For any integer n ≥ 1, C(6n, 3n) C(6n, 3n-1). O True O False

Q: 2) (D² +6D+91)y= 16e-3x x² +1

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Q: f $9,000 had been invested in a certain investment fund on September 30, 2008, it would have been…

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Q: (x) Job(z) (x) Bof(1) :puy's+xz = (x)6 pue x = (x)/(

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Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…

A: Slope is derivative of y with respect to x. And equation of tangent is (y-y1) =m(x-x1).

Q: The solution of the differential equation 3+6 Y-7Y=0.

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Q: o) +6x² + 5x + 30. q) 2³-102²-3x+15. p) ³3x² + 4x - 12. r) 2x³+x²10 - 5.

A: We need to write the following expression in multiplication forms  p. x3-3x2+4x-12  q.…

Q: 2 f(x, y) = x² + 3xy

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Q: We consider the example from class for approximating f'(2) for f(x) = sin(x) using a finite…

A: To Prove:  f'(x0)≈f(x0+h)-f(x0-h)2h for a function f and truncation error is to be O(h2) using…

Q: #1 Solve the systems of equation "manually" using Gauss Elimination (10%), Jacobi Method with 10…

A: Since you have posted multiple questions (i.e., three different methods), so we will solve only the…

Q: Solve the following system by using Gauss-Seidel method when the initial value is X(0) = 0, & = 5 x…

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Q: 5. Cy² = x² + y

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Q: if f(x) = x²√√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: Solve the following using the golden ratio. (Show your complete solution) 1. Given: 6th=8, Find 17th

A: The number: 1+52 is called the golden ratio. The 6th terms is 8 and we need to calculate the 17th…

Q: Complet X f(x) the following 0.0.5. 0.5 1 2.71828 table: 1.5 1.75 5.75460

A: The interpolation techniques are used to establish the functional relationship between any two…

Q: balue for @ the Inverse Laplace of F (s)- F (0) F (S) 542 5 (8²41) S 3 s(544) 28 +1 (5²+45 +4)

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Q: 2) Find the homogeneous linear ODE for which the given functions are Basis. -2x -2x , N, = Xe ", y3…

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Q: Find the general solution for the following ODE. State which rule you are using. If the initial…

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Q: 1. Use the tables to find the z transforms of the following a. 6 b. 2 C. e 2n

A: a. since Z[1]=zz-1 now Z[6]= 6 Z[1]=6zz-1

Q: Exercise 5. 1) Show that the metrics dp, p ≥ 1 and dmax on Rª are all Lipschitz equivalent. 2) If X…

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Q: 1) If w= Inz, then the family of straight lines u = constant in the z- plane is mapped into 21 the…

A: Note: Since you have asked a question, we will solve the first question for you. If you want any…

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A: What is Open Set: Open sets in a metric space are those that, for every point P, include all other…

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Q: Consider a wire with variable density lying along the curve r(t) = (√2t, √2t, 4-t²), 0 ≤ t ≤1 a)…

A: We will draw parametric curve and then by using integral will find mass and length of the wire .

Q: 3- Complet X f(x) the following table: 0.0.5. - J 2.71828 1.75 5.75460

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Q: 18. Given the polynomial irrational roots. f(x)=2x²-x²-5 . use linear interpolation to approximate…

A: Given: The polynomial is fx=2x3-x2-5. To find: The roots of the given polynomial.

Q: (3x² - 2y²) y' = 2xy

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Q: $11,000 is invested for 3 years at an annual simple interest rate of 13%. (a) How much interest will…

A: For the given problem  Principal amount P=$11,000                  Time   t=3 years…

Q: 1. t. Determine the order of each of the following differential equations, and state whether it is…

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

Q: (3x² - 2y²) y' = 2xy

A: Given: The differential equation is (3x2-2y2)y'=2xy. To find: The solution of the given differential…

Q: 1. Use the tables to find the z transforms of the following j. 2n k. (-3) 1. sin(nπ/2)

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Q: 3) If the bisection method is used to solve the equation 3x² = e* in [3.5,4] then the value of c3 is…

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Q: Q2) Solve the BVP utt = Uxx ux (0, t) = 0 u(x,0) = 0,_u₂(x,0) = f(x) = {100 00 01

A: Given: utt=uxx  0<x<∞,  t>0 ux (0,t) = 0 u(x,0)=0    ut (x,0) = f(x) =1000<x<10…

Q: ات (0 )Porve ere کرے if: erf de نامع

A: Find the solution below.

Q: If Do, D1,..., Dn... nEN, are dense open sets of reals, then the intersection D = 0 Dn is dense in…

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Q: The total cost C for a manufacturer during a given time period is a function of the number N of…

A: a) for N = 300  p= 50 - 0.05 x 300 = 50 - 15 = 35 For N = 500 p = 50 - 0.05 x 500 = 50 - 25 = 25

Q: Show the complete solutions. Family of circles centered at (h, k) Ans: y" [1 + (y)²]- 3y'(y")² = 0

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Q: The number 12 can be written as a sum of consecutive numbers, 3+4+5=12 Another example of a…

A: We shall answer for the first part only as per answering guidelines. For others, kindly post again…

Q: The currents I₁, I2, and 13, measured in Amperes, in the three branches of a parallel circuit are…

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Q: Use the data given below to estimate f(3) by X 1 4 f(x) 2 5 62 Constructing: a. Linear polynomial b.…

A: The regression technique uses a data set to determine an equation such that the equation fits the…

Q: QI complet the table: X f(x) O LOWE 0.5 1 2.71828 Lix) (x-xo) (x-x2) (X1-X 0) (X₁-Y2) L₂(x) =…

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Q: Let T₁, T₂, be the following bounded linear operators ¹ T₁(x₁, x2. X3,) = (x₁, X₁, X₁, X₁, ...)…

A: Here, in the question, there are given the bounded linear operators l1→l∞ which are given as…

Q: The solution of the system by Gramer's method x + 2y + 3z = 6 2x + 3y + 3z = 8 5x + 2y + 2z = 9

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Q: Create a radical equation with variables on both sides. Then solve the equation.  Write some…

A: Solving Radical Equations A radical equation is an equation in which a variable is under a…

Q: Find F de finition set for following functions. a ₂) f(x) = √ x² + b) g(x) = cosx c) f(g(x)) domain…

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Q: 4) Under the bilinear transformation w = Im(z) ≤ 0 Im(z) ≥ 0 O Re(z) ≤0 O Re(z) ≥ 0 (z+i) (z − ₁),…

A: Under the bilinear transformation w=(z+i)(z-i), |w|≤1 is mapped to (a) Im (z)≤0 (b) Im (z)≥0 (c)…

Q: A 12.5-inch candle is lit and burns at a constant rate of 1.2 inches per hour. Let t represent the…

A: Given:  Candle length = 12.5 inch Candle burn rate=1.2 inches/hr To find: (a) Expression in terms of…

Q: 2. Use the tables to find the inverse z transforms of the following b. Z Z-3 C. 2z Z+5 d. 3z Z-2

A: Part b We need to find Z-1zz-3 Now, we have the formula: Z-111-az-1=anun So,…

Q: X ecx) 0 O 0.5 1 1.5 1.75 2.71828-5.75460

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Q: J(2cot 2x² - 2e²) dx A. 3⁄cot 2x³ + 2e² + C B./cot 2x³ - 2e³ + C C. 2 cot 2x³ - 2e²+ C 2 D. /cot 3x³…

A: Please find attachment below

Q: 7. (1) Let g(x) = sin 1. Complete the following table of values. a g(x) -0.1 -0.01 -0.001 0.001 0.01…

A: Given: 7) (I) g(x)=sinπx To complete: 1) The following table of values. x -0.1 -0.01 -0.001 0.001…