Find the eigenvalues and eigenvectors of the given matrix. 18 3 6-1 The eigenvalue(s) is/are (Simplify your answer. Use a comma to separate answers as needed.) The eigenvector(s) is/are (Use a comma to separate vectors as needed.)

Q: The width of an irregular curve is 1 mm, the initial leftmost height of the rectangle is 49 mm and…

A: It is provided that the width of the curve is 1mm and the total number of rectangles under it is…

Q: Solve the given DE using 3 possible solutions: x³-2y³ 3.xy-2 ||

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Q: Let G and L be relations on A = {1, 2, 3, 4} with G = {(1, 2), (2, 3), (4, 3)} and L = {(2, 2), (1,…

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Q: 2. Show that the sum of the squares of the distances of the vertex of the right angle of a right…

A: In this sum we are going to use the Pythagorean theorem and the concept of similar triangle.…

Q: S Find the nadius of convergence and the intenval of convergence ton the following powern serien…

A: We use Ratio Test.

Q: Use the False Position method of finding roots of equations to solve the following:…

A: Consider the given function, fn=40n1.5-875n+35000=0 Find the value the function, n 50 55 60 62 63…

Q: Solution:- Given H(jw) -(4+jw) 6+5jw-w² -(jw+4) 6+ (jw)² + 5jw It Can rewrite as: - (: j² = + 1)…

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Q: definitions

A: Definition of application of integral calculus , area of plane region ,surface area of solid of…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Here we use the formula of area of triangle. First we differentiate area with respect to time and…

Q: Evaluate the iterated integral below. π 1 S. *S'y cos (x) dy 0 0 dx

A: Here in above question we have to find iterated integral.

Q: Determine whether the differential equation (8x² − 2xy + 4) dx + (4y² − x² + 8) dy = 0 is exact. If…

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Q: Consider the first order differential equation t et y² + ² = 3 y' -y t² 4 ach of the initial…

A: By existence and uniqueness theorem differential equation has unique solution in a<t<b if…

Q: Consider the function f(x) = 2x³ slope of the function on this interval. By the Mean Value Theorem,…

A: given function f(x)=2x3-12x2-30x+9 given interval -4, 9 We have to find average slope.

Q: Use the Midpoint Rule and Simpson's Rule to approximate the given integral with the specified value…

A: Given integral is ∫01e−xdx and n=6. a We have to approximate the given integral by using midpoint…

Q: Consider the following applications: I. T: R³ R², such that T(x, y, z) = (10z, x + y) II. S: R³ → R,…

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Q: n each system, at least one pair of planes are parallel. Describe each system in words. ( no math…

A: Two planes are parallel means they do not cut each other any point. Solution a: Given system is…

Q: Describe the steps in words that you would use to show that (x - a) is a factor of x" - a". Your…

A: Let f(x)=xn-an. Now using binomial expansion…

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)…

A: Null space: The set of all the vectors x such that Ax=0 is called the null space of the matrix A. It…

Q: Find the solution of the given initial value problem: y(4) + 2y"" +y" + 8y′ − 12y = 6 sin(t) +80e¯t;…

A: We use method of undetermined coefficient.

Q: 7. Count the dots of each hexagonal shape and fill in the table. Terms a2 A3 Dots 6 16 8. What is…

A: Total poitnts in outer =24 in scond inner shelf =11 third shelf =7 fourth =3

Q: Prove that Co is a Banach space by showing that it is a closed subspace of l

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Q: Consider the function f(x) = 2√x + 4 on the interval [1, 6]. Find the average or mean slope of the…

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Q: "The auxiliary equit of the given diff- egnn is m² +6m +8 = 0 d 2 m² + 4m+ 2m +8=0 17 m (m+4) +2…

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Q: Consider the function f(x) = 2x³ - 3x on the interval [-5, 5]. Find function on this interval. By…

A: Given function fx=2x3-3x on the interval [-5,5] The average or the mean slope is given by mean slope…

Q: Test the series for convergence or divergence. 97² n! n = 1 O convergent divergent

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Q: Consider the initial value problem (1+x+2x²)y” + (1 + 7x)y' + 2y = 0, x > 0, Characterize x = 0 as…

A: Given DE is  (1+x+2x2)y"+(1+7x)y'+2y=0.....(1) y(0)= -1, y'(0)= -2

Q: O True O False (pvs) Ⓡr

A: Given the propositions p,q,r and s. The truth table of p∨s⊕r is given by:    p     s     r…

Q: Consider the function f(x) = 6√√x + 4 on the interval [3, 6]. Find the average or mean slope of the…

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Q: Given that 2r + 1 = sin 0. (a) Test the symmetries of the above equation. (b) Construct a table for…

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Q: Suppose U = {1, 2, 3, 4, 5, a, b, c) is a universal set with the subset A = {a, b, c, 1, 2, 3, 4).…

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Q: Write a system of equations to model the problem. Be sure to define your vairables. Solve the system…

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Q: F, (w) -1 a+jw -8 7 a + jw

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Q: a) What is the number of units at break-even? b) What is the revenue at break-even? $ c) What is the…

A: from the given data, we get  break event point is at 5,45 (a) what is the number of units at break…

Q: How did he get the 2t1 = x (zt-1) = d* value inside the circle 2 dz 11 인(豐)(x(z) 한(豐)로 e dz j(엘) x(t…

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Q: Which one of the following options regarding the binary operation is FALSE? a b c d aadcb bbada…

A: We find Correct option.

Q: Suppose the functions f and g are continuous on [a, b], differentiable on (a, b), and g'(x) ‡ 0 for…

A: Introduction: Rolle's theorem is an advanced property exhibited by a continuous and differentiable…

Q: dx S Jo 16+x²

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Q: Which of the following subsets of P2 are subspaces of P2? □Ā. {p(t) | √√√p(t)dt = 0} B. {p(t) | p'…

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Q: 1. r+∞ e dx x ln x - dx

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Q: Use the power series method to solve the given initial-value problem. (Format your final answer as…

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Q: 9) Find and perform each of the following for the given functions. a. All zeros and their respective…

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Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: c) x²y" + 5xy + 4y = 0, x > 0, y(1) = 5, y(1) = -9

A: To solve the following problem, we use the couchy homogeneous linear differential equations method.

Q: LeAnn flipped her lucky coin 13 times and got 8 heads. LeAnn used these numbers to estimate the…

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Q: 2. By finding an antiderivative, evaluate each of these integrals, where the path is any contour…

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Q: Describe the steps in words that you would use to show that (x - a) is a factor of x" — a". Your…

A: Introduction: A statement P(n), where n is a natural number, is an example. Then, employ the…

Q: Let f(t) be a function on [0, ∞). The Laplace transform of f is the function F defined by the…

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Q: A plane contains the point B(-3, 2, -4) and the line with parametric equations x= 1 + 2?, y = −t, z=…

A: Explanation of the answer is as follows

Q: Evaluate the iterated integral below. π | 1 S. S'y cos (x) dy dx 0 0

A: Here in given question we have to find value of iterated integral.