Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o, a), (p, g),(s, e), (w, b)}. Let g: Y → Z where g = {(g, 3), (e, 2), (b, 9), (k, 7), (a, 1)}. Answer each of the following questions. (gof)(o) (gof)(s) (gof)(w) = = =

Q: This question deals with complex numbers. (a) Find the cubic roots of √5 + i√13, namely all the…

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Q: 4. Using the definition of a Taylor series, find the Taylor series generated by f(x) centred at x =…

A: Taylor series expansion of f(x) about x=5

Q: 9.) Find the function whose 2nd derivative is given by f"(x) = 1 - 4x where f(−1) = 1, and f(-1) =…

A: Given that , f''(x)=1-4x  ------(1) Now integrating both sides of (1) with respect to 'x' we get,…

Q: 6. All polynomials of the form p (t) = a + t², where a is in R.

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Q: -If A is invertible, then the columns of A are linearly independent. Explain why. 06

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Q: Q3: A: Find the volume of the solid bounded by plane z=0, x=y² and x + z = 1;

A: The solid is bounded by the surfaces z=0, x=y2,  x+z=1. To find the volume of the region.   The…

Q: Which subgraph (1) f (III) f has the adjacency matrix [001 10110] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1…

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Q: Using the Venn Diagram find: A' 8 U 1 A 2 9 5 3 11 7 6 B 4 12 10

A: Here from given venn diagram we have to find the value of A'.

Q: 4. A company has a total of 500 light bulbs that are 100 watts each. The cost for electricity is…

A: Given that A company has a total of 500 light bulbs of each 100w The cost of electricity is 0.18…

Q: Evaluate 3y1+y³ dA where D is the region described by: D ≤ y ≤ 2,0 ≤x≤ 6. Enter an integer or a…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = (0, 1,…

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Q: Home values in town have declined 29% per year for each of the past fours years. What was the total…

A: Introduction: The percentage is a method or technique which varies from 0 to 100. The percentage is…

Q: S Let H be the set of all vectors of the form 3s 2s such that H = Span {v}. Why does this show that…

A: H is the set of all vectors of the form s3s2s.  s3s2s=s132 where s is arbitrary. Thus any vector in…

Q: 15 Let A= 1 6 Construct a 2x3 matrix C (by trial and error) using only 1,-1, and 0 as entries, such…

A: A matrix is given as A=1516111. The aim is to construct a matrix C of order 2×3 such that CA=I2.…

Q: Find 12¹ (mod 17) the inverse of 12 modulo 17

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Q: Based on the coefficient of determination (R² )value given for Graph A, which is the best…

A: Given that  R2=0.9073 for graph A linear regression. We have to determine the best possibility of…

Q: Find the general solution to the linear system and confirm that the row vectors of the coefficient…

A: Finding the row reduced echelon matrix of the augmented matrix.

Q: Let A be a 3x3 invertible matrix. The reduced row-echelon form of A is obtained by performing the…

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Q: The parametric equations for a line L₁ are as follows: x=-4+6t y=3-4t z = 1+4t Let L₂ be the line…

A: The given problem is to find the point P on the line L2. Given Line L2 is parallel to line L1 and…

Q: It is assumed in the problems below that all mixtures are kept uniform by constant stirring. 1. A…

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Q: Sketch the graph of the plane curve r(t) and the vectors T(t) and N() at the given value of t. r(t)…

A: The objective is to graph the plane curve r(t) and the vectors T(t) and N(t) at the given value of…

Q: In Exercises 1-6, find the general solution of the differential equation specified. 3 ==y = ²³²y +…

A: dydt=-yt+2 The integrating factor of the differential equation of the form  dydt+Pty=Qt is…

Q: Let X = {a, e, h, l, r, t, w}, Y = {1, 2, 5, 7, 17, 18, 21, 27, 30}, and ƒ : X → Y with ƒ = {(a,…

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Q: If A, B, and C are 3×3 matrices; and det(A) = 2, det(B) = 5, and det(C) = -5 then compute: det…

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Q: 2. Solve the differential equations: y" +9y = 2x y" + 5y' + 6y = x³ + x²

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Q: Number of terms What is the minimum order of the Taylor polynomial required to approximate the…

A: The minimum order of the Taylor polynomial required to approximate the following quantities with an…

Q: Consider the sequence (yn) defined recursively by, Y0 = 2 for n ≥ 0, _Yn+1 = Yn². Show that for all…

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Q: Find the absolute maximum and minimum of the function f(x) = x³ +1.5x² - 6x +3.5 on the interval…

A: The given function fx=x3+1.5x2-6x+3.5. We have to find the absolute maximum and minimum of the…

Q: Let A� and B� be matrices. Select all items below that apply. A. If A� and B� are row equivalent,…

A: A. True. If two matrices are row equivalent, it means that they can be transformed into each other…

Q: Determine the x-intervals where the function f(x) = x² + 2x is increasing and decreasing. Also…

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Q: 3. dy R dt = y 1+t +1²

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Q: Determine which of the following games are strictly competitive. X A 2,9 B 5,6 с 9,1 Y 6,5 8,2 Z (a)…

A: Given information: Pay-off matrices of two games.  To find: Determine which game is strictly…

Q: Find the absolute maximum and minimum of the function f(x) = 4x-x² on the interval [0,6]. Give your…

A: Given: The given function is fx=4x-x2. To find: We have to find the absolute maximum and minimum of…

Q: Evaluate the integral for the following data. F = [2x, 5y, 0], S: r = [u, v, 4u + 3v], 0 ≤ u ≤ 1,-11…

A: Given: F=2x, 5y, 0S: r=u, v, 4u+3v, 0≤u≤1, -11≤v≤11. To Find:∬SF·n dA.

Q: Use a least squares approximation to find the best linear fit (i.e., the best line), L(t) = C + Dt,…

A: The given problem is to find the best fit line L(t)=C+Dt by finding the values y-intercept C and…

Q: 1 3. What minimum number of terms of the series pi = Σ(-1)" - 10"n! n=1 find the sum with [error] <…

A: We have to find the what is minimum number of terms of the series pi find the sum with error…

Q: 3. Orthogonally diagonalize the following symmetric matrices. (a) (b) (c) 1 3 2 2 1 2 2 4 -4 -2-4 4

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Q: 4. Let a and ß be arbitrary statement forms, and consider the following general claim: If a is…

A: Given that, α is consistent and α→β is consistent. The objective is to check whether: β is…

Q: Let A be a 3x3 invertible matrix. The reduced row-echelon form of A is obtained by performing the…

A: Let A be 3×3 invertible matrix :A=a1a2a3b1b2b3c1c2c3

Q: Find 3 values of r n =120 o(n) such that

A: Ok

Q: A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at…

A: Introduction: The continuity equation is a fundamental equation in fluid dynamics that shows the…

Q: Orthogonally diagonalize the following symmetric matrices. (a) 13 2 2 (b) 23 2 (c) 1 2 2 4 -4 -2-4 4

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Q: In Exercises 15-18, let W be the set of all vectors of the form shown, where a, b, and c represent…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

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Q: Evaluate the following 4 x 4 determinant. Use the properties of determinants to your advantage.…

A: Given: The given matrix is -21211116100101325-7. To find: We have to evaluate the determinant of the…

Q: The surface defined by z = f(x, y) = 2x + y hovers above the region defined by the graphic below.

A: For the given surface  F(X,y)=2x+y The region bounded by curves is shown in figure  To find the…

Q: If the velocity of an the point (x, y, z) is given by 3x3 313 332 - r2 r5 r5 imcompressible fluid at…

A: Here  u=3xzr5, v=3yzr5, w=3z2-r2r5 where r2=x2+y2+z2. Then,       ∂u∂x=3zr5-15x2zr7,…

Q: Show that 2xyz (x² + y²)² W = y (x² + y²) ²′ V = (x² - y²)z (x² + y²)²² are the velocity components…

A: A liquid motion is only possible when the  velocity components satisfy the equation  of continuity.…

Q: OX Find the absolute maximum and minimum of the function f(x) = 2x² + 2' on the interval [-4, 4]…

A: There are some following steps to find the absolute max and min of f(x).(a)  Find all critical…

Q: 2. Prove (choose the most convenient method of proof) For 2 ≤ n ≤4,n² ≥ 2".

A: To Prove: For 2≤n≤4,  n2≥2n.