Given the recursive formula, ƒ (n) = f (n − 1) + ƒ (n − 2), n ≥ 3, and f(1) = f (2) = 1. What is f (8)?

Q: Let Σ={a, b} 1- Find a CFG defining the language of all words that contain exactly two b's not more.…

A: Given: Let Σ=a,b.   To find / build: (1.) A CFG defining the language of all words that contain…

Q: the parentheses are gcd (5) Let a and b be relatively prime integers. Show that (a) (ab, a+b) = 1 or…

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Q: Use Stokes' theorem to calculate JJ (A) nds by A = 3yi-xzi+yz²k where S is the surface of the…

A: The given vector field is: A=3yi-xzj +yz2k The surface S is the paraboloid 2z=x2+y2 bounded by z=2.…

Q: A point is moving along a curve that is given as: R() = (cos 31)i + (sin 31)j + (3r)k. Find: a) The…

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Q: For the linear transformation T: R² R² given by a -b A = [8 [b] a 6 find a and b such that T(8, 15)…

A: The transformation: T: R2→R2 is defined as: A=a-bba.  We need to determine the values of a, b such…

Q: Determine the indicated characteristics and graph each function. y = x²(x - 1)(2x + 3)(x - 5)³…

A: Given equation is y=x2(x-1)(2x+3)(x-5)3 Zeros:  The values of x, where y=0. So, for zeros…

Q: If ap can be written as ua + va+wa at the point P(2.45, 247.65 degrees, -4.29), find u+v+w. X y

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 5t³ L{f(t)} = =

A: Given function is f(t) = 5t3

Q: Given: x³y""-3x2y" + 6xy' - 12y = 2x + Inx, what are the roots of the equation. A. m = 3,2 ± √2i C.…

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Q: Three students have each saved $1000. Each has an investment opportunity in which he or she can…

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Q: ght adults were asked how many different jobs they have had. Their answers are shown in the line…

A: 0

Q: Determine the coordinates of the centroid of the shaded area. 20 60 Answers: x= y y= i i 35 |20| 135…

A: Below given clear explanation

Q: ove that there does not exist a linear map T: R³ → R³ such that range T = null T (or uivalently…

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Q: Consider the matrix mapping A:R6→R³ where 1 0 A = r2 0 LO 2 0 2 0 4 0 0 1 3 1 2 4 0. and the…

A: We are given the matrix A=210400022131000240 To find basis for kernel, find rrefA.…

Q: By inspection, find the eigenvalues of the following matrix: Enter the eigenvalues in increasing…

A: Eigenvalues of the matrix

Q: . 53.Tokyo is located at (139° E, 39°N) while Manila is at (121° E, 14° N). Find the distance…

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Q: Let G be a group and g E G. Show that Ø:Z→G by Ø(n) = g" is a homomorphism and isomorphism.

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Q: A rectangular box without a lid is to be made from 272 of cardboard find the maximum value of such a…

A: Given that a rectangular box without a lid is to be made from 27 m2. We have to find the maximum…

Q: Find all distinct (real or complex) eigenvalues of A. Then find a basis for the eigenspace of A…

A: Given matrix is A=10168-9-16-9101810   To Find: all eigenvalues of A and then find a basis for the…

Q: Rewrite the set G by listing its elements. Make sure to use the appropriate set notation. G={x| X is…

A: Use the given information.

Q: Let a, b R and consider the function f defined by: (a) Suppose that we were asked to determine the…

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Q: An interior designer wants to decorate a newly constructed house. The function f(x) = 49x² - 200…

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Q: When using the quadratic equation to solve, a negative value inside or under the radical indicates…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

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

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Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

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Q: Verify that the given functions y(t) = t and y2(t) = te³t satisfy the corresponding homogeneous…

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Q: A matrix of order n is diagonalizable if and only if A has n distinct eigenvalues. True False

A: To Find: If the statement is True or False: "A matrix of order n is diagonalizable if and only if A…

Q: Define a linear T: R₂[x] → R3 [x] by T(p(x)) = x²p"(x) − 2p'(x) + xp(x), where p'(x) and p''(x) are…

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Q: Test the convergence of the following series 2. Σn=0(-1)+1 (n!) ² (2n)!

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Q: 3. Evaluate: (i) x¹8¹; (ii) 8,8/8/ (iii) 8¹,8

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Q: (a) Find x, y, z and B, where Го 3 A = 1 -3 y 4 4 ; A² = 1 ; c(4+1)+3BT = 2A and I: unit matrix

A: (a) To Find: x, y, z, and B, where A=0x31-3yz44;   A2=I;     cA+I+3BT=2A and I:unit matrix

Q: 20). Find the solution to the initial-value problem. y' = −6x tan(y), y(0) =  ? 2 y =     PLEASE…

A: An initial value problem is an ordinary differential equation together with an initial condition…

Q: Prove (An B) SAUB

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Q: A real estate company balances the books for its business on the first day of each month. It hopes…

A: It is provided that s-1=t2+3t-4t2-6t+5. We need to calculate S.

Q: Let T: R³ R³ be a linear transformation such that 7(1, 1, 1) = (4, 0, -1), 7(0, -1, 2) = (-5, 3,…

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Q: What is the solution of the given ODE * xy' + y = √x

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Q: Let (x) be a solution to the initial value problem: y" - 6y' +9y = 0; y(0) = 2, y'(0) = 3. Let (x)…

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

Q: (b) Find the derivative of g in the direction of a=2i+curl w at point (0,-1,1) where u u +2 g= In. J…

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Q: Find the volume generated if the area described is revolved about the indicated axis. Solve using…

A: Area is bounded by x2=ay,   y = 0 and.   x = b

Q: Disproof the statements below. a) Define f: Z → Z by f(n) = 3n-7, VEZ. This function f is onto. b)…

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Q: 20. Stoke's Theorem A. cannot be used as a substitute to find the line integral. B. will require the…

A: it is known that  (i) Using stoke's theorem, we can transform a surface integral into a line…

Q: Quaterback quick release can throw a football in a perfect parabolic arc to receiver 40 yards…

A: Given: Quarterback quick release can throw a football in a perfect parabolic arc to receiver 40…

Q: The definition of the Euclid Algorithm (EUCLID(a, b)) is given below. Calculate EUCLID(270,192) by…

A: calculate EUCLID270,192 by showing each step we can write 270=1·192+78192=2·78+3678=2·36+636=6·6+0

Q: Find the eigenvalues and eigenfunctions of the following periodic Sturm- Liouville systems: (b) y" +…

A: As per the question we we are given the following periodic Sturn-Liouville systems : y'' + λy = 0…

Q: EXAMPLE 5 Use graphs of circles EARTHQUAKES The epicenter of an earthquake is the point on Earth's…

A: Given that epicenter is 7 miles away from A-2,2.5. epicenter is 4 miles away from B4,6. epicenter is…

Q: Find the 9th term of the following geometric sequence. 1, 5, 25, 125, ...

A: The nth term of a geometric sequence is an=arn-1 where r is the common ratio and a is the first…

Q: ts Integrate using an appropriate method. State whether this integral is convergent or divergent.…

A: Sol:- ∫-121x3dx If exist b, a<b<c, fb=undefined, ∫ac fxdx=∫ab fxdx+∫bc…

Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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Q: Q1. Find the equation of the plane determined by the lines : L₁: (x = -2+1, y = 21 +3₁ Z=4-1), L₂:…

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Q: 1. How many elements are there in Z 2. List all elements in Zis 3. Answer either'true' or "false"…

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