The product of x* +x3 + 2x² and 2x2 + 4x + 6 in z, [x]/< x5 + 1 > is: 4x+1 O5x^2+ 5x +1 None Ox*2+2 7iam TheO reserzes:

Q: %3D 2. Prove that -24y of 3. =2x

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Q: is intea rable Primitive aR 2 > X 3 1 2. 1 ラメラ 。 (今さ うx 31 ラ× %3D >入う。

A: we have Fx=0            0≤x&lt;12x-1    1≤x≤2and fx=1     0≤x≤12    1≤x≤2 i The primitive of a…

Q: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

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Q: rivial of

A: To find the non trivial of Z8 as,

Q: Verify that (AB)T = BTAT.

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Q: Hiw- prove that %3D

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Q: Let 1-ff Sysin(r' dvdy . By reversing the order of integration of 1,

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Q: 3dz 1. S 4-5z

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Q: Evaluate the double integral: 4 LA LE 2ydydx

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Q: In Z3×U3, Find the order of (1, 2). Show your work.

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Q: Evaluate the integral. ds 7s- 2 ds = V7s-2

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Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2. a) Show why exactly one…

A: Basic properties of modular arithmetic and gcd will be used in solving this problem. The detailed…

Q: Given: mTRV = 60° M2TRS = (4x)° %3D Prove: x = 30 Z. 60° R (4x)° W

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Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 2. Find the desivative ofy= Binx

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Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

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Q: Prove that the equation x+5x=4cosx cannot have more than one real ro

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Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

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Q: 9. Show that 4x - 251 + 10x? – 15x + 20 is irreducible over Q.

A: Answer

Q: Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn +…

A: The objective is to explain Bessel equation and prove that  (i) Jn+3x+Jn+5x=2xn+4Jn+4x (ii)…

Q: Is z(√2) isomorphic to z(√3)?

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Q: Prove using the IVT. ex + In x = 0 has a solution.

A: IVT: If f is continuous on the closed interval [a, b], f(a) ≠ f(b) and k is any number between f(a)…

Q: Verify Eular,s theorem for z =ax2+2hxy+by2

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Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: use method of false position. to Selution acccurate to- within lo -3x°=0 for osxsI and 3€x<

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Q: Evaluate the integral 4-x² ^2+/4-x²-y² 2 (x² + y² + z²)³/²dzdydx -2 J-V4-x² J2-V4-x²-y²

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Q: 4x 1. Зу': y? %3D

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Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: How can we prove to get dual from primal standard form? from this primal standard form Max.z = c'x…

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Q: Evaluate the integral

A: ∫xndx=xn+1n+1+C

Q: 7P is separable for 1sps0 ylan O ihi

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Q: Use substitution to evaluate the integral. (1) [3x x° 3x²Va +1dx

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Q: Given two polynomials in from of x^3+x^2+x+c =0 x^3+x^2+x+c =0

A: Given: To find their intersection using matrices. Given two polynomials in from of…

Q: 4. Prove that x – 15x³ + 10x² – 21x + 2021 is irreducible in Q[x]. -

A: Given :-  Prove that x5 -15x3 +10x2 -21x +2021 is irreducible in ℚx.

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: How can I find all monic divisors of degree 1 in Z_7 [x], 5x^2+5x+4? please help me get started with…

A: Set of all Polynomials over a field ℤ7 is given by ℤ7x=anxn+an-1xn-1+ . . . +a1x+a0  where a0,a1, .…

Q: The term r ryis homogenous of degree two. -

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Q: the infinite integral of 3x^4-2x^3+6x^2+23x+7/x^2-2x+5

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Q: Evaluate the integral. 0.8 V 16 - 25x2

A: The given integral is  ∫00.8x216-25x2dx

Q: Express x8. -x over Q[æ] and over F2[x] as a product of irreducible

A: Let f(x) = x8 — x. Over Q,f(x) = x(x7 — 1) = xϕ1xϕ7x=xx-11+x+...+x6 Note that  ϕ1x and ϕ7x are…

Q: Which is the expandison of x2-y2

A: Given data:- The given equation, (x2-y2)

Q: Find the interval and radius of conv. of In(1 – x²)

A: The power series representation of given function ln1-x2 is given by: ln1-x2=∑n=1∞-x2nn

Q: Prove that le-2z| 0.

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Q: Solve for z: Inz + In(z – 6) = In(2z), %3D

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Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: 1. Use substitution technique to show that ++x+2+x- v2 +C dr 1 In rV+r+2 +x+2+r+ V2

A: As per our guidelines we are supposed to answer only one question that is the first question. For…

Q: Prove that: 3-4x² dx 4VIn3

A: The given integral is I=∫0∞3-4x2dx. The idea is to evaluate the above integral using gamma function.…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.