10. An irreducible polynomial f(x) over a field of characteristic p> SECA ELM
Q: Example 10.33. Applying Euler's method to the equation dy/dx = hy, given y(x) = yo determine its…
A: We need to solve this problem using Euler's Method.
Q: The volume of the solid generated by revolving the region bounded by x2-4y and y2=4x about y = 4 is…
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Q: using the following: a = 2i + 3j + 6k, b = i - j - k a) find the component vector of a onto b b)…
A: Given a = 2i+3j+6kb = i-j-k
Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…
A: There are so many subparts, as per our guideline we can solve only first three subparts. Please…
Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…
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Q: Being careful to allow for parts of the curve being both above and below the x-axis, determine the…
A: Divides the region in two parts .
Q: s these functions O(x) ? f(x) = 10 f(x)= 5 logx f(x)= x2+x+1
A: The big O notation is very significant in analyzing a function. It represents the efficiency of a…
Q: If A is a 5 × 5 real matrix with trace 15 and if 2 and 3 are eigenvalues of A, each with algeraic…
A: Solution: Given A is 5×5 real matrix and trace(A)=15 and we have to find det(A)
Q: a = 3i - j - 4k, b = 2i +4j - 2k, c = -i +6k a. 4a - b b. b * (c - a) c. ||a * b|| d. the angle…
A: Solution : Given, a=3i-j-4k b=2i+4j-2k c=-i+6k a.) 4a-b=4(3i-j-4k)+2i+4j-2k =14i-18k b.)…
Q: 9.W.1 The Gram matrix of an inner product on R2 with respect to the standard basis is G = 1 2 -1 ].…
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Q: Q11) Determine if 8 (t) and 8' (t) even or odd by utilizing properties of Fourier transforms. What…
A: Solution : δ(t) and δ'(t) are real functions. Fourier Transform property : Fourier Transform of even…
Q: Example 10.3. Using the shooting method, solve the boundary value problem y") = y(x), y(@)) = 0 and…
A: Here, we need to solve this boundary problem using shooting method.
Q: Let K be a field extension field F and let a € K be algebric over F.
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Q: Given that A and B is a group. Find out if : A→B is a homomorphism. If it is a homomorphism, also…
A: We have given a map , ϕ : A → B , where A = ℝ , + , B = ℝ* , · such that , ϕx = 2x We know that…
Q: QUESTION 2 A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are…
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Q: Which first order DE is variable separable? dy dx =y²cosx-y²sinx = 1 + xy =ycosx-xsiny =(x-y)² dy dx…
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Q: Solve for the indicated value, and graph the situation showing the solution point. The formula for…
A: Given: The sound intensity D is defined by the equation D=10logII0, where I0=10-12. To find: How…
Q: Q₂/ solve the differential equation. ху 3 xể ý yếu 4 eo
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Q: LUE OF MONEY It is now January 1, 2018, and you will need $1,000 on January 1, 2022, in 4 years. If…
A: Given: P=$750, t=3 years, FV=$1000, n=1 To find: r=?
Q: Find the steady-state vector for the matrix below. (Enter exact value for components as an ordered…
A: To find- Find the steady-state vector for the matrix below. 0.90.20.10.8
Q: Solve the system of differential equations. Jx₁' = 6x12x2 x2 = 2x1 + 10x2 x₁(0) = 16, x₂(0) = − 16…
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Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…
A: Given Liquid density=9000 N/m3. Equilateral triangle with side 2m. Consider a equilateral triangle…
Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…
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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…
A:
Q: 5. An object attached to a spring oscillates around a position and is represented by the function y…
A: Solution
Q: | Example 10.34. Solve the equation y" = x +y with the boundary conditions y(0) = y(1) = 0.
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Q: . Use linear algebra techniques to find the center and the radius of the cle a(x² + y²) +bx+cy + d =…
A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…
Q: c). For each of the given paths, verify Green's Theorem by showing that [y³dx + xºdy=ff(xXx dA.…
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Q: The region E between the paraboloid z = 1 - 2² - y² and the plane z = 0 is shown in the 3D model…
A: We will use cylindrical co ordinate system to find volume
Q: It will be really helpful u can provide detailed solutions... Like show all working
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Q: Rectangle A is the pre-image, and rectangle B is the image. Find the scale factor for this dilation.…
A: Given: Rectangle A is pre-image and rectangle B is image. To find: Find the scale factor for the…
Q: Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t- Transpose of A) Option A))…
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Q: acid, HO₂C H, the first ionizatio Ka₂=4.2. Why is the second carboxyl g
A: Acids will sour substances with the pH values less than 7. Acids can donate their protons. There are…
Q: Prove that the following graph does not contain a Hamilton cycle. a b с d h g e m k
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Q: The sum of the series n-n+1 n! is
A: Solution : To find, ∑n=0∞n2-n+1n! Taylor expansion of ex around 0 ex=∑n=0∞xnn! put x=1; e=∑n=0∞1n!
Q: Example 12.14. Find an optimal solution to the following L.P.P. be computing all basic solutions and…
A: The problem belongs to the concept of L.L.P.
Q: Q3: The polygon traverse ABCDEA shown in figure 2. is to be divided into two equal areas by a…
A: If polygon vertices are(x1,y1),(x2,y2),...............(xn,yn)then…
Q: Use a software program or a graphing utility with matrix capabilities to find the transition matrix…
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Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6
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Q: Complete the following table to evaluate the limit lim Step lim x+√x Step 1 Step 2 Step 3 Step 4…
A: The answers for each step are as follows.
Q: Let S be the solid inside the sphere p = 6cos and below the cone Ø = π/4 Set-up the iterated triple…
A: We have to Set-up the iterated triple integral representing the volume S using Cartesian…
Q: an ellipse from t
A: In the graph we have graphed an ellipse x252+y232=1
Q: If Ø: R→ S is a ring isomorphism. The Ø preserves: O Nilpotent elements O Idempotent elements O…
A: Let ϕ : R → S be ring homomorphism We know that a mapping ϕ : R → S is ring homomorphism if for all…
Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…
A: The shaded region is our required area
Q: 3. Make drawings on a separate page to show your calculation a. I have R249.50. Tickets cost R10,00…
A: # as per the guidelines we are entitled to solve one question(maximum three subparts) at a time,…
Q: What is the value of y in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)? Rectangular form answer please
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Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = secx about…
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Q: 20. Sketch the region enclosed by the given curves. Then find the area of the region enclosed by the…
A: As per our guideline, we are supposed to solve only first three subparts, kindly repost other…
Q: Set up the iterated triple integral that will give the following: (please provide a clearer and…
A: In general, volume integrals are triple integral, which involves the integral with respect to x,y,…
Q: There are three numbers in geometric progression whose sum is 26. If the first is increased by 2,…
A: The arithmetic and geometric progressions are two important rule that terms of a sequence follow to…
![Theorem 10. An irreducible polynomial f (x) over a field of characteristic p>0, is insep
rable if and only if f (x) = F [x²], that is, f (x) is a polynomial in xº.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff615d4af-0f10-456d-810b-66712485e0b6%2Ff760fd26-cb60-489b-8682-abb50e1f279e%2Fvw8fcmi_processed.jpeg&w=3840&q=75)
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- Prove that a polynomial f(x) of positive degree n over the field F has at most n (not necessarily distinct) zeros in F.Suppose that f(x),g(x), and h(x) are polynomials over the field F, each of which has positive degree, and that f(x)=g(x)h(x). Prove that the zeros of f(x) in F consist of the zeros of g(x) in F together with the zeros of h(x) in F.Prove Corollary 8.18: A polynomial of positive degree over the field has at most distinct zeros in
- If a0 in a field F, prove that for every bF the equation ax=b has a unique solution x in F. [Type here][Type here]Let F be a field and f(x)=a0+a1x+...+anxnF[x]. Prove that x1 is a factor of f(x) if and only if a0+a1+...+an=0. Prove that x+1 is a factor of f(x) if and only if a0+a1+...+(1)nan=0.Prove Theorem Suppose is an irreducible polynomial over the field such that divides a product in , then divides some .
- Each of the polynomials in Exercises is irreducible over the given field . Find all zeros of in the field obtained by adjoining a zero of to . (In Exercises and , has three zeros in .)Use Theorem to show that each of the following polynomials is irreducible over the field of rational numbers. Theorem Irreducibility of in Suppose is a polynomial of positive degree with integral coefficients and is a prime integer that does not divide. Let Where for If is irreducible in then is irreducible in .In Exercises , a field , a polynomial over , and an element of the field obtained by adjoining a zero of to are given. In each case: Verify that is irreducible over . Write out a formula for the product of two arbitrary elements and of . Find the multiplicative inverse of the given element of . , ,
