t²y" + 3ty' + y = 0, t> 0; y₁(t) = t-¹

Q: The position of a baseball (in ft) is represented by r(t) = 45√2ti + (3+45√2t - 16t2)j. Find the arc…

A: Given rt=452ti+3+452t-16t2j

Q: Suppose xo = 2√3, yo = 3, Prove that 2xn-14-1 Xn-1+Yn-1 and Yn √xn Yn-1 for all n € N. (b)x=y and…

A: Hints: It is given that x0=23 and y0=3 and  xn=2xn-1yn-1xn-1+yn-1 and yn=xnyn-1 for all n∈ℕ.…

Q: 4. (a) Find the general solution to the following ODE. dy r+y² + xy² +1 dr (b) Given that y(0) = 1,…

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Q: LEG. III. Sys. of Equations III.2. LU Decomposition: Consider A = 162 2 12 5 -1 -3 -1 CHEA SARUN…

A: If any one of  the determinants of the leading submatrices  is 0 then LU decomposition is not…

Q: The following differential equation x³ homogenous D.E. True False -y=0 is a first order

A:

Q: (5) a-1 1 (a) For all n € N and a + 0, show that q" (b) For a sequence (x) in R, suppose that there…

A: Given: (b) xn+1 - xn≤ bn for all n∈N

Q: 8. Define a relation R on the set J = {0, 1,3,4,5,6} as follows: For all x, y EJ, x Ry ⇒ 4x² + y².…

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Q: Q2 (a) A cubic function is given, as follow: f(x) = (x+3)²(x - 2) (i) By taking h = 0.1, determine…

A: Given that: fx=x+32x-2 The objective is to determine the final answer for 2a.1 and 2a.2. Using…

Q: (a) Find the Fourier series for the extended function. (b) Sketch the graph of f(x) as well as the…

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Q: a. Find the area of the shaded section. b. Find the centroid of the shaded of the section from the…

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Q: QUESTION 4 Suppose f is differentiable at a; set d(x) = f(x) - f'(a)(x - a)-f(a). What is d' (a)? O…

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Q: (c) (d) Calculate the following line integrals by using Green's Theorem, where C is the path from…

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Q: Let x²y" + 4xy' - 4y = 0 be an ordinary differential equation. Knowing that y, (x) = x is a solution…

A: we use the standard formula to solve this problems .

Q: Find the solution of the given initial value problem. y (4) — 6y"" +9y" = 0; y(1) = 10+e³, y'(1) =…

A: Sol:- y''''t-6y''' +9y'' =0Rewrite the equation with y=eγteγt'''' -6eγt''' +9eγt''…

Q: Consider the following vectors: a = 5337 -3 Nº 71 = = For each of the following vectors, determine…

A: Given vectors are a→=53-3-1, b→=-501-1, c→=-5-672, v1→=1015-16-6, v2→=-503-2, v3→=75-2-2   To…

Q: Example #3,1" Aid I T LT Is it possible to walk through the warehouse so that you pass through every…

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Q: Given f''(x) = 6x + 5 and f'(0) = 6 and f(0) Find f'(x) and find f(3) = = = - 6.

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Q: A country's census lists the population of the country as 261 million in 1990, 283 million in 2000,…

A: Sol:- Let polynomial be y = ax2+bx+c Given  Year x - value Population 1990 0 261 2000 10 283…

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A: Given differential equation is y''-y'-2y=2 e-x   Let the particular solution of this differential…

Q: 5. Use element proof to show that for any sets A and B, if A ≤ B then A U B = B. 6. Construct an…

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Q: Yn+24yn = 3n-5, yo = y₁ = 0

A: given difference equation yn+2-4yn=3n-5, y0=y1=0

Q: For the system dx dt - It is Choose one ▼ 4 -26 -6 1 ) x + ( =²), determine the critical point x =…

A: Given,            dxdt=4-261-6x+-2-1

Q: 1. A circle with centre C has equation x² + y² − 6x + 4y = 12. (a) By completing the square, express…

A: given equation of the circle x2+y2-6x+4y=12 its has center C

Q: d) sin(arcsin [Select] (4³)) = 1/³ by the Cancellation Property of Inverses 2 2 e) arctan(tan(-g))…

A:

Q: City high school had a student reduction and lost 1/10 of its students. if 198 of its students were…

A: The original number of students were = 220

Q: ) Find the general solution in terms of real functions. From the roots of the characteristic…

A: Given below clear explanation

Q: Consider the following system of linear equations, 3x3 + X4 2x3 + 2x4 3x3 X4 2x1 + X1 3x1 -2x1 X2 +…

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Q: 2. Find the eigenvalues and eigenfunctions of the given boundary value problem. y" + xy = 0; y(0) =…

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Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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Q: x=linspace(1,5*pi/3,50); y=linspace(-pi/2,pi/2,50); z=3*sin(x)^2+y^2+7; how many square units of…

A: The given function is z=3y2sin2x+7 and x=1,5π3,50 , y=-π2,π2,50. To determine: How much fabric is…

Q: i=1 let fi [a, b] →> IR and a) Suppose of and g Prove that fog b) Suppose I and we is g до…

A: let f:a,b→ℝ and g:c,d→a,b (a) suppose f and g are continuous . prove that f∘g is integrable on c,d…

Q: 3. In each of the following problems, determine whether the given function is periodic. If so, find…

A: To Find: (a) cos2πx (b) tan(πx)(c) sin(πnx/L)(d) x2

Q: Find the exact sum of the following series 3 0 In (²) 2 3 5 010 ( 17 ) - 1/1/2 ln 2 3 2 (²) - ²/3 2…

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Q: 3) Suppose that xo 22 and x = 2 + √x-1-2 for n € N. Use the Monotone Convergence Theorem to show…

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Q: Evaluate the iterated integral. Triple Integral: (Outside to inside) Integral from 1 to 7, Integral…

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Q: *Use the following property of the definite integral to estimate the definite integral: f/4 cos x dx…

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Q: 3 2 -5 -4 -3 -2 -1 -1 -2 -3 1/2 3 4 LA At the point shown on the function above, which of the follow…

A: We want to find true option.

Q: The tangent plane to the surface with equation at the point where (x, y) = (1,0) has the equation z…

A: According to guidelines I solve the first question only.So kindly request you to repost the…

Q: What value is printed as a result of executing this algorithm?

A: The algorithm says that how difference of two sets can be evaluated.

Q: 2Q. (b) The set of following data points is given x 1 1.5 2 5.2 y 3.8 4.9 Determine the second order…

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Q: Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the…

A: We have the inequality 17f+2+45.99≤200 We need to solve this inequality. Consider:…

Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A:

Q: The eccentricity is incorrect.

A: As per the question we are given the polar equation of a conic section, and from that equation we…

Q: How do i put this answer in dimensional analysis form with fractions?

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Q: Suppose xo=3 - 2√3, yo = 3, 2xn-14-1 Xn-1+Yn-1 and Prove that (a) xnx and yn ↑ y as n→ ∞o for some…

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Q: Find the focus, directrix, vertex and axis of symmetry for the parabola -8(x + 2) = (y + 1)². Focus…

A: Sol:- Parabola Directrix:-A parabola is the locus of points such that the distance to a point the…

Q: (a) Find the direction for which the directional derivative of the function f(x, y) = 9xy + 2y is a…

A: Formula for directional derivative Du→fP=∇f(P).u^=∇f(P)u^cosθ Du→fP to be maximum angle θmust be 0.…

Q: 1Q: Using Newton's Method solve the following system of equations by taking the initial guess as x =…

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Q: City high school had a student reduction and lost 1/10 of its students. if 198 of its students were…

A: The school lost 110 of its student. The number of students left after reduction was equal to 198. We…

Q: Given ξ= {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q}, P = {b, e, c, j, m, n}, R = {c, l, m,…

A: Given- ξ = a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, P = b, e, c, j, m, n, R = c, l, m, n,…