Let (Q, +..) is field of rational numbers and f(x) = 6x² - 3 € Q(X), show that whether f(x) reducible polynomial or not?

Q: . Find the parametric and Cartesian equations of the line connecting the points A (1, 2, -1) and B…

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Q: Which of the following equations is a linear differential equation? (choose all possible answer) A B…

A: We have to examine which of the differential equations are linear

Q: 4. Select the statement that is the negation of the statement "Some pilots are pirates." A. All…

A: Want : To find negation of given statement.

Q: atebnu) drog temban 90X19 Perform the mathematical operation and express the answ standard form. 1.…

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Q: Σ() k=0 1. Give a combinatorial proof of the identity - - 2" by using lattice paths...

A: Given : ∑k=0n nk=2n Prove : ∑k=0n nk=2n

Q: 2. A.tank initially contain Water runs into the ta out at the same rate. E 15 min? How long do the…

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Q: 3) dx 2 ·0 CSC csc y dx + sec ³x d y = 710185²³ 3x dup бу

A: Here we have to find the solution of the differential equation cosecydx+sec2xdy=0.

Q: x²+x-6 x -3x²5x - 24 1. Consider the limit lim (a) Use a table to estimate the value of the limit…

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Q: Let R1 = {(a, b) ∈ P^2 ∶ a divides b} and R2 = {(a, b) ∈ P^2 ∶ a is a multiple of b} where P is the…

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Q: (d) Is the original statement true or false? If true, explain. If false, give a specific…

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Q: Newton's law of cooling says that the rate at which a body cools is proportional to the difference…

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Q: Q1. Find the general solution for the following differential equation: -y² (x²ex² - y²)dx + xydy=0

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Q: 2. Let V₁, ..., Vk be points in R³ and suppose that for j = 1, ..., k an object with mass mj is…

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Q: Solve the ordinary differential equation 6x2y” + 6xy’ = 294y - 6x2y . Then evaluate the first four…

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Q: 2. For each of the following sequences, determine whether or not a graph exists that has this degree…

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Q: Suppose f(): R" → R (n = 3) is given by fy:=x²z-2xy + 4yz. 0 (a) Find Vf(x) where x := 3 2 (b) With…

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Q: Use any of these formula (an = 1/2 (ª₁ + an ) or an = 7/7 [ 2ª₁ + (n − 1)d ] to solve for the sum of…

A: For across   1. Sum of the first 15 counting numbers  Applying the provided formula. It is given by…

Q: Solve the given problem completely. Show your solution. In a dance crew with 32 members, 9 are are…

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Q: Show that the following limit does not exist: Given f(x, y) = ey (xy + x), show that xy ³ lim…

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Q: Evaluate and express in Polar Form T=j06-j08 + j2022 a.

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Q: Let us divide the odd positive integers into two arithmetic progressions; the red numbers are 1, 5,…

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Q: jKk 2 -1 -4 -2 +1 1-2 Solve Matrix

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Q: 4.2 Related Rates (#differentiation) Solve the following problems using the related rates method.…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: II. Suppose that the total worldwide sales for a song album are approximated by the function: 150x³…

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

Q: 4) dx + (x +ln(x + 2y- +In(2x + y

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Q: If g(x) = ln(6−x / 2x+1) (a) What is the domain of g(x)? (b) Verify (with a sketch and/or short…

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Q: 2. Solve the initial value problem. (1 + tª)dx + t(1 + x²)dt = 0, _x(0) = 1

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Q: . Find the values of the unknowns which satisfy the following equations: a) (sin x, sin 2x, ln e)…

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Q: Let U, V are two orthonormal matrices of Rnxn Prove or Reject: a. Sum of U + V is also orthonormal

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Q: B: Solve the equation f(x) = e¯* + sin™x use Newton Raphson Method, Xo= 0.

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Q: U =R A = {a EN a is a multiple of 3 less than 15} 1 B = {be Z-15 4} Describe set A using roster…

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Q: 4. (4x 2+1)y'-y² 5. (y-1) dx-(x + 1) dy=0 6. (x²-1) dy + (y + 1) dx=0

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Q: 1. State whether the following statements are true or false. Justify with a short proof c counter…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

Q: x sin(x) lim x+0 x - x cos(x)

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Q: y²dx+x(x+y) dy=0 A xy² = c(x+2y) x²y=c(x+2y) xy² = c(2xy) x+y²=c(2xy) B C D

A: Given: The equation is y2dx+x(x+y)dy=0. To find: The correct option for the solution of the given…

Q: Question 21. Let In be the n×n identity matrix. Let ū be a unit vector in R". Define H₂ = In − 2ûû™…

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Q: 3. A seventy-liter tank initially is half full of water. A solution containing 20 a well-stirred g/L…

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Q: 1. Below is a drawing of a graph G = (VG, EG), and then the vertex set and edge set of a graph H…

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Q: 1-7 65-4 52-45+16 2-L-¹ [ 6 25-8 3-2S 95²-16 + 8+65 4 S²+9¹

A: We will use inverse  Laplace transform table  Only one question is allowed to be solved at a time ,…

Q: The velocity of a particle along the s-axis is given by v = 659/8 where s is in millimeters and vis…

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Q: The histogram Height for 355 students. Frequency 40- 30- 20- 10-

A: A histogram is a visual depiction of how values in a set of data are distributed. A histogram is…

Q: Let y = e¯* (Acos(x) + Bsin(x)) be the solution of the initial value problem for the differential…

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Q: Let u, w R" with |||| = 2 and |||| 2w = 6v. There are two parts to the proof. Part 1: Suppose 2 =…

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Q: What is (n) gi equal to in e-notation? Σ

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Q: You are calibrating a temperature sensor that you believe will have a linear input/output…

A: Given: The below table: The relation is linear and is described by the equation V=a1T+a0. To find:…

Q: 3. Complex Variables as: Given the following complex function expressed C. w = f(z) = 6z² + 8z +…

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Q: Simplify the following functions. Show your work: (a) F(A,B,C,D) = Σm (2, 4, 7, 10, 12, 14) (b) F(x,…

A: Given:   (a) F(A, B, C, D) = ∑m(2, 4, 7, 10, 12, 14)(b) F(x, y, x) = ∏M(3, 5, 7)(c) F(x, y, z) =…

Q: Using the Fundamental Theorem of Calculus, show that the integral 0² f дхду SSR 2 2x² -(x, y) dA, R…

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Q: dy dx 3x+2y Ans: 3e-2 +2e³x =C

A: Solution : Given differential equation  dydx=e3x+2y

Q: B: use Lagrange interpolation formula to determine the relationship between the force and velocity…

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