(b) Find a prime p> 5 such that 2 and 3 are both primitive roots modulo P.

Q: Consider the basic feasible solution of a transportation problem given below: 14 10 13 Ou1 11 14 12…

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Q: Find the rank of the matrices sin 0 cos 0 0 0 cos - sin 0 0 where x, y, and z are distinct. A = cos…

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Q: -3 2 B)x0- [14]x0 X'(t) X (t) -

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Q: Find an orthogonal set with the same span (and same number of elements) as 9 27 12 11 9 12 11 -9 13…

A: Here we have to find the orthogonal set of vectors with the same span.

Q: cos - sin 0 0 where x, y, and z are distinct. sin cos 0 0 A: 0 0 cos - sin 0 0 sin 0 cos and B 1 x…

A: For a square matrix of order n×n , the greatest integer r ≤ n , such that there is at least one…

Q: Consider the function f(x) given by the equation. f(x) = 2023 + 2022 + 2023 2021 + 2022 2021 2020 +…

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Q: A stone is thrown straight up from the edge of a roof, 950 feet above the ground, at a speed of 20…

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Q: 4. Compute ind2 (27) modulo 101.

A: We have to Compute ind2 (27) modulo 101.

Q: 4. Let the function x(1) be given by the conditions x (0) = 1 and x(1) = 1x(1) + 2[x(1)]² S…

A: A function  given by conditions, and To find: The second order Taylor polynomial for  about..The…

Q: Suppose that X is a nonempty subset of R that is bounded above. Prove that for every € > 0 there is…

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Q: 4. Solve the Laplace equation on a disk of radius r. with boundary condition given by U(r.,0) =…

A: The Laplace equation on the diskUrr+1rUr+1r2Uθθ=0For symmetrical on θ of U(r,θ)U(r,−π)=U(r,π) ,…

Q: Given the graph of g(x), sketch the graph y=f(2x+2)-3.

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Q: canonical form

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Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm² and whose…

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Q: Determine for which polynomial(s) (x+2) is a factor. Explain your answer. P(x)=x-3x³-16x-12…

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Q: Let U = {10, 11, 13,14,15,16,17,20} be a universal set, and the ordering of elements of U has the…

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Q: 3- Suppose u, v EV and||u|| = ||v|| = 1 and = 1. Prove that u = v

A: Given: Vectors  such that ,  and .To prove that .Concepts used:Properties of Inner Product Spaces:…

Q: S is defined by R(u, v) = (2u + v, u - 3v, u + 4v),0 ≤u≤ 2,1 ≤v≤ 3. Determine the surface integral…

A: We have to determine the surface integral .

Q: (6) Compute ind2 (19) modulo 101.

A: We recall the definition of a primitive root.

Q: Consider the basic feasible solution of a transportation problem given below 14 5 10 14 5 10 13 11…

A: first of all we have to do allocation in the given transportation problem.After allocation, we have…

Q: Problem 2(*). Find [1 1 1 2 1 1 1 3 4 5 det 1 4 9 16 25 1 8 27 64 125 1 16 81 256 625 using…

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Q: Suppose that a linear program with bounded feasible region has I optimal extreme points v1, ..., vl.…

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Q: Everything we've done with systems of 2 linear, constant co- efficient, homogeneous differential…

A: Let     let the charecteristic equation of A is  (or)    ------- (1)       where…

Q: B = {sin(t), sin(2t), sin(3t), sin(4t)} is an orthogonal set in C( [−π, π] ) with (ƒ,9) = = {…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: B = {sin(t), sin(2t), sin(3t), sin(4t)} is an orthogonal set in C( [−â, π] ) with 1 (f,9) = = [**…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 3. Prove that 2 is a primitive root modulo 101.

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Q: Proof by contradiction ● Show for √5 Q.

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Q: Use the minimum-entry and u-v methods to solve the following minimum-cost transportation problem.…

A: Find the solution using Voggel's Approximation method also find optimal solution using the modi…

Q: - Another bowl has the shape of a paraboloid. The equation of the cross- section with the…

A: According to the question, To find the magnitude of the force exerted by the particle on the bowl…

Q: Are the two linear transformations the same? Yes ● S: R² → R², shear such that H maps to H then…

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Q: 6. dk = 2dk−1 +3, for each integer k ≥ 2 d₁ = 2

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Q: 2. Solve for a € [0, π] with the boundary conditions and the initial conditions Hint: cos²x =…

A: Given pdeUtt−c2Uxx=0Boundary conditions:Ux(t)=0 , Ux(π,t)=0Initial conditions:U(x,0)=0 ,…

Q: Use the definition of limit to prove lim = 2x3 = 7. x-5

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Q: (e) Show that va € R, Ve > 0,38 >0 such that f((a-8,a+5)) (f(a)- e. f(a)+c) is equivalent Ao the…

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Q: Let f(x) = x x+1 g'(x) = X . Calculate g'(x), where g(x) is the inverse of f(x).

A: Let f(x) = x/(x + 1)We have to calculate g'(x) , where g(x) is the inverse of f(x).

Q: Which of the following is the best estimate of f f(x)dx where f(x) is given in the figure below? (x)…

A: The area of rectangle is given by length x breadth

Q: .. Let G be a subgroup of E (2) and suppose that I is the translation subgroup of G. Prove that the…

A: We have to Prove that the point group of G is isomorphic to G/T.

Q: d²y dy dt² dt +c- Dirac delta function and F m- = -mg + Fod(t-1) in the 1. CUL

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Q: Determine the Fourier transform of the following signal: _(t+1) u(t+1) x (t) = è

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Q: A large puddle in a field has waves in it on a windy day. The data below gives the depth "d" of the…

A: As per the question we will use desmos to solve the questionAt first we will plot the data points…

Q: f(x)=tan(x)-sin(x)-2.75=0 where x is in radian. Calculate f(x) at .5 and 1.5, and show that a root…

A: We have to do three iterations of Newton-Raphson method and Secant Rule.Also Calculate the…

Q: (a) In cell A6, type 1. Rather than copying the numbers 2 to 25, we can fill down based on the…

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Q: Consider the following functions. f₁₁f₂ R² OR + S₁ (x₁, x₂) = x² sin(x₂) + X₂ exp(x₁) 12 (X₁1×₂) =…

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Q: Assessed Question 4. Suppose you roll a pair of dice until you get a double-six. What is the…

A: According to the given data, find the smallest number of times must be roll the pair of dice at…

Q: 6. If f(x)= 9x²+3x -10, determine f(-1) (2a5b)³ 7. Simplify the following using only positive…

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Q: 7. Evaluate the upper and lower sums for f(x) = 2 + sin x. 0<x<T, with n = 2, 4, and 8. Illustrate…

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Q: Q-1: Given the function f(x) = y = 2x² - 8x + 9 (a) Use completing the square method to convert the…

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Q: S is the portion of the plane z = x + 1 that is inside the cylinder x²+²=4. Determine the surface…

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Q: 2. (Section 17.6) Evaluate Jy²ds where S is the part of z = 3 + y inside a² +y² = 9. S

A: We have to find ∫S∫y2ds where S is the part of z = 3 + y inside x2 + y2 = 9

Q: For an outdoor concert by the city orchestra, concert organizers estimate that 14,000 people will…

A: Given, The numbers of people will attend if it is not raining is 14000=a (say) .And the numbers of…