Give a combinatorial proof of the identity: -1 k(²) = n(n=¹) k-1.

Q: • Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: A. In a navy control system, a radar signal moves in three-dimensional space to catch a suspected…

A: Given that: w=5,0,4z=2i+4j,6k The objective is to justify your answer. Now solving, Let consider,…

Q: Show justifying that if A and B are square matrixes that are invertible of order n, A-¹BA then the…

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Q: Determine the form of a particular solution yp of y" - 8y' + 25y = 5x³e-x - 7e-x. Do not solve the…

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Q: Let A be an nxn matrix with real entries, and let λ be an eigenvalue of. Which of the following…

A: It is given that A be an n×n matrix with real entries and λ be an eigen value of A. Then we have to…

Q: (a) State the Fundamental Theorem of Calculus Part I

A: As per our guidelines only first question is solved. For remaining questions kindly repost the…

Q: 1. The Laplace transform of a function () is given by the expression F(0)-LIS()}-(ede Find the…

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Q: 2. (a,b) and Consider : R₂[1] → R² defined by ƒ(ar² + br + c) = (a,b) 9: R² → R³[2] defined by 9(a,…

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Q: Answer True/False   D) The zero vector is always an eigenvector for a linear transformation. E)…

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Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 7e…

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Q: To identify the most efficient model for a windmill, Gandalf Engineering Company designs the…

A: Consider the diagram from the given figure, here we have given that O is midpoint of BF this means…

Q: Find the radius of convergence, R, of the series. R= Σ n = 3 I= X²+2 4n! Find the interval, I, of…

A: We use ratio test.

Q: Answer all Questions Apply Newton-Raphson method to find an approximate solution of equation e-3 = 0…

A: We need to find the solution of the equation ex-3x=0 using Newton-Raphson method f(x)=ex-3x,…

Q: f(x, y) = xey (a) Evaluate f(1, 2). 7.39   Correct: Your answer is correct. Evaluate f(1.05, 2.1).…

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Q: Question 1.5 Find the steady-state(s) of the logistic differential equation dar *(1-²). dt ih. hiel…

A: Introduction The logistic differential equation is represent to population of organism. This…

Q: 12. The part of the cylinder x² + z² = 16 that lies between the planes x Find the area of the…

A: We know that if height of a cylinder be h Units and radius be r units then curved surface area of…

Q: Let V₁, V2, V3 be the vectors in R³ defined by 16 11 3 12 34 (a) Is {V₁, V₂, V3} linearly…

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Q: Suppose that (a) n=0 Cnxn converges when x = -4 and diverges when x = 6. What can be said about the…

A: As per company guidelines we are allowed to solve maximum three sub-parts so i am solving first…

Q: Use the method of reduction of order to find a second solution of the differential equation ty" +…

A: Please see the attachment

Q: Consider the function To/R₂ [x] →> R₂ [x] given by T (a+bx+cx²) = (a +2b) + (C+2a) x + (c+1)x² Prove…

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Q: solve: ch= ㅎ I/2 드 (1) 애플 To dt

A: Given integration is c(x)=1T0∫-Τ2Τ2(1)e-jx2πT0dt

Q: Set-up the integral that would find the volume of the solid of revolution when given region bounded…

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Q: P Let Q represent a mass (in grams) of carbon (14C), whose half-life is 5,715 years. The quantity of…

A: Given that quantity of Carbon-14 present after t years is Q=612t5715 Solution (a) Initial quantity…

Q: 3) Plove that (3-21) (x+2₁) = 3+2i iFiTwas very valuable x, y

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Q: solve: ch= 긍 I/2 들 (1) in 20 애플 dt

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Q: espect to some norm on X, but discontinuous with respect to another orm on X. To illustrate this,…

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Q: Sketch the function. p(x) = 0.2(x+3)²(x-3)³

A: Sol:- Sketch the Function : First we need to find some information about graph :- Domain of…

Q: Let S be the universal set, where: {1, 2, 3, ..., 18, 19, 20} S Let sets A and B be subsets of S,…

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Q: Exercises 4.2 13. x²y" - xy + 2y = 0; y₁ = x sin(lnx] Answer: y₂ = x cos(in x)

A: Solution 13: Given differential equation is x2y''-xy'+2y=0        (1) one solution is y1=xsin(ln x)…

Q: 9- Determine the type and convergence of the improper integral e -2x √2x dr. 3rd type (both first…

A: The given integral is ∫0∞e-2x2xdx To find: the correct option.

Q: the lengths of a female humerus and a male humerus are equal when

A: We will find length of  humerus when height of both male and female become equal .

Q: Let x, y, z be (non-zero) vectors and suppose w = 12x + 6y + 4z. If z = -2x - y, then w = 4 ✔B.…

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Q: verzvalaable X/2 2 (2+xi) (x +i). 2 tua GX 92+49 3 2 + 71

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Q: 5. Determine whether the series converges or diverges. b. Σ... (1+2n)" a ΤΟ n=1

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Q: (a) Use the method of variation of parameters to show that the solution of d²y + k²y = o(x)…

A: According to guideline I only solve the the first question. Please post other question as new post.

Q: 3. Consider the 2nd order equation y" - y = e² (a) Find the solution of the associated homogeneous…

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Q: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: Use arcs and lines to construct perpendicular lines. Draw a line and a Construct a second line…

A: The arcs can be drawn on a sheet of paper but the construction is to be done on any tool software…

Q: Use the least squares approximation to obtain a formula of the type P(x) = Aekx from the following…

A: To fit an exponential curve y=aebx, take logarithm on both sides of the equation and convert it as a…

Q: 1. (a) Find the Fourier series of the function f(x) = 1 |x|, -2<x≤2 (b) Hence prove that 1 + 3/2 +…

A: 1. (a) Given,                 f(x)=1-x, -2&lt;x≤2

Q: 19. Σ(-1 (1-3) n=1 η?

A: Solution:- ∑n=1∞ -1n1-2nn2The series has positive and negative elements, check for…

Q: The number N of trees of a given species per acre is approximated by the model N = 2000 (10-0.12x),…

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Q: 1. For f(x + h) + k.... a. How does the value of h change f? b. How does the value of k change f?

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Q: (2η)! (n!)². 2n 8. Σ(-1)n-1. n=1

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Q: 13 Find the derivative of the function. Y = 2² + cos" (xx) a

A: Solution:- Given function is  y= a4+cos4(x)           ----------(1) Here, the variable is 'x' and…

Q: Το test the series Σ n=1 so we could also investigate convergence using other methods.) - 3n for…

A: Here given series ∑n=1∞e-3n

Q: 6. Construct a chart giving values of u and v to satisfy the equation 1.2v +0.64u = 0.85 the range…

A: We know that, if  ax+by=c be an equation, where    x,y are variables and a,band c are constants.…

Q: Q10: X and Y are acute angles in quadrant I, with sin x = 7/25 and cos y = 5/13. Without using a…

A: Sin(x+y) = (323/325) tan(x+y) = (323/36)

Q: Solve: ch= 긍 I/2 برایم (1) -on? To dt

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Q: 1) Find the mass of the cable lying x² + y² = a² circle with density function fixin) = 3+x+y

A: Introduction: The mass of a given density function is often determines by using line integral. It is…