Solve all Find gcd(2,3+5i) in Z[i]. Show that 3 + 4i and 4-3i are associates in Z[i]. Determine the splitting field of x4 + x2 + 1 over Q also find its degree over Q.

Q: Let X = (!,2) and T3} U = (1,2-)inel,2,U+ jult. %3D n+1 show that X is not T - space

A: This is a problem of Topology.

Q: Determine the real roots of f(x) = x – 4x – 9 (a) Solve graphically using excel (b) Solve by hand…

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Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

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Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

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Q: Spent students. The equation of the line of best fit is y = 0.9x+18.98. Amount Number of hours spent…

A: Note: The residual for each observation is the difference between actual values of y and predicted…

Q: Find 4³f(x) if f(x) = (3x+ 1)(3x + 4)(3x+7)... (3x+ 19).

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Q: O The circle drawn around a rectangular triangle wit legs long v2 is itself long : a) V2n b) 6л c)…

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Q: True or False. Provide reasons a. Let {A,} be an unbounded sequence of positive terms. Then, lim A,…

A: Introduction: A list of terms is called a sequence. There are two main types of sequences:…

Q: Question 4 a) Jack deposited $1000 in saving account earning 6% interest rate. How much will Jack…

A: According to our company guidelines we are supposed to answer 1st question.  Kindly repost the other…

Q: Using the techniques described in section 2.6.4 of the Course Notes, find the global extrema of the…

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Q: (26. Ax)= x//x² + 1

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Q: Solve the given ODE using Laplace Transform x"(t) – 4x'(t) + 4x(t) = 4e2t; x(0) = –1,x'(0) = –4 %3D

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Q: Find 4°f(x) if f(x) = (3x + 1)(3x + 4)(3x +7) ... (3x+ 19).

A: See answer below

Q: Calculate the flow in the field F along the path C. Flow means line integral F = (x - y) i - (x 2 +…

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Q: Recall that the radius of convergence R of a power series with coefficients a, is found by first…

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Q: 22. Show with one picture that 2/3 is equivalent to 10/15 in a continuous case. Explain how your…

A: Note: To find the equivalent fractions for any given fraction, multiply the numerator and the…

Q: 3.1 If the Laplace transform of coswt is then find the Laplace Transform of the s2+w? following…

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Q: iyz(x)= 20 (1) x-by=D0 (2) A) yo= (1 Blyn= C + 20 Cz こ (1 Cz e 2+x-2

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Q: Calculate the circulation of the field F around the closed curve C. Circulation means line integral…

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Q: (c) A storekeeper has 60m' available for storage of two brands of mineral, drink X and Y. The volume…

A: We will form a linear programming and then solve it graphically

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: To find The volume of the solid in the first octant bounded by the coordinate planes and the plane.

Q: Define a function S: Z + --> Z+ as follows. For each positive integer n, S(n) = the sum of the…

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Q: find The aea bounded by the and the line y-3* Eunve X-+4

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Q: Find the area of the region that is inside the circle r = 6 cos e and outside the cardioid r = 6(1 –…

A: The given problem is to find the area of the region bounded by given curves. Region that is inside…

Q: Let {B,} C R be a sequence and x E [0,1]. Prove that if |B,,41 – B„| 1 'n+: then {B,} is Cauchy and…

A: We give the detailed solution below correcting a slight typo in the problem.

Q: A thermometer reading 60° F is placed in an oven preheated to a constant temperature. Through a…

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Q: Solve the following Cauchy-Euler differential equation: x'y-3xy 3 In(x)-4, x>0 1. Possible answers…

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Q: Find the area of the region bounded by the curves y^2= 2px, y^2= 2qx, x^2= 2ry, x^2=2sy (0<p<9, 0<r…

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Q: Find the number of slacks variables needed and use slack variables to convert each constraint into a…

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Q: Find the curvature and the radius of curvature at the stated point. T r(t) = 11 cos(t)i+ 10 sin(t)j+…

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Q: You want to design a paper cup in the shape of a right circular cone, so that its generatrix has a…

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Q: Find the global maximum and minimum of f (x, y) = (2² – 1)(y² + y) www on each of the following sets…

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Q: enclased by the loop of the curved y= x (x -3)° i's Find the volume generated . 19. T He area…

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Q: y" – 10y + 25y Consider the differential equation It is proposed as a particular solution Yp =…

A: We will find out V'(x) and U'(x) from given system and then we will integrate the get V(x).

Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y = e6 -x 0…

A: Given: the relative maximum of y = ex/6-x2 closest to x = 0 occurs. When you need to solve for an…

Q: Find Fourier series for the function f (x) = x\,- <x< T

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Q: Problem 2. Consider the (covariant) powerset functor P: Set → Set. (a) Define faithful functor.…

A: Solution :-

Q: Evaluate determinant D by:

A: Here we have to solve the determinant of given matrix using Chios method.

Q: Its known that y, = y2(x) = are solutions for the differential equation x²y" – by = 0 the general…

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Q: A spring of constant k=8 N/m hanging from the ceiling is placed at its lower end with an object of…

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Q: For the following function f(2) = Asinz + B cosz, for some non zero constants A and B, defined on…

A: Given,f(x) = Asin(x) + Bcos(x)     where x∈(0 , 2π)or f(x) = A2+B2sin(x+α)where α∈[0 , π] such that…

Q: O If f (y) > f (x*) for any y in R", then x* is the global minimum. If f (y) > f(x*) with ||y – x*||…

A: This is a problem of multivariable calculus.

Q: If the rate of inflation is 3.4% per year, the future price p () (in dollars) of a certain item can…

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Q: Which of the following statements is (are) false if all vectors are in R"? O None of the statements…

A: Solution :-

Q: 3. Let C be the code consisting of solutions to AxT = 0, where %3D 1 10 1 0 1 1 1 0 0 0 1 1 1 1 A =…

A: (i) Consider the given matrix, A=111010111000111 Substitute the value int the equation AxT=0, so we…

Q: 01 11 1.

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Q: Using a specific method, your calculated density of aluminum is d1 = 2.74 g/cm3. Using a different…

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Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

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Q: 2. Let f: (0,-1→ R be a function defined by f (x) = x¯* for every x E (0,-1. Sketch its function…

A: This is a problem of the application of differential calculus.

Q: please send step by step handwritten solution Q1

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