Describe the steps in words that you would use to show that (x - a) is a factor of xn - an. Your explanation must include proper mathematical vocabulary, terminology, theore covered in the chapters.

Q: The auxiliary equit of the given diff- eqnn is m² +6m +8 = 0 2 m² + 4m+ 2m +80 m (m+y)+2 (m+4) = 0…

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Q: 6. Let a = (1, 0, 3) and u = = (2,-1,5). ) Evaluate projau. Find a vector that is orthogonal to…

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Q: If P100,000 is invested for 6 months at 1.5% per annum, what is the maturity value? O P100,750…

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Q: Use the transforms of some basic functions (i.e., theorem 4.1.1 in the textbook) to find ¹£{f(t)}•…

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Q: Consider the function f(x) = 2√x + 4 on the interval [1, 6]. Find the average or mean slope of the…

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Q: Suppose P. q. r, and s are propositions with truth values v(p) = T, v(q) = F, v(r) = T, and v(s) = F…

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Q: You invested $7,500 in a stock whose value is depreciating by 9% per year, compounded annually.…

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Q: long would it take R20 000 invested today at a nominal annual continuously compounding (NACC)…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

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Q: The number of times a new pop song has been downloaded t weeks after its initial release is given by…

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Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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Q: b. C. Let an be a sequence that satisfies a recurrence relation an-an-1 +5 for n=1, 2, 3, ... and…

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Q: Consider the initial value problem (1+x+2x²)y” + (1 + 7x)y' + 2y = 0, x > 0, Characterize x = 0 as…

A: Given DE is  (1+x+2x2)y"+(1+7x)y'+2y=0.....(1) y(0)= -1, y'(0)= -2

Q: Use the inverse transforms of some basic functions to find the given inverse transform. 1 x = {(5²…

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Q: 2. State why the function f(z) = 2z²-3-ze²+e-² is entire.

A: Introduction: Every complex valued function corresponds to a power series. The convergence of power…

Q: (N) (R) (V) = (A - y)² (B −y) = (y-A) (B-y) = y(y² + B) Answer: Answer: (P) = (A+y)(B+ y)² da (S) dx…

A: 1st we have to decide about equilibrium solution and then depends on inclination of slope line…

Q: Which of the following about matrix A is not true? A = [1 2 2 3 [3 1 31 3] 1 2]

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Q: Determine the shortest path from A to I. A-B-D-F-I A-B-E-H-I A-C-D-F-H-I O A-B-D-F-G-I E

A: We have to find the shortest path from A to I

Q: G= G(2:3,:) G= ? 1 4 7 2 5 8 3 6 9

A: It is provided that: G=123456789. We need to evaluate the expression: G2:3,: using a computer…

Q: Given't fltje [ The Fourier Series f(t) = findi 1 a b 17750! 27751 a + b + = 2 I sin nit Ž b TT n…

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Q: For the data (1, 9), (2,28), (3, 65), (4, 126), (5, 217) the highest order will be the fourth order…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The convergence of the bisection method is slow as it is simply based on halving the interval. O…

A: We want to find the given statement is true or false.

Q: 3. Use the theorem in Sec. 44 to show that La (z-zo)"-1 dz = 0 (n = ±1, 12,...) when Co is any…

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Q: The uniform beam has a mass of 47 kg per meter of length. Determine the reactions at the supports.

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Q: O True O False (pvs) Ⓡr

A: Given the propositions p,q,r and s. The truth table of p∨s⊕r is given by:    p     s     r…

Q: 2. Given that F(x, y, z) = (e", xe" + e*, ye*) is a conservative vector field. a. Find a potential…

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Q: (a) Draw a direction field and describe how solutions seem to behave. (b) Find the critical points.…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Given that F(x, y, z) = (e", ze" + e, ye*) is a conservative vector field. a. Find a potential…

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Q: (1) An object with a mass of 3kg is attached to the end of a spring that is stretched 20cm by a…

A: Given that A mass (m) = 3 kg is attached to the end of a spring that is stretched 20cm=0.2m by a…

Q: X 3. Solve the equation y'+ xy = with the Bernoulli substitution method. y

A: To solve the following problem, we use the Bernoulli substitution method. Then the problem convert…

Q: Use the defir tion of the Laplace transform to £{f(t)} = exp(-s)/s1/s² 2/s² - exp(-s)/s 2 exp(-s)/s…

A: Given function is f(t) = -1,0≤t<11,t≥1

Q: Find the critical numbers of the function f(x) = 12x³ + 15x¹ At x = At x = At x = the function has a…

A: In this question, the concept of critical point is applied. Critical Point The critical points of a…

Q: Evaluate f sin5 cosº x dx. A 1 1 14 B D sin¹2x 1 3 sin ¹4x + C 1 sin¹²x + sin ¹4x + C 14 E None of…

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Q: Use the method of reduction of order to find a second solution of the differential equation xy" − y'…

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Q: Use the Newton 2nd order method of finding roots of equations to solve the following: f(c) = a-1-1=0…

A: As per the question we have to find the root of the equation : f(x) = 2.5 - 1/x = 0 {we've replaced…

Q: -. Let g be the piecewise linear function g(t) t = [0,5) (t-5), te [5, 10) t≥ 10. -- Express g using…

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Q: 8 The function s(t) = ³ t³ - 30t² + 28t represents the position function along a line (1 dimensional…

A: The given function is st=83t3-30t2+28t find the derivative s't=383t2-60t+28 simplify s't=8t2-60t+28…

Q: A plane contains the point B(-3, 2, -4) and the line with parametric equations x= 1 + 2?, y = −t, z=…

A: Explanation of the answer is as follows

Q: (2) Solve the following differential equations (Hint:- use Ricatti's technique) dy (0) TYT (i) dx =…

A: We solve given differential equation by using Ricatti's technique.

Q: SA (cm/s) 20 10 0 10 20 T (°C)

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Q: If B has a column of zeros, then so does BA if this product is defined. True O False 4

A: Given B has a column of zeros , then to find BA has a column of zero or not :-

Q: Let y = sin(5x). If Ax : = Ay ~ = Find the percentage error error = 0.2 at x = 0, use linear…

A: Linear approximation of y=f(x) at x=x0 is L(x)≈f(x0)+f'(x0)(x-x0)

Q: Show that the function y1 = 1 / t is a solution of the first order Riccati differential equation…

A: Given differential equation is y'=1t2-1y2- 1t2-1 Rewrite it,  y'=1t2-1y2-1  ------(1) Also, given…

Q: 2 3. Let A be an invertible matrix such that A-¹ = 0 1-1 2 1 3 01 4 1. Solve the system (2A2)x= b,…

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Q: Use the Bisection method of finding roots of equations to solve the following: ƒ(n) = 40n¹ – 875n +…

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Q: Suppose that U cr|xyer F4 y EF, U is a subspace of F4- you don't have to! Find a subspace V of F4…

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Q: 1 Given that x, x², and = are solutions of the homogeneous equation X corresponding to x³y"" + x²y"…

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Q: Solve the initial value problem O y(t) = y(t) = Oy(t) = O y(t) = c₁cost + c₂sint Oy(t) = 6cost…

A: Given differential equation is y'' + y = 0

Q: 3. The number (in millions) of employees working in educational services in a particular country was…

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Q: Question 2: Tutorial 10 x² and g(x) (b) If f(x) x³ with x € [1,1], find the c € (-1, 1) by using…

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