Find the centroid of the volume formed by revolving about the x – axis the area bounded in the first quadrant between the parabolas x² = 2ky and x² + k² – 4ky = 0. %3D -

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A: Answer is 10.1

Q: 7- The function f(z) = z is: a) Analytic on C b) Analytic only at zo = 0 c) Not analytic

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Q: Use a graphing utility or computer software program with matrix capabilities to write v as a linear ...

A: u1 = (2, 2, -2, -4, 4, 1)u2 = (2, -2, 4, -1, 3, 4)u3 = (4, 3, -2, -1, -1, 2)u4 = (2, 1, -1, 3, 4, 3)...

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Q: 2. K-5InX+3 find dw dr dw

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Q: Q1) For the functions yl-f1(x)-r y2-f2(x)-(*+2)%+1 a) Draw the functions e) Find their domains and r...

A: y1=x5, y2=(x+2)5+1 According to the guidelines I am answering first three parts only.

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Q: i) Obtain the complete and singular integrals of = px+qy + p°q. -31 ii) Find the Laplace transform o...

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Q: Determine the rank and nullity of the matrix. 2 -1 0 1 5 2 1 -4 -1 -4 -1 6 -8 -5 -2 9 The rank of th...

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Q: 1. Consider problem min xí + x5 s.t. ai + x3 0. Verify that the KKT necessary and sufficient condit...

A: We are given a non-linear optimization problem. min x12+x22subject to,x12+x22≤5x1+2x2=4x1,x2≥0.........

Q: For the function:     F(x) = x3/3 – 3/4x2 – 27/2x +39 (i) What is the range of values over which ...

A: Introduction : The function F(x) will be concave downwards if F"(x)<0  

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A: Given: A matrix A∈Mn×nℝ   To show: A=PQ, where P,Q∈Mn×nℝ such that P is positive semi-definite and Q...

Q: Use substitution technique (Vp+qx + x² = z – x) to show that dx 1 Vr2 + x + 2 +x – /2 - In Vx² + x +...

A: see the attachments

Q: a) Determine the perimeter of the triangle with vertices at A (0, −3, 0), B (−3, 0, 4) and C (2, 1, ...

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Q: Problem 4: (Finding and using Taylor series) 1 to show that the Taylor series centered at a = 0 for ...

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Q: Apply Gauss- seidal method to sulve the fotlowing fottowing Lineor Lineur equations 5 X-2 Xz -2X1+lo...

A: Let x1 = a, x2 = b, x3 = c So given equations are5a - 2b = 18-2a + 10b - 2c = -60-2b + 15c = 128

Q: The solution of y' = 5y + e-2¤y2, y(0) = 2 satisfies:

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Q: 1. x(2y – 3)dx + (x² + 1)dy = 0 - dy et-y dx x2 +1 3. xe dy + dx = 0 2.

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

Q: esz+1 dz, where C:|z- 5|= 1, counterclockwise, is z - 25 The value of

A: We have to evaluate the integral ∮ e3z+1z2-25dz over the circle z-5=1. We have to find the points wh...

Q: 1. Use the Euler, improved Euler and Runge-kutta methods to solve the follo wing ODES: dy 9. 3 = x (...

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Q: The force of attraction P = - 10 y-Yo 2-ZO r3 between two particles at points Po: (xo,Yo,Zo) and P:(...

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Q: On each chord of 9x? + 16y? = 144 perpendicular to the x-axis is erected an isosceles right triangle...

A: Given: A chord is drawn perpendicular to the x-axis on the ellipse 9x2+16y2=144 with the ends of the...

Q: n²x, 0<x<1/n fm (x)== { --n²x+2n, 1/n<x<2/n ( 0, 2 n<x<1 uniformly convergent on [0, 1}

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Q: The loudness of sound (L, measured in decibels) perceived by the human ear depends upon intensity le...

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Q: Consider the initial value problem y = sin(xt), y(4) = 1 Use Euler's Method with five steps to appro...

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Q: dy of the following and simplify if possible: dx Determine 3.1 y= Jlnx -8x 3.2 y = 32x + tan x 3.3 y...

A: We have to find dy/dx.

Q: :B Solve the initial value problems dy + 2y = 3, y(0) = 1 1- dt

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

Q: if võ =o, Ji=1 and Ja= 2 estimute 3 %3D by constructing Logrange pelynemial, Ithen with the exact va...

A: It is given that 0=0, 1=1 and 4=2. Estimate the value of 3 by constructing Lagrange polynomial. Find...

Q: that to Sulve the fullowig Apply Jucobis equatisns me =4-5 yu=1-6 - 4 +37

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Q: Which of the folowing functions has +++1°x² + 1 the partial fraction decomposition AEPartialFraction...

A: Given that  Ax2+Bx+Cxx2+1+Dx2+1 i.e. Ax2+1+Bxx2+1+Cx3+Dx2x2x2+1 i.e. Ax2+1+Bxx2+1+Cx3+Dx2x4+x2 i.e. ...

Q: Follow Up: Find the exact value of all 6 trig functions at the given angle. Rationalize all denomina...

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Q: Find the Laplace transform of sin t cos t

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Q: Find the determinant by row reduction to echelon form. 1 -1 9 6 0 1 -7 3 - 1 0 - 8 4 4 -4 30 0 Use r...

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Q: Consider the inner product space R with the usual dot product. Applying the Gram- Schmidt algorithm ...

A: Here given vectors as v1=11, v2=30  

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

A: The vector that passes through the points: Ax1, y1, z1 and Bx2, y2, z2 is defined as AB→=x2-x1i+y2-y...

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

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Q: ipounded instantaneous interest rate curve is given by 6. Assume that the ri(t) = 0.02 + 0.05 In(1 +...

A: Given :The Continuously compounded zero rate curveri (t) = 0.02 + 0.05 ln(1+0.2t)  

Q: Use metaphor/layman's term to discuss Bisection method for solving nonlinear equations.

A: This is a problem of Numerical Analysis.

Q: 15-20 1 Solve the initial-value problem. 15. х*у' + 2ху 3 In x, у(1) 3 2

A: Since you have posted a multiple question according to guildlines I will solve first question(Q15) f...

Q: Consider the region R bounded by the curve y = ln(x), the x− axis and the line x = 5. Determine the ...

A: We will draw the region bounded by given curves and line . and then will find limits for x and y and...

Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are...

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Q: 7.3 0.2 -3.7 1. Diagonalize A = -11.5 1.0 5.5 17.7 1.8 -9.31

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Q: A circle of radius r has area A = r. If a random circle h

A: Given, a circle of radius r has the area A=πr2.  If a random circle has a radius that is uniformly d...

Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide dire...

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Q: Consider the system of linear equations below. Solve for E. 2A - B + 3C -D = 5 A + B - 2D +E = 0 -B ...

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Q: 1. Evaluate the following integrals: g) . dx sin-1 x V1 – x2 h) . cos(sec¬1 x) dx 2/V3 xVx² – 1

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Q: 10. Find the dimension of the subspace of P3 consisting of all polynomials ao + ajx + a2x² +a3x³ for...

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Q: Solve the system of linear equation (SLE) using Inverse Matrix Method. Indicate and label the Invers...

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Q: Find the singular value decompostion of th 1 1 -1 -1 1

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