Find the volume of the solid form by revolving the region by the r-axis, the y-axis 3²=1 9 and + = 1, y 20 around the z-axis.

Q: Consider the (scalar) ODE '(t) = ax(t) with initial data (0) = IO.

A: To check the given function x(t) =x0eat solves x'(t)=ax(t) with x(0)=x0

Q: For the following systems, the origin is the equilibrium point. dž a) Write each system in matrix…

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Q: Show that the tangent at any point of the curve whose equations referred to rectangular axes are x =…

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Q: Statement 6.25 Let & denote the set of even integers and O the set of odd integers. Then |E| = |0|.

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Q: 3 ={0.2) 14 The vectors B = 1 (2³) B = [ ²5 ] form a basis. Find a vector x given the B-coordinates…

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Q: You borrow 25500 DHS from your brother and promise to pay back 30000 DHS in twelve (12) months. What…

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Q: Prove that the set {a + b√2 | a, b ∈Q} is countable.

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Q: Product mentally 56 x the power 10 to 3

A: Product mentally 56 x the power 10 to 3

Q: Determine which of the following statements is true about the following tableau: (a) It is the final…

A: Given a tableau for maximization LPP problem, BV P x1 x2 s1 s2 RHS x1 0 1 0 1 -12 20 x2 0 0 1…

Q: How many [1 9 3 0 5 -1 0 3 least-squares 0 -7 -1 -3 X = solutions does the equation below have? 0 6…

A: Given: The matrix equation is given by:                               19030-75-1-103-3x=06-100 To…

Q: (b) Let B be an n × n matrix that satisfies Bk = 0 for some k ≥ 1. Show that every nxn matrix has…

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Q: Q3A. Compute b11 for the inverse matrix B-¹. B O - 2 -5 2 -6 -3 12/07 -1 1 3 12/07

A: B-1 can be calculated by calculating determinant of a matrix and then dividing adjoint of the matrix…

Q: B Evaluate the piecewise function f at the given x-values. Write the answer using function notation…

A: In the given graph, the bold line indicates the function. The open circle is not included in the…

Q: Find the eigenvalues of A, given that A = 4 00 -7 -3 0 -4 -4 1

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Q: 2. Let consider given points: (1,1), (3,2), (4,3), (5,6). (a) Find the best least square fit by a…

A: The least square method is the process of finding the best-fitting curve for a given data set. . The…

Q: Classify each series as absolutely Convergent, Conditionally Convergent, or Divergent. (−1)k+1 6k ∞…

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Q: 10. Using Cauchy's Residue Theorem, evaluate -2π (cos 30)² 1-2p cos 20+p² d0,0 < p < 1.

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Q: Given the initial-value problem: dy dt = 1- t + 4y a) Euler's Method y(0) = 1 Using h = 0.05,…

A: dydt=1-t+4yy0=1h=0.05 Given interval 0≤x≤2

Q: Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

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Q: Consider the following differential equation. (x-y5+ y² sin(x)) dx = (5xy + 2y cos(x)) dy Let M =…

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Q: Evaluate the surface integral ff 4x dS, where S is part of the surface of a paraboloid with…

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Q: Find the area of the region that is bounded by f(x) = r², the tangent line to f(x) at x = -6, and…

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Q: Given the initial-value problem: dy dt = 1- t + 4y y (0) c) 4th Order Runge-Kutta (RK4) Method = 1…

A: Given: The initial problem is given by:                                    dydt=1-t+4y…

Q: points Use the graph of f(x) shown below to find the following integrals. (Click on the graph for a…

A: Area under the bounded region is obtained by using the definite integral . area of rectangle is…

Q: Let the matrix of linear transformation L: L: R² →R¹ be defined -{[1] et S= ].[]}be ordered basis…

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Q: Approximate the root of the equation √x + x² = 7 using the initial value xo = 7 and using the 4th…

A: Given equation is: x+x2=7 and the initial value is x0=7. We have to approximate the root using the…

Q: Let f: C C defined by f(z) = 1 (z-2)(z-1)³ Express "f" as a Laurent series which is valid for the…

A: Laurent series expansion represents an power series with positive and negative terms as well.  So,…

Q: units (of oxygen) per 7. Find the oxygen consumption of a fish that is moving at a speed of 2 feet…

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Q: the system -3x+y+ 6z = 20 8x + 2y + 3z = 51 2x + 5y + z = 23 0) as initial soluti

A: Solution :- first 4 iterations of Gauss-Jacobi Total Equations are 3-3x+y+6z=208x+2y+3z=512x+5y+z=23…

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: Suppose 4 coins are tossed. Find the probability of tossing no heads. (Round to - decimal places.)

A: Given 4 coins are tossed. We have to find the probability of tossing no heads.

Q: Ibu Tami has an antique painting whose value increases following the following functions: V(t) =…

A: Given the value of the painting increases that is governed by the function Vt=1201.3t23. The growth…

Q: 2 g(x)=(x-3)² 2 4 6 X g(x) = 4 0 4

A: Parent function is the function in which some transformation is done to obtain a new function.…

Q: Evaluate the surface integral Fds for the given vector field F and the oriented surface S. In other…

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Q: 2. Consider the following space of measurable functions defined on [0,1]: X = {ƒ : [ ² zf²(x)dx < ∞…

A: As per the question we are given a functional space X along with its norm || ||X Now we have to :…

Q: First derivative of ₂F₁(x): d{2F₁ (a, b; c; x)} = a.b 2F₁ (a +1, b+1; c+1; x) dx C

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Q: 65–68. Improper integrals Improper integrals arise in polar coordi- nates when the radial coordinate…

A: To Evaluate: ∬R11+x2+y22dA, using polar coordinates and taking r as arbitrarily large.

Q: Consider the convergent alternating series If n = 4, then Sn = (-1)" = L. Let S₁, be the nth partial…

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Q: 1- Use the method of Frobenius to obtain series solutions of the following. y" -xy' +y = 0.

A: Given a differential equation y''-xy'+y=0. Let y=∑n=0∞anxn be power series solution of given…

Q: Describe all numbers n EN that satisfy oo(n) = 3. Justify your answer.

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Q: Find the matrix A of the quadratic form associated with the equation. 3x²2xy + 3y2 + 8z² - 27 = 0 A…

A: Given 3x2-2xy+3y2+8z2-27=0 The quadratic form of the equation ax2+by2+cz2+dxy+cxz+fyz and its…

Q: Find the length of the curve 2 ܐܨ 1, a² 6² from the point (a, 0, 0) to the point (x, y, z). x = a…

A: The equation of the given curve is x2a2-y2b2=1, x=acoshza To find the length of the curve from the…

Q: s the set {x ∈R| x2 ∈N} countable? Justify your answer.

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Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

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Q: First derivative of F(x): 4/{2F₁ (a, b; c; x)} = a.b C 2F₁ (a +1, b+1;c + 1; x)

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Q: Solve by a successive approximation procedure, and obtain a result accurate to four significant…

A: Fixed point successive approximation:   (a)  Given equation is     x+x2+1=tan(x)       Rewrite the…

Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions. Label all…

A: We will use following relation between f , f' and f" to draw the graph of y=f(x) * graph y=f(x) will…

Q: For the demand function q=D(p)=square root of 338−p​, find the following. ​a) The elasticity ​b) The…

A: Formulas to be used: Elasticity of Demand The formula to calculate the elasticity of demand is…

Q: Consider the following differential equation. (sin(y) - y sin(x)) dx + (cos(x) + x cos(y) - y) dy =…

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