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Q: Prove that l17 is the only prime number of the form n²- 64.

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Q: Exercise 6.1.8. Let G be a group and H <Ga cyclic subgroup of G. For any gE G, show gHg¯1 is cyclic.

A: Let G is a group and H≤G a cyclic subgroup of G.   To Show: For any g∈G, gHg-1 is cyclic

Q: Let phi / Q * (sqrt(2)) -> phi(sqrt(2)) be the map given t phi(a+b sqrt 2 )=a-b sqrt 2 . Show that…

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Q: 5. Let F(x, y) = x² + y² + xy + 3. Find the absolute maximum and minimum values of F on D = {(x, y)|…

A: The main objective is to find absolute maximum and minimum of f(x,y) subject to given condition.

Q: A particular antibiotic is introduced to a petri dish co discovered flesh - eating bacteria. The…

A: Since the decay is continuous   therefore at any given time, the population will be N=N01-rt where N…

Q: There are 8 balls in a box: 3 red balls, numbered 1 through 3, and 5 green balls, numbered 1 through…

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Q: If the point density of the solid is determined by the function p(x, y, z) = 3x kg/m³ and if the…

A: To find the mass of the solid that is bounded by the below equations and has a density function of…

Q: 3. Two n xn matrices A, B are called similar if there exists an invertible n x n matrix S such that…

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Q: 00 The series (-1)" In n is n=3 divergent by the Divergence Test O divergent by the Alternating…

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Q: Consider the equation of the surface S given by 3x-3y®z7-2xy = 8, where a is an odd number and B is…

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Q: 3. Consider the vector space V p<? = {ax? + bx + c : a,b, c E R} of quadratic polynomials. Let B be…

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Q: and Suppose z is a function of a and y, and tan Vy2 + x² = z*e6y. Solve for dx dy

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Q: Consider the following statements about the surface of equation 2 = ye- – 2xy? and the point P(0,-2)…

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Q: fined the genral solution

A: Given,         Dx2+Dy2u=0

Q: Test the convergence and ergence of the following ser h+ 2 in

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Q: Next, we must find the total distance traveled by the particle in the given time interval. This is…

A: To find the interval for which the velocity is negative and positive.

Q: 1.0 1.0 -7 -3 for 0< x < 4, Let f(x) 6 - x for 4 < x < 6. Compute the Fourier sine coefficients for…

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Q: This answer is incorrect. :-(

A: Given that,r=6 ftR=12 fth=24 ftDensity of water=62.5 lb/ft3The work required tp pump the water out…

Q: Suppose that a power series 00 f(x) = L anx" %3D n=0 has the radius of convergence p > 0 and that…

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Q: Critic points of an equation problem: Consider the equation f(x, y) = -x* - y3 – 4xy – 6x – y In the…

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Q: Answer the following using Jacobi Method. Show complete solutions. 2.)  9x1 - 13x2 + 4x3 = 111…

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Q: 2.4 If (x, y) = -r* - y" + 2ry – 8r" + 7y, , then in the process of obtaining its critical points…

A: Given a function f(x,y) = -x4-y3+2xy-8x2+7y   Also given the equation obtained during the process of…

Q: 15'C -15°C 26'C Non-Routine Problems Involving Temperature em. d the afternoon sun. The room…

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Q: 10. Find the sum of the series 25 (a) 75 (b) 2 (c) (d) None of the above

A: We have to form a series which sum is 25/2

Q: 5. Solve by finding series solutions about x=D0: (x - 3)y" + 2y' +y = 0

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Q: et A be the sphere having diameter with endpoints (1, –9, –2) and (7, –1, 8). (a) Give an equation…

A: This is a problem of 3D geometry and multi-variable calculus.

Q: Question 4. For the following two graphs, answer the following questions. If your answer is yes,…

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Q: Find the volume of the solid that results by revolving the region enclosed by the curves x= 10 –…

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Q: 2 4 -2 -1 W = span({ 0 }) -1 -2 (a) Find a basis B for W. (c) Write down the dimension of W.

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Q: Draw a suitable control chart for the following data pertaining to the number of foreign coloured…

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Q: Q4. A salesman has to visit the cities A, B, C,D and E. The cost matrix is given below. Solve the…

A: Given: The cost matrix is given below: To solve: The given travelling salesman problem.

Q: 4) Find the area of the region common to the interiors of the cardioids r =1 + cos 0 and r%D 1- cos…

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Q: 1. In how many ways can we distribute eight identical white balls into four distinct containers so…

A: Number of ways of distributing n identical balls into r distinct boxes =n+r-1r-1 Number of ways of…

Q: Consider the function g defined by 1 g(x, y) = cos (Tx /y) + log3 (x – y) In what direction does g…

A: A function g have maximum directional derivative in the direction of  ∇g Maximum rate of change is…

Q: Prove that 17 is the only prime number of the form n°- 64.

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Q: The heights of the 430 National Basketball Association players were listed on team rosters at the…

A: We can solve this by using formula of given problem Part a) (x-µ)/ƒ   Part b) (x-µ)/ƒ   Part c) X…

Q: For the convex set C = {(z,9)+ 13 y.0 < 2.0 < y } (a) Which points are vertices of C? (52/9,35/9)…

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Q: Prove that l17 is the only prime number of the form n²- 64.

A: We have to prove that 17 is only prime number of the form n2−64. Since, n2−64=n+8n−8 Let for some…

Q: If we use the Method for Variation of Paramet nonhomogeneous differential equation for wh W, =…

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Q: 2) Consider a bicyclist whose position s(t), in feet, is given by the table where t is in seconds. t…

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Q: 12. Consider the solid Q bounded by the surface of equation z = x*+ y° and the plans z = 4, yv3 = x,…

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Q: suppose we have a 2m long rod whose temperature is given by the function u(x,t) for x on the beam…

A: The given problem is to find the solution for the heat equation partial differential equation with…

Q: Question #6 C13: "Use derivatives to describe and analyze key features of a graph and sketch…

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Q: Find the general solution for the following differential equations: (a) (1 – xy + x²y²) dx + (xy³ –…

A: As per policy, we are allowed to answer only one question at a time. So, I am answering the second…

Q: Suppose we ALREADY KNOW that this field is conservative in Octant I: F (x, y, ±) = In (æ) + =, In…

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Q: 16. Consider the equation of the surface S given by z = 3r*ya + 3y – 4 Where a is an even number and…

A: Linear approximate equation is the equation of tangent plane.

Q: 2x3 + 2x2 + ax + 3 3. Let f(x) = Which of the following is an oblique asymptote %3D x² + Bx + 1 of…

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Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

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Q: Use The Runge-Kutta Method SoNe the: dy X(I+x), y(0)=3,h20.2

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Q: Use a truth table to show the following equivalence: ~ (~p^q) ^ (p V q) = p

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