A: Use the given set and relation.

Q: Which statement below best describes the graph? 8 6 A X +2+ -4 -6- O Domain = {-4,-3, 0, 2, 7);…

A: We want to find domain and range of given graph.

Q: t²e³t sin 2t 3t

A:

Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: Example 7.31. Obtain the cubic spline for the following data x: 0 1 2 3 y: 2 - 6 -8 2

A: To find:  Cubic spline for the following data: x 0 1 2 3 y 2 -6 -8 2

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A: Matrix and whose columns which are linearly independent

Q: Evaluate the following integrals. *x*+5x x*+5x³+20x+16 2. x(x²+4)² dx

A:

Q: Problem 3 Using Variable Separable, solve x² (y + 1) dx + y² (x - 1) dy = 0

A: Given differential equation is x2(y+1)dx + y2(x-1)dy = 0

Q: Let A and B be two matrices innRREF , if they are row equivalent then A=B.

A:

Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: 1. Determine whether the series ż 1 2n+1 1 2n-1) converges or diverges by examining the

A: Given series is ∑n=1∞12n+1-12n-1

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Q: Use double integrals to find the Moment about the y-axis of a thin plate which occupies the planar…

A: Introduction: The moment My of region R about the y-axis is given by, My=∬Rxδ(x,y)dA where δ(x,y) is…

Q: b) Approximate [₁₂²² + y²dA where D is region inside the upper unit semi-circle centered at the…

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Q: Let M be the surface given by z = y^2 − x^2. Compute its Gaussian and mean curvatures at all points

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Q: Let p and g be continuous functions in an open interval I and ão E I. Show that if Yı and Y2 are any…

A: If y1, y2 are any two solutions of dydx+p(x)y=g(x),    y(x0)=y0. where p and g are two continuous…

Q: Theorem 9.6.1. Let V be a real vector space. A norm ||· || is induced by an inner product if and…

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Q: Rest I Source 1 2 3 15 12 3 Demene 20 2 3 2 8 7 2 4 Supply 25 15 12 52 3 25 7 using North west…

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Q: Industry Sectors Service Trade and Transporation Total sector United States Total Employment 68%…

A: Percentage change for Services: Percentage for 2010 is 68 and for 2020 it is 69% Hence Percentage…

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Q: Let D be the planar region occupied by a thin plate with n and density function 8(x,y) = y². If C C…

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Q: X1 - 3Х2 - 4 X3 = 1 -X1 + X2 - 3x3 = 14 X2-3x3=5

A:

Q: H = {n: n is a positive even integer from 1 to 50} K = {n: n is a prime number from 1 to 50} J = {n:…

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Q: INSTRUCTION: Prove or disprove 1. Show that f: R-{-}→R - {} defined by f(x) 3x-5 = is bijective.…

A: We have f:ℝ--12→ℝ-32 defined by fx=3x-52x+1 We need to check one-one and onto. If a function is…

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Q: Use least-square regression to fit a straight line to the given data below: x y 3 12.3 5 14.1 6 13.0…

A: We have to find the best fitted curve for straight line.

Q: Evaluate curl of A and divergence of curl of A, if A = x²yax + y²zay - 2xzaz

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Q: Use the Simpson's Rule to evaluate the integral fx sin(x)dx. W/H N/" N /H 02/ O

A: We have to evaluate the integral ∫0πxsinxdx. Here, a=0 and b=π Let n=2 Hence, Δx=b−an=π−02=π2.…

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Q: 4, The hardness of ten steel samples was measured and the results were as follows. Sample 1 2 3 4 5…

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Q: Evaluate S(-x+y+z) dx + (x+y-3) dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: A firm faces the production function Q = 4K0.5L0.5 where K is capital and L is labor. a. Find the…

A: Note: As per our guidelines we are supposed to answer to only 3 sub-parts Q=4K0.5L0.5 where K is…

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Q: Drag the three points so they simultaneously follow both a LINEAR pattern and an EXPONENTIAL pattern

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Q: Find the characteristic polynomial of the matrix [200 A = 1 3 2 If the polynomial is 42 3 -1³ +C₁1²…

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Q: Let C, be the curve satisfying |2|=1, C₂ be the curve satisfying |2+1|=12, and C, be the curve…

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Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

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Q: Q.2 The train resistance R(lbs/ton) is measured for the following values of its velocity V(km/hr).…

A: to find a, we take the following three Values of V which are in G.P.

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Q: Let C₁ be a straight line in the Argand plane from (0, 0) to (3, 3), and let C₂ be the path…

A: We have to calculate the following integrals i∫C1z2dz  and ii∫C2z2dz where C1 and C2 are given…