Find the four roots of the equation z4 +81=0. Write the roots in the form a + bi.

Q: 3) het fix) = x² + 2x + 2 (a) Explain why fiel is irreducible in 24₂6x5. (5) Why is field? How…

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Q: Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R³…

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Q: 6. Express the negation of each of the following open sentences using quantifier notation, but…

A: Q6(d,e) asked and answered.

Q: For any a ony 1 RIGHT (₂ m)-f(x)d₂] ≤ / (bud) ² max [1/(20) d > ohy f: [dsb] → IR and ony n ≥ 1…

A: (a) Given fx=a3x3+a2x2+a1x+a0 Given SIMPf,n-∫abfxdx≤b-a5180n4maxx∈a,bfivx…

Q: For ony d If'(x)) (V) (x)) SIMP (fin) - f(x) dx | ≤ (b-a) 5 180n4 ETabyl max b where RIGHT(fin) is…

A: (a) Given fx=a3x3+a2x2+a1x+a0 Simpf,n-∫abfxdx≤b-a5180n4maxx∈a,bfivx…

Q: NAROL is a long range hyperbolic navigation system. Suppose two NAROL transmitters are located at…

A: The standard form of the hyperbola is x2a2-y2b2=1. Here, a is the distance between the vertex and…

Q: 1. Find the work done by the force F(x, y, z) = (y² − z²)i +2yzj — x²k on an object moving along the…

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Q: What is the value of x that will give g(x) = 3-13x² - 6x³ a relative min value?

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Q: Now we can do something similar with the two 2-point DFT's to get equations for a; for j = 0,1,2,3:…

A: Given: D.F.T.α0,.....αN-1j=∑k=0N-1αke2πikjN,   j=0,1,....N-1To find: Expressions of two 2-point…

Q: For each of the following equations, find the most general function N(x,y) so that the equation is…

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Q: Problem 1: Given the differential equation ( x²y² + x + y²+ 1) dx + x 2 dy = 0 with the condition y…

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Q: For ohny • ohy f: [dsb] → IR and ony n ≥ 1 RIGHT (f. m)-f(x)dz) ≤ (b-d) ² max [1/(20) n d | SIMP…

A: Given fx=2πe-x22 Therefore f'x=-x2πe-x22 For critical point f"x=0 ⇒x22πe-x22-2πe-x22=0⇒…

Q: Determines the acute angle of intersection of ellipses 4x² + y² - 32x+56= 0 & 6x² + 8y² = 86 at one…

A: 4x2+y2-32x+56=0      (i)6x2+8y2=86      (ii) Putting substituting the value of y2  from equation ii…

Q: dy (a) Find the explicit solution to the initial value problem (x + 1) +y=6re with de y(1) = 10.…

A: x+1dydx+y=6xe-x⇒dydx+yx+1=6xe-xx+1 The integrating factor is  I.F=e∫1x+1dx     =elogx+1=x+1…

Q: Show that 38 = -1 (mod 17). Using this, deduce that 3 is a primitive root of 17.

A: Premitive root modulo 17

Q: Which statement below is the proper way to negate the statement: "Some A are not B (A) No A are B…

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Q: Use exponential regression to fit the following data set. 12 3 4 5 8.8 7.0 5.6 4.5 3.6 model. (Round…

A: The exponential regression is done to fit a dataset into an exponential equation of the form: y=abx,…

Q: Let X = {x|x 2-2), and Y = {x|x <5). Determine the given intersection X n Y. Express the answer in…

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Q: X₁ X₂ 0.S 1.5 2.5 -1.S -S2 S -4-12S ] 1 1 4 3 2 375 1.25 0.75J

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Q: Let T be the linear transformation whose standard matrix is given. Decide if T is a one-to-one…

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Q: 2. (LI-1) Compute the Wronskian for each set of functions below and determine whethe the set is…

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Q: The sum of 2 positive numbers = 70 Find the smallest possible sum of their squares.

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Q: #/2 cos x Reverse the order of integration for f(x,y) dy dx. 00 Given x2y²-2 and x ≤y. Find ffydA R

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Q: Let T: R³ R³ be a linear transformation defined by T(x) = Ax for all x € R³, where 1 0 2-1 A = 0 1…

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Q: You get a new credit card and make an initial charge, but then charge nothing else. The table below…

A: Given that the table below shows your balance B, in dollars, after you have made n monthly payments.…

Q: Solve for the relative min value of y = 5x - 17 In (4x)

A: We have to solve for the relative min value of  y=5x-17ln(4x)

Q: Suppose gcd(a, b) = 1. Prove that ab | c if, and only if a|c and b| c.

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Q: Alicia likes to fence 3 sides of a rectangular lot for his cat. The 4th side of the lot will be a…

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Q: Determine the equation of the pinto contact chord P(3,1) for the ellipse + 2y² - 2 = 0.

A: Given equation of the ellipse is x2+2y2=2 ∴x22+y2=1, a=2, b=1 Given point P3,1 We have to find the…

Q: Determine the interval of convergence and the radius of convergence of the power series x²n n-2 n…

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Q: Which choice gives an example that supports the conjecture, and a counterexample that nows the…

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Q: Problem 5 Consider the function f: R→ R2 given by f(x) = (x,x²). a. Is f a bijection, surjection, or…

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Q: Given the following matrices A and B, find an elementary matrix E such that B = EA: You can resize a…

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Q: (d) The student has just finished learning the first 30 percent of the words. (Give your answers…

A: given dydt=k(M-y) with initial condition y ( 0 ) = 0.    from variable separable method we have…

Q: Let f(x) = Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever…

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Q: 7. Use the Chinese remainder theorem to solve this problem: N = 1 (mod 3) N = 4 (mod 5) N = 6 (mod…

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Q: (9) Consider the substitution homomorphism given by My (Peas) = p (6₂) (You can assume it's a…

A: Given :  μ2 : ℤx → ℤ2 defined by  μ2p(x) = p2 is a homomorphism. a) Show that μ2 is onto. b)…

Q: t dw 4. (i) For t> 0, find the general solutions of +w-t, where p≥ 1 is a constant. 2 dt (ii) For x,…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Through the point P(-2,-7) tangents are drawn to the…

A: The equation of the ellipse is given by     2x2 + y2 + 2x - 3y - 2 = 0 . . . . . . . (1)  Let, the…

Q: 2. Verify that the vector field F(x, y) = (2xy + x-3y)i + (x² −3x+y)j is conservative. Then use the…

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Q: The following matrix A has a triple eigenvalue at Aλ = -1. Compute its Jordan canonical form, and…

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Q: M The function f is discontinuous at x = 1 because f is not defined at x = 1. The function f is…

A: Continuity of the function

Q: 1. Find and Sketch the domain of the function: f(x,y)=√x + Determine the range of the function as…

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Q: The left, right, trapezoidal, and midpoint rule approximations were used to estimatex) dx, where is…

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Q: For the following exercises, consider the scenario: The profit of a company decreased steadily over…

A: Straight line equation is y=a+bx.The normal equations are∑y=an+b∑x∑xy=a∑x+b∑x2The values are…

Q: A rotating light is located 19 feet from a wall. The light completes one rotation every 3 seconds.…

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Q: Solve for the relative max value at x of h(x) = -6x 3x²+3

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Q: Consider the following Gauss-Jordan reduction: [10 -7 00 7-7 Find B₁₂ 1 <-17 10 0 0 -7 0 BA 1-6-6-6…

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Q: Problem 3 points. Give the definition of the image of a function f. : S→T, using the curly-bracket…

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Q: .

A: Given: A=1111 To solve parts (a) , (b) and (c)