Let D be a UFD. Show that a nonconstant factor of a primitive polynomial in D[x] is again a primitive polynomial.

Q: y" - 4y + 4y = 0, y(0) = 8.1, y´(0) = 3.!

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Q: Solve the system of equations in three variables. 2x+y 2z=-1 3x - 3y-z = 5 z-2y+3z=6

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Q: 3. How many 4-digit positive integers are there that are even or contain no O's?

A: Suppose that ,   A -  denotes the 4 digits positive integers that are even. B- denotes the 4 digits…

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Q: Write the following complex numbers in Cartesian from. Simplify as much as possible. (2 – 3i)(3+5i)…

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Q: 3. Residential power consumption has shown certain trends over recent years. Based on date…

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Q: Construct a truth table for the given statement. q~p

A: Truth table: The truth table is a tabular view of all combinations of values for the inputs and…

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Q: = 0 has solutions that generate a vector subspace V. The system of equations Ax i. Solve the system,…

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Q: We select 38 even positive integers, all less than 1000. Prove that there will be two of them whose…

A: Given statement is Here we can select 38 even positive integers all are less than 1000. let…

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A: Euler circuit by adding an edge

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Q: 1.Find the eigenvalues and eigenvectors of the matrix

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Q: The system of equations Ax = 0 has solutions that generate a vector subspace V. i. Solve the system,…

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Q: Determine whether the following statements are True or False. (Select your answers from the dropdown…

A: False-    since we know that a graph can cross a horizontal asymptote but it can never cross the…

Q: Activity (DO THIS IN YOUR NOTEBOOK) A. State whether f(x) is an exponential growth or exponential…

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Q: (d) Give a subset of R2 that is both open and closed, and give one that is neither open nor closed.

A: A subset of R2, that is both open and closed is the empty set. Since, there is no point in empty…

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Q: Design a circuit to take input signals P, Q, and R and output a 1 if, and only if, P and Q have the…

A: It is given that the output signal S is 1 if ad only if P=Q≠R. So, the truth table for the circuit…

Q: Suppose that f(x) < g(x) for all x in an interval I. What would be true regarding a graph displaying…

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Q: the limit cannot be zero for part b?

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Q: Compute the Taylor polynomial of degree 3 of f(x) = ex around x = 1. How do you think the one of…

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Q: Use Laplace transforms to solve the initial value problems y" - 6y + 5y = 29 cos 21, y(0) = 3.2,…

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Q: Select all of the graphs in which the intermediate value theorem would apply for the interval [1,5].…

A: Intermediate value theorem: If a function f is continuous on [a, b] then the function will take any…

Q: f(x)=x². [-9,1] Yes, the Mean Value Theorem can be applied. O No, because f is not continuous on the…

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Q: -0.5 1. The graph of f(t) is shown below. 8,2 0,5 Carefully sketch a graph of F(x) = f(t)dt on the…

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Q: find an explicit solution of the given initial - value problem

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Q: Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue 8.…

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Q: dy exy- dx = e-y +e-2x-.

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Q: Remaining Time: 00:38:40 If the points Z and A and B are represented by the complex numbers z and…

A: We draw the triangle AZB with the complex number written in the diagram. A = (4 -7i) B = (-2 -7i) Z

Q: The principal represent it an amount of money deposit in a savings account, subject, and compound…

A: Given Principal  amount P=$30000Interest Rate  r =5.0%=5100=0.05Compounded daily , n=365 Time t = 20…

Q: If the inflation rate is 4% per year and the market interest rate is known to be 10% per year, what…

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Q: use Equation in the picture to verify that λ and v are an eigenvalue/eigenvector pair for the given…

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Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

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Q: Q3 a. The slope of the tangent at x = 0 slope=y, у-вн f(x)=y=32²-6 y-y₁ = m(x-x₁) For the function y…

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Q: 5. Simplify the expression using a Pythagorean identity: 6. Simplify the expression using a…

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Q: large church's organ is divided into two parts, one in the front and one in the back. When both…

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Q: II. Determine the point(s) of intersection, m, and m₂, and the angle(s) of intersection of the given…

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Q: Evaluate the limit. lim ||A||-0 Δ ο Σ. (x - x;) Δx, where i = 1 and Ax = - 1 n where x, = an n…

A: Given,               lim∆→0∑i=1nxi2-xi7∆x,  Where xi=1n and ∆x=1n.

Q: Can anybody review this, and maybe submit it in a format that can be followed?  The response should…

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Q: What is the coefficient of ?^11?^13 in the expansion (−3?+4?)^24.

A: It is asked to find coefficient of x11.y13 in the expansion of (-3x+4y)24.

Q: differential Solve the fy' xy² + 2xy = ху ху (9 (0) = 1 equa hon

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Q: (b) Let G be a group and let x E G. Suppose that (x) is a cyclic group of order N. Let m and n be…

A: We make use of the gcd to answer this question. DEtails are given in step 2.

Q: 2v 2ycos3

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Q: Problem 2: Twelve cars were equipped with radial tires and driven over a test course. Then the same…

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Q: Solve: y' + 7y +9y' +9y=0 y(x)

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Q: Find the first derivatives. 1. f(1) = (1² + 1)5 2. f(P) = P³ + 3. v(1) = 41² +11V1 + 1 4. g(y) =…

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