Let [a] be a non-zero element of Z43. w| 42. When is an element of Z43 said to be a primitive root?

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Q: II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy) + log3(x – y)" Do as indicated. 1.…

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Q: II. Let U = R I = {x € R|x° – 14x³ + 45x = ( J = {x €R|x° 2}. Find the following. All infinite sets…

A: I={-3,-5,0,5,3} We have I={x∈ℝ|x5-14x3+45x=0} Solve for x in  x5-14x3+45x=0 We get I={-3,-5,0,5,3}…

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Q: 7. Given 2x2y" + xy' + 3y = 0 show that 2x² yn+2) + (4n + 1)xy(n+1) + (2n² – n+ 3)y(n) = 0 %3D

A: To show that the given relation is true we will use the mathematical induction. In mathematical…

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A: Given LPP is Maximize P = 3x1 + x2 + 8x3 Subject to constraints -x1 + x2 + x3 ≥ -103x1 - 8x2 ≥ -15x3…

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Q: Consider the function: 1. Using the laws of Calculus, provide the expression for f'(x)- which will…

A: Given fx=3x3ex. 1.  The first derivative is  f'x=3ex·3x2-ex·x3e2xf'x=33x2-x3ex.

Q: 6. The average value of f(x, y) over the rectangle R = {(x,y) | a<x< b, c<ys d} is 1 fave %3D (6 –…

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Q: 4: Solve the following differential equation using Laplace transform 1. y y, +3yz, y = 4y, - 4e y(0)…

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Q: Problem 2: 2.5 Evaluate the integral using the composite trapezoidal rule with the indicated number…

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Q: Express each of the following in the form a + bi. cosh(1 – i2)

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Q: If X x2(m, mµ²) find the corresponding (a) mgf; and (b) characteristic function.

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Q: Exercise 4: For V = R³, define U = a +b+c= 0}w = { b a - b+ 2c= 0 1. Find bases for U, W 2. Find a…

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Q: Theorem 8. Let B = {u, u,., u,} be an orthonormal basis of an inner product space V. Then a linear…

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Q: Q2 Consider nonnegative integer solutions of the equation…

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Q: 1. If the statement "for some x, P(x)" is false, then the statement "for every x, P(x)" is false. 2.…

A: This is a problem of Logic.

Q: 2. Let L={x,y,z}with the topology r={L,ø,{x},{x,y},{z},{x,z}}. Verify whether L is normal or not.…

A: The given problem is related with topology. Given that L = x, y, z with the topology τ = L, ϕ, x, x,…

Q: 8 3log3 * (16x² – 6)12dxr

A: We will use the property of logarithm function  aloga(b)=b so 3log3(x)= x then we get…

Q: 11. If J = {x € Z|0 |0|. %3D 13. Let F = {x E R|x° is defined }. Then, F is a proper subset of R.…

A: 11) J={x∈ℤ|0&lt;x&lt;4}.  then J={1,2,3}that is order of the set is 3.Thus the number of elements of…

Q: Given the first order differential equation 1.1 using the substitution y = vt. 1.2 dy 2y2+12 = dt…

A: Given differential equation is  dy2y2+t2=dt2yt⇒dydt=2y2+t22yt         .........(1)

Q: [P-2] (kindly provide complete and full solution. i won't like your solution if it is incomplete or…

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Q: Use the method of variation of parameters to find the general solution of the following systems: 16.…

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Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 3s + 2 4s2 + 12s + 9

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Q: Do as indicated. 1. Use Venn diagrams to exhibit A - (BnC) = (A – B) U (A – C). %3D |

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Q: 1. Find the greatest number which divides 64 and 80 completely. 2. Find the least number which when…

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Q: Theorem 1 (For open convex domain). Suppose 2 is a convex open set. Let f be analytic in 2 \{a} and…

A: We can break the integrand {\displaystyle f}, as well as the differential {\displaystyle dz}…

Q: QUESTION 1 Consider the graph G(7,8) With V = {A,B,C,D,E,F,G} and 8 = {AB, AC, AD,AE, AG, BB, BF,…

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Q: A for the following matrix A and let 5 be the vector given below. 1 1 2 -4 A = 0 1 8. - 3 1

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Q: The motion of a liquid in a cylindrical container of radius 2 is described by the velocity field…

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Q: 1 limx→ limx→*" orcosx

A: We have to solve given problems:

Q: II. Let U = R - 아} I = {x € R|x5 – 14x³ + 45x = | 1= {x €R]x° 2}. J = Find the following. All…

A: Given that U=R I=x∈R|x5−14x3+45x=0 that is I=−5,−3,0,5,3 J=x∈R|x2≤6 that is J=−6,6 S=x∈R|2x&gt;2…

Q: 4. Let f:R→Rbe a function defined by f(x)=x for every xe X . Show that f is a continuous.

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