Sketch graphs of the following curves: (a) x² − 2x + 8y +2 = 0 2 (b) x² + 4y² − 16 = Ook

Q: 4. Solve the following system of linear, ordinary, differential equations. dx dt dy dt = 3x - 2y =…

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Q: Show that the tangent to the locus of centre of curvature tan of original curve and makes an angle…

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Q: Here are some counting problems on graphs to challenge you. (g) How many Hamiltonian cycles are in…

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Q: A curve is drawn on a parabolic cylinder so as to cut all the generator. expression for curvature…

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Q: Calculate sin x So √1+x with an estimate error less than 10-6, using Romberg's integration? -dx.

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Q: Which of the following is NOT a property of a binomial experiment?   a. The trials are independent.…

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Q: If one of the vertices of the square circumscribing the circle |z1|= √2 is 2 + √√3i, find the other…

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Q: Solve the non-homogeneous differential equation 2x (3x − 1)y" — (3x + 2)y' — (6x − 8)y = (3x −…

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Q: = function given by llowing heat equation. du at 0x² 1₁ f(x) = X₂ if 0 ≤ 2-x, if1< u(0, 1) = u(2, 1)…

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Q: Let z₁ = 10 + 6i and z₂ = 4 + 6i. Then prove that all the π complex numbers satisfying arg (2) 4 -…

A: The given problem is to prove that for all the complex numbers arg((z-z1)/(z-z2))=π/4  that also…

Q: Find an LU factorization of the matrix A (with L unit lower triangular). [83] - 4 - 3 A = L U = ||

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Q: Consider the plane that passes through the points P = (2,7,3), Q-(-1,7,1) and R= (2-1,3). Two…

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Q: 0, Consider the function f(t) = 1, 0, -2 ≤ t < -1 −1≤t<1 1< t < 2 . Find the Fourier series on [-2,…

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Q: A root of equation tan(x)-tanh(x) lies in (7.0,7.4). Find this root with three decimal place…

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Q: Use the simplex method to solve the problem:  Maximize: P = 3x1 + 2x2  subject to: 5x1 + 2x2 ≤ 20…

A: We Use the simplex method to solve the problem:  Maximize: P = 3x1 + 2x2  subject to: 5x1 + 2x2 ≤ 20…

Q: Setup the Riemann sum S x³ dx = lim n→∞ n k=1 [ f(x) f(x) dx = lim Σ f(x₁)x for the given integral.…

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Q: Q4. Consider the hyperboloid surface z=f(x,y)= 4+x²-4y², Let po be the point (2,-1) find: a. The…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" - y = 5t-10e¯t,…

A: The given initial value problem is        y" - y = 5t - 10e-t . . . . . (1)        y(0) = 0 , y'(0)…

Q: Suppose that OABC is a parallelogram. Let M be the midpoint of OA and let P be the point of…

A: 1st we will draw diagram of the given situation and then find position of P using section formula…

Q: Define the Taylor series of the functions below, up to fifth degree: a. y = sin x @x₁ = 0 b. y =…

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Q: Find an invertible matrix P and a diagonal matrix D such that P¹AP=D. -7 0 -5 A 18 0 18 = 10 0 8 P =…

A: First we will find out eigenvalues and corresponding eigen vectors of the matrix A.

Q: x"+ 4x + 40x = -208(1-1) Initial Conditions: x(0) = 10, x'(0) = -2 8= the Dirac Delta function Find…

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Q: Packaging Find the dimensions of an open rectangular box of maximum volume and having an area of 108…

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Q: Given, f(x)=x2-4x, [−4,8]. Find R3,L3,and M3 and give accompanying accurate sketches

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Q: 4x² - 5y = 34, (√6, −2) Tangent line is 6ху = −72, (−2,6) Tangent line is

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Q: (0)8 (2) — 228(s) + 2n(s) = 0 =

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Q: 5. [3] The life expectancy (in years) for a particular brand of microwave oven is a continuous…

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Q: Consider using the method of Gaussian elimination to solve the following system of linear equations:…

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Q: Gauss method ANG AMTY ple. Solve the system by Gauss (In. many solution) X - + 2z 4 3x + + 2x + 3y…

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Q: If z, and z2 are complex numbers and u = √√₁22, then prove Z1 Z1 Z2 that (23/+1231-5+32 +4+5+23.. =…

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Q: Determine the partial fraction expansion for the rational f - 17s+51 (s+5) (s² +9)

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Q: 10) Consider the following election with five candidates and 21 voters. a) Use the Hare System to…

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Q: 2²2 F = 3xi + 3yj + zk and o is the portion of the cone z = √x² + y² between the planes z = 2 and z…

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Q: Consider the system of differential equations dy 6x - 2y, dt da dt The coefficient matrix […

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Q: Determine all the primes p such that p^2 77 has exactly 5 positive divisors.

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Q: 5. Solve the problem Urr +Urx=0, x, y = (0, π), u(0, y) = u(π, y) = 0, u(x, 0) = sin 5x2 sin 3x,…

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Q: Prove that's is primep, then (a + b)P = (a + b)(mod p), Va; b EZ

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Q: Evaluate the surface integral. [[ xz dS, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: A window has the shape of a parabola above and a circular arc below. Find the area of the window.…

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Q: From the list below select ALL properties of the given function f. f: Z→Z, f(n) = [n+1] f is not a…

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Q: Find the rest of 777 in the division by 3864

A: Solution :- Rest of 777 in the division by 3864First calculate 77=823543Now to find the rest of…

Q: 3) Solve the following boundary-value problems. c) y"(x) + 2y(x) = 0; y(0)+y'(0) = 0; y(2) + y'(2) =…

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Q: Find the rest of 777 in the division by 3864

A: Solution :- Rest of 777 in the division by 3864 First calculate the value of 77=823543Convert the…

Q: For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. -24-14] 84…

A: Given matrix is A = -24-148446

Q: 39-46. Definite integrals Use geometry (not Riemann sums) to evaluate the following definite…

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Q: Find the area of region enclosed by a = t-t², y = t-t³, 0 < t < 1 using Green's Theorem.

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Q: Let f(x) = = cos (2x²) — 1 x² Evaluate the 10th derivative of fat x = 0. f(10) (0) Hint: Build a…

A: Given function is f(x) = cos(2x2) - 1x2

Q: 5) U₂ = 5 Uxx t U(0,€) = 2 U(3,4)=-1 U(x,0) = -x

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Q: A curve is drawn on a parabolic cylinder so as to cut all the generators at same angle. Find the…

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