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Q: For all positive values of a,b and c, determine the equilibrium points of the system * x1 = ax1 -…

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Q: a+b+c+d=13 2a + 3b-c-1 -3a + 4b + 2c + d = 10 a + 2b + c d = 1

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

A: We want to calculate the limit limx→3(x-3)tan(9-x2)sin2(2x-6) To solve this we use the following…

Q: a. 2 uxx = Иxy - 4uy azu J2u azu ди b. + +4 +3+u = 0 ?х у дуг ?х ?x2 ди c. k = 2 ,k < 0 ду 02u ?хг

A: Classification of the Partial Differential equations

Q: Example 8.10. Evaluate by using (i) Trapezoidal rule, 1+ (ii) Simpson's 1/3 rule, (iii) Simpson's…

A: To evaluate ∫06dx1+x2 Using  (i) Trapezoidal rule (ii) Simpson's 1/3 Rule (iii) Simpson's 3/8 Rule.…

Q: 2 – 26s – 47 ( s - 1 ) ( s + 2) ( s + 5) 2ی

A: # As per the guidelines we are entitled to solve one question at a time ,please resubmit the other…

Q: eeded to be solve correctly in

A: Given, the helix                r(t)=cosπt2, sinπt2, t intersects the sphere x2+y2+z2=2 in two…

Q: A Suppose A € M₁ (R)and B. Find the eigenvalues of B = [ = [2lin in terms 2A of the eigenvalues of…

A: Given A∈MnR and matrix is B=0AA2A. We have to find the eigenvalue of B in terms of A. The eigenvalue…

Q: IV. Find Do not simplify your answers. dx 1. cos x + =xcoshy - 2y, where x > 0 cot ¹(x³) sec³ x 2. y…

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Q: Ex. (8) Sol Solve [D²-6D+9] y = 54x+18 k

A: Given differential equation is (D2-6D+9)y = 54x+18

Q: Let f be an arithmetical function (not necessarily multiplicative). Prove that there is a…

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Q: For the following linear system, find the inverse of the coefficient matrix using Gaussian…

A: Solution:-

Q: Is the following a linear combination of A = [-29]. RJ 11 O Yes O No B = = [ ²₁ - ²2 ] · c = [₁ 2] ²…

A: We want to find the given matrix is in linear combination of other or not.

Q: e point of intersection of the lines [4 0] and

A: As per our guideline we are supposed to answer only one question. Here question 8. answered.

Q: Use Cramer's rule to solve the linear system of equations; 2x2 + 5x3 = 1 2x₁ + x₂ + x3 = 1 3x₁ + x₂…

A: Given equations are 2x2 + 5x3 = 12x1+x2+x3 = 13x1+x2 = 2

Q: For this math A = 30, B = 20, C = 11, D = 22. 8 Evaluate the real integral (x ² + A -8 cos(B*x) 2 2…

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Q: 2. Use sketches of regions or number lines to show each pair of equivalent fractions: a. 10 15 95

A: Given :Fraction :                      23 =  1015

Q: Given f(x)=√x-5; x+5 and g(x)=x+3. Find the domain of (gof)(x)?

A: Given f(x) = x-5g(x) = x+3

Q: 1. Use forward and backward difference approximations of O(h) and a centered difference…

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Q: ·25x +8x +43x" (3x4-11x² +9x²-11x+6) (9x²+12x+16) Find f Ax+B C(3x+2)+D 9x²+12x+16 + x²+1 dx if this…

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t"…

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Q: Find the value of F(s) given that; sin 3t, o<t<tπ f(t) = { sin 3t, t<πT Let L[sinzt u(t)-sin3(t…

A: Use the definition to find the Laplace transform of the function sin3t ut-sin3t-πut-π.

Q: -13 2 6 1 The matrix I 09 4 3 3 2-8-1 -2 3 2 10 The Augmented matrix is as follows: -13 2 6 1 -7 09…

A: Given: -13w+2x+6y+z=-7  0w+9x+4y+3z=4  3w+2x-8y-z=-5  -2w+3x+2y+10z=0 To solve the system of…

Q: Use variation of parameters to solve the given system sin 2t x² = (2-1)x - (₂002)¹ X' (4 + Je4t cos…

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Q: Approximate the area of the region enclosed by y = -x² + 4x and x-axis using trapezoidal rule with 8…

A: Given y = -x2 + 4x h = b-aNh = 4-08 = 0.5

Q: 1. State the amplitude, period, and phase shift for y=2 sin(0+20°). Then graph the function.

A: Given function is y=2sinθ+20°. We have to find the amplitude, period and phase shift of the given…

Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

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Q: What is the radius of curvature of the polar curve r = 02 at 0=3/2?

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Q: Find d(u, v), if u = (2, -4,2,-1,-6) and =(4,-6,2,-1,-6). OA √93-√61 O B. √300 OC √73 OD. V8 O E √32…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. log(x+3) 4. lim…

A: Limit of the function

Q: Outline the analysis of variance table for a 22 x 32 factorial design. Discuss how this design may…

A: We need to analyze 22×32 factorial design and its confounding arrangement.We will use an ANOVA…

Q: Find the derivatives of the function x²(xy² y)² = x² - y² )

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Q: Consider the function f(x) = ₁, x = [0, 2]. Construct the 1+z² Lagrange interpolation polynomial…

A: Given function is fx=x21+x2, x∈0,2. We have to construct the Lagrange's interpolation polynomial of…

Q: Find the Fourier Cosine Series of the following periodic function. f(x) = x² 0 < x < 1

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Q: x: 1 f(x): 1 cubic spline interpolation for the data : 2 3 4 5 0 1 0 1

A: We need to find cubic spline interpolation of given data.

Q: Q1): The concentration of salt is given as a function of time by: dx -37.5-3.5x dt at the initial…

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Q: Integrate the following functions over f(x,y) = (x-1) R the given regi and y=x²

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Q: ITI 7 6 5 4 -3 ·2 1 -2-1 -2 12 3 45 5 6 7 8 II x

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Q: Let G=(V, E) be a graph such that • V| ≥ 3, G has exactly 2 leaves, and in G all the non-leaf…

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Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: Given function is y=x2+4x−5. We have to find the first derivative if the given function at x=0 using…

Q: How many meters of cloth 5.2 metre wide will be required to make a conical tent, the radius of whose…

A: Solution

Q: -3.8 The integral 28x³e-x² dx is approximated by Simpson's 3/8 rule with 9 intervals. Let f(x) =…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: Find the 2 x 2 matrix P such that Po is the orthogonal projection of in R2 onto the line consisting…

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Q: Express the following numbers in Cartesian form using either exact expressions or rounding to 2…

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Q: The pressure on a particle at a point (x,y) is given by P(x, y) = x²ln(xy²) a. Find the rate of…

A: As per the question we are given a pressure distribution of a particle moving on xy-plane as :…

Q: PROBLEM: Derive the z-transform for f(t) = sin oot u(t). z¹sin(@T) ANSWER: F(z) : = 1-2 z ¹ cos(@T)…

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Q: What is the Cartesian product of A = {1, 2} and B = {a,b,c}?

A: Given A = 1, 2   and   B = a, b, c

Q: 6x-25x+8x+43x--8x-12 (3x4-11x3 +9x²-11x+6) (9x² +12x+16) + C(3x+2)+D 9x²+12x+16] Find f - [Ax+B x²…

A: Given integral is      (1) Its reduction is ∫Ax+Bx2+1+C(3x+2)+D9x2+12x+16dx We can write it as…

Q: For this math A = 30, B = 20, C = 11, D = 22. | 4. Given the function f(Z) = Z/ (C² – Z²), C as…

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