II. Use the Remainder Theorem to find the remainder when each polynomial is divided by the correspondi binomial. 2x³ +8x²-3x - 1 12. x ; x-2 13. x³-4; x 4 14x3+6x²-x+5x+3 15. 2x4 + 7x² - 6; x + 1 16. 2x4-5x³ + 3x - 6; 2x - 1 17. x³ + 3x² + 2x - 9; x - 1 18. 3x³ + 12x² + 3x + 12; x-4 19. 4x³ +57x² - 4x - 3; x + 3 20. 2x³+4x²+x-8; x+2

Q: The equation 0.5(e* + e*)-5=0 has at least one solution in the interval [1.5,2.5]. True False

A: Let   ex = y The equation will become 0.5(y + 1/y) - 5 = 0 0.5(y2 + 1) - 5 y = 0 y2 + 1 - 10y =  y2…

Q: Show that Y=22.4sin(1.1x) is an eigenfunction of the operator (d²/dx²). What is the eigenvalue? O O…

A: Here we have given that Y=22.4sin1.1x is an eigen function of the operator d2dx2. So, we have,…

Q: What are the largest steps you take to solve -4y, y(0)=1 dt (without getting an overflow!) using the…

A: (a) Given the IVP dydt=-4y, y0=1. The solution to this equation is given by yt=e-4t---1. The Forward…

Q: The market for a particular product is characterised by the following demand and supply functions:…

A: Sol:- At equilibrium price :- Qd = Qs 25-3P+0.2P2=-5+3P-0.01P221P2-600P+3000=0P1, 2=--600±-6002-4·…

Q: Assume a function such that Y = (2x410)/(6x² + 5x). Obtain the first derivative. O f'(X) = (8x³ -…

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Q: Given: B and D are midpoints of the sides AC and CF, BD = DE Prove: BD || AF. (Use two-column…

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Q: The figure on the right shows the intersections of four one-way streets. Complete parts (a) through…

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Q: Question 4 A 4 3 B 7 3, 5 4 D 12 C What is the minimum total weight of a path from vertex A to…

A: Minimum total weight

Q: Determine the y-coordinate of the centroid of the shaded area shown. 16" Parabolic Y 5" 1 Answer: y…

A: Solution :-

Q: Determine the y-coordinate of the centroid of the area under the sine curve shown. y Answer:y- Mi…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Determine whether the equation is exact. If it is exact, find the solution. If the differential…

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Q: 4. Let S be the triangular region in R3 with vertices at (2,0,0), (0,6,0), and (0, 0, 3) with upward…

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Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: e the following constrained optimization problem using the method of Lagrange multipliers: max (x³ +…

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Q: The profit function of a certain firm is f(x) = −2x² + 396x - 400, where x denotes units of product…

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Q: Express the following function in terms of unit step function and hence find their Laplace…

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Q: 11. x²y" - 2xy + 2y = 0, y (1) = −1, y (2) = 1

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Q: Use u j+1, j+ Ui, j+ 1 + U j−1, j⋆ U ¡‚ j−1 −4ui,j-0 to approximate the solution of Laplace's…

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Q: Theorem: if I is a Positive implicative Bck-algebra Then (Lx),,Lo) is a BCK-algebra

A: Consider the given theorem, '' if X is positive implicative Bck-algebra then Lx,⊙,L0 is a…

Q: Solve the given system of diff-equ by using Laplace Transformations // 2₁²" + 10x₁ - 422 // 42₁ +2₂²…

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Q: Find the general solution of the DE: y"+y' + 2y = 0

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Q: Let f(x,y,z) = g(√√x² - 4y² +₂²)√√x² +16₂² +₂², + 16y² + z², where g is some nonnegative function of…

A:

Q: Given: f(t)= -3 Evaluate F(2). Use 2 decimal places.

A: It is provided that f(t)=-3t. We need to calculate F(2).

Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A:

Q: 3. The equation e* - 4x² = 0 has a root in the interval [4, 5], To find this root by fixed point…

A: Given : ex - 4x2=0    , 4 , 5  To Find : Roots of given equation by fixed point iteration.

Q: Prove that the messenger number M19 is a prime hence the integer n = 218 (219 -1) is perfect

A:

Q: Let f: A → B and g:B → C then the condition (gof) (D) = f(g(D)) holds if a) DCB b) DCA c) DCC d)…

A: It is given that,  f : A→B and g : B→C. Then, the condition gof-1D = f-1g-1D holds if ; a) D⊂B b)…

Q: 3. Let x² +16y² + 2², where g is some nonnegative function of one variable such that g(1) = 3. Let S…

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Q: Use a Taylor series centered at r= 1 to approximate the value of the integral farctan(x) dx accurate…

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Q: a. RM9338 b. RM9385 c.RM 9583 a EXAMPLE 2 2. Johan won an annuity that pays RM1000 every 3 months…

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Q: find the missing term 689, 481, 377, 325,299,____

A: Solution:- given that  689, 481, 377, 325, 299,_____ And we want to find out missing term.…

Q: Find whether the direction s= (-1,2,) at point x = (0,1) is desce function: f(x₁\x₂) = x + x² -…

A: Given: The function, fx1,x2=x14+x23-2x12x22-10x1x22, the direction s=-1,2T and the point x=0,1T.…

Q: Use the row operations method to find the inverse of the given matrix, or show that no inverse…

A: The given matrix is                          A=   1 2   4 1-1 0   2 1   2 1-4 0   1 1   2 1 We have…

Q: Use Bairstow's method to determine the roots of f(x) = 9.34 - 21.97x + 16.3x² - 3.704x³ r = -1 and…

A: Given : fx = 9.34 -21.97 x +16.3x2 - 3.704x3            r=-1 and s=-1 To Find : Roots by Bairstow's…

Q: Check if set X is linearly i ndependent, spans r3 and check for basis of r3 X={(1,0,0),(0,1,0),…

A: A set is a BASIS if it linearly independent and spans the vector space

Q: Consider the following ODE with boundary conditions y" + λy = 0, y(0) = 0, y' KN ㅠ = = 0.

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. √ 5…

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Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: A firm faces the following total revenue and total cost functions: TR = 150 - 0.20² and TC = 60+…

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Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A: Properties of Laplace transformation. L-11=δ(t)L-1as2+a2=sinatL-1aF(s)+bG(s)=aL-1F(s)+bL-1G(s)

Q: f(x) = x⁹ - 9x intercepts relative minimum relative maximum point of inflection (x, y) = (-1.316,0…

A: This is a question of real-valued function.

Q: Given the information below, find the following: Round all answers to 3 decimal places. If no answer…

A: Solution:

Q: Let S be the part of the plane 2x + 4y + z = 4 which lies in the first octant, oriented upward. Find…

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Q: vation organization releases 35 Florida panthers into a game preserve. After 4 years, there are 204…

A: According to guidelines we solve three subparts of a question.

Q: Consider the following function. T: R² R³, T(x, y) = (√x, 3xy, √y) Find the following images for…

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Q: f(t) = t, 0 st < 1 1, t2 1

A: Given function is f(t) = t,0≤t&lt;11,t≥1

Q: Lesson 24 Supplementary Exercises B. Complete the table by finding the unknown. Present Value Rate…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the determinant of the given matrix without expanding by cofactors. -400 070 005 det(C) =…

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Q: 8. dy de = azte-c 2-ex

A: To Solve: The differential equation dydx=x2+e-xy2-ey