Find all solutions of the systems of congruences: = 12 (mod 25) 22 (mod 35).

Q: Compute the double integral of f(x, y) = 6x²y over the given shaded domain in the following Figure :…

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Q: egiven differential equation is a model of an undamped spring/mass sy

A: For solve this numerically, we need to convert 2nd order differential to the 1st order code.…

Q: True or false: The series Σ n=1 a. true b. false (-1)"+¹ n 62 +4 converges.

A: We have to check the convergence of the series .

Q: For the system of differential equations, 6 - 5 18 16 a) Find the characteristic polynomial of the…

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Q: Sketch the region of integration for O A. -9 Choose the correct sketch of the region below. 81- O B.…

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Q: Prove the conjecture bn= 2(bn-1)+1, n>=3 using strong induction. Recurrence is given bn=3bn-1-2bn-2…

A: We shall solve these question by use of induction

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros…

A: First we find a root and then use division algorithm

Q: Let c(t) = (cost, sin(2t)). a. Make a table for the parametric curve using t = {0,7,7,7,7,7,7,7, 2n}…

A: The given parametric curve .The aim is to find the values of  and  using the given values of  and…

Q: 2. Let u₁ -8 ] 10 4 Determine if x is in the span of ₁, ₂, and 3. If x is in the span then express…

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Q: Vector field F is given by F(r) = (x, y, z+1) and surface A is the locus of points satisfying z + x²…

A: The given vector field is  and surface A is the locus of the points satisfying  for .To find the…

Q: For each of the following vector fields F, decide whether it is conservative or not by computing the…

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Q: Let E be the 3 x 3 matrix that corresponds to the row operation R3 = R3+3R₁. (a) Find E-¹. (b) Find…

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Q: 2. Is R bounded with respect to this metric? 3. Compare the open balls B(0,2), B(0,4), and B(1, 4).…

A: Sequential compactness.

Q: Wayne’s snowboard is 90 cm long. Luke’s snowboard is 120 cm long. i. Luke’s board is what percent…

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Q: Problem10 a. Euler circuit b. Euler path In the following graph check whether the given graph has an…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5. If A = 1 (6¹), 0 then eª = e 0 e

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Q: Sketch the region of 1/² √1-2² 6x dy dx = V3x integration and evaluate by changing to polar…

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Q: Consider the vector field F (x, y, z) = (3z + 4y)i + (z+4x)j + (y + 3x)k. a) Find a function f such…

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Q: Second Order Diff Eqns: Use the Cauchy-Euler Equations to solve the Initial Value Problem where…

A: The differential equation of the following form is called the Cauchy-Euler equation:It is given that…

Q: x and time t of a particular heat equation is: U(x,t) = [Cn(e-6tn^2)sin(nx) where the sum goes from…

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Q: Shot that f(x) = x^2+ x - 3 has a solution in the interval [0,2]. Determine the number of iterations…

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Q: 4. Let S be a sphere of radius r and P a point inside or outside the sphere. Show that 1 √√₂₁ P |dx|…

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Q: In an M/MA queueing system, the arrival rate is 3 customers per hour and the service rate is 6…

A: Given data Arrival rate  customer per hour Service rate  customer per hour

Q: The matrix A has eigenvalues λ = 1, 2, 3, 4. Is B -4 555 -6 2 6 6 -7 0 3 7 -8 5 5 9 = -3 55 5 -6 3 6…

A: Given that the matrixhas eigenvalues .andWe have to check whether the matrix B is diagonalizable or…

Q: The payoff matrix and strategies P and Q (for the row and column players, respectively) are given.…

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Q: 4. Show that R¹ and R² are not homeomorphic. How about R¹ and Rn for n ≥ 2?

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Q: Use the numbers x0=1, X2=1.5, and X2=2 to find the second lag-range polynomial to F(x)=1/x+1 Then,…

A: (.) Given,  and  (.) Lagrange polynomial for the function  with  data points  is given by,

Q: 3. Find the volume of the solid generated when the area between the two curves is rotated about the…

A: Using cylindrical shell method:The radius of the cylindrical shell is AB=y+1The length of the…

Q: Use Stokes' theorem to evaluate // V x 7.1 ds where 7 = (9y²z, 3xz, 6x²y²) and S is the paraboloid z…

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Q: 5. Consider the series below ∞ 1 n² + n n=1 1 (a) Use partial fraction decomposition to rewrite as…

A: First we partial decompose the given sum. And then find the limit of the partial sums.

Q: Identify the equation of the quadratic function with a vertex of (0, -1), that passes through the…

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Q: the expected payoff to th

A: (a) From the Payoff matrix for row player minimum  elements in R1 is -3 ie 2nd elementR2 is -4 ie…

Q: Using contour integration, evaluate the following integral •2πT 1 4+3 cos 0 de

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Q: . Let S denote the sphere centered at (5, 0, 4) with radius 3, oriented so that the top of 5 points…

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Q: Follow the steps for graphing a rational function to graph the function F(x)= x² +7x-8 x+2 OC. The…

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Q: Use arithmetic series formula to calculate: 15+10+5+0+(-5)+(-10)+(-15)+...+(-5m)

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Q: A company wants to lay cable across a lake. To find the length of the lake, they made the following…

A: Suppose that the  length of the  lake  is  ftFrom the  given figure suppose  that  the  given…

Q: 1. Let D = {(x, y) = R²|x² + y² ≤ 1} be the unit closed disc in R² and E := {(x, y) ≤ D\y = mx for…

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Q: Each character in a password is either a digit [0-9] or lowercase letter [az]. How many valid…

A: We shall count this using basic mathematics.

Q: Write the system given system of differential equation in matrix form. Y₁' = 3y₁ + y2 + 3 sin(4x) Y2…

A: Given, system of differential equations,

Q: Determine the domain of the rational function. (Enter your answer using interval notation.) x³ + x +…

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Q: -18 [7] B -10 -17/9 18 2.0 -10/9 Find the coordinates of in the basis B = {ã,6}. Your answer will be…

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Q: Let b₁ = [¹3] and 62 = [₁¹]. T(62) = 661 +362. (a) The B-matrix of T (in other words, the matrix of…

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Q: Follow the steps to solve the below differential equation using series methods. Assuming the…

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Q: Find the length of the cardioid r= 3-3 cos 0. The length of the cardioid is (Simplify your answer.)…

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Q: Use the Laplace transform to solve the following initial value problem: y" +10y' +25y = 0 y(0) = -1,…

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Q: a) S SR y dA. Y b) S Sy dA

A: Given, D is the region inside the unit circle centered at the origin.L is left half of DR is the…

Q: Problem #10: Consider the following differential equation, (x² − 9)² y" + (x + 3)(x — 7) y' – (x +…

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Q: low many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if…

A: To find the number of different sequences of 4 digits following the given conditions, we can…