Show that the straight lines whose direction cosines are given by the equations al + bm + cn = 0 and ul+ vm²+wn = 0 are parallel or perpendicular as 2²6² 2² — + - + = = 0ora²(v + w) + b²(w + u) + c²(u + v) = 0. U V W

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Q: Evaluate the following intergral: S6√³36 - x² -6√√36 1 5-x2 (1+x² + y2)2 dy dx

A: We find the value of the integration by transforming the coordinate system from polar to Cartesian…

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A: We know  n persons can be arranged in a circular table in (n-1)! ways.   Given, 12 basketball…

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A: (a) Given I=∫αβftdt The range α,β is divided into m equal subparts  each of width h, that is β-α=mh…

Q: Graph the piecewise function below by dragging the endpoints of the lines to the correct locations,…

A: We draw the graph of piecewise function.

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Q: Determine the radius and interval of convergence of the following power series. Σ sin k = 1 6 3 5k…

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Q: 2) Find the volume of the region in the first octant bounded by the coordinate planes and the planes…

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Q: X xp x soɔ x [x³ 3

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Q: Which of the following is the inverse Laplace transformation O +10 O ¹-10 O +¹0 +4 L-1 O None of…

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Q: 2. Rewrite the expression as the sum and/or difference of logarithms. Simplify completely. In 7² e

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Q: 2 1 4 b 3 d 1 2 5 2 4 3 f bo g 3 3 Longest Path: Shortest Path: *write your answer in this forma *no…

A: In that figure we find longest path and shortest path.

Q: Compute the matrix exponential eat for each system x' = Ax given below. a. x₁ = 5x₁ - 4x2, x2 = 2x1…

A: Note: “Since you have posted multiple questions, we will provide the solution only to the first…

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Q: Suppose the RSA system that is used for sending secret messages has private key (15, 3) and the…

A: General concept of RSA Algorithm, Steps: 1) Consider two large prime numbers p,q2) Calculate n =…

Q: Let F =   Find the outer flux of F through the surface S that is the portion of the paraboloid z =…

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Q: Suppose the RSA cryptosystem is used with public key (35, 7). What is the corresponding cipher text…

A: The general concept of RSA Algorithm is: Steps:1) Consider two large prime numbers p,q2) Calculate n…

Q: Suppose that A = 2 -2 1 0 0 1 0 0 -1 . Find the eigenvectors of A

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Q: What is the ciphertext that corresponds to the message ``4?"

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Q: where G₁1=[ a = G22 b= " and G33 = C =

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Q: Carla and Harry are solving the following word problem: and Sunday Combined? Gina is training for a…

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Q: Let A = -1 - 10 5 1 12 3 7 - 3 - 3 9 3 - 3 3 Find a nonzero vector Submit Question in Col(A).

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Q: Let Describe all solutions of Ax = 0. x = x2 0000 +x3 A = 1 2 +x4 -4 8 10 8 -20 - 16 0000

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Q: Find the 3rd roots of the following complex number: 24cis(111∘) Do not round and type "degree" for…

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Q: Determine if h(x, y) e* sinyī + e*cosyj is a gradient vector. If so, find f(xy) so that Vf=h(x, y).…

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Q: A math tee shirt business is expected to generate $39,000 in revenue per year for the next 5 years.…

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Q: Find the sum of the series: Check Answer ∞ n=0 (-1)^36¹+3 2n + 1

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Q: 4. Verify the Divergence Theorem for F(x, y, z) = (xz, yz, 3z²) and D is the solid bounded by the…

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Q: Determine all the points, nearest to the point (0.0.2) on the following graph: 3x^2 + 2y^2 -z = 0

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Q: Prove that for every natural number n, 1+3+5+...+(2n-1)=n^2

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Q: Use a graph and/or level curves to find the local maximum and minimum values and saddle points of…

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Q: Which of the following is a known property of fractals? O self-similarity dilational symmetry O…

A: The objective is choose the appropriate properties of fractals from the given options. A fractal is…

Q: c) Use Stoke's theorem to evaluate SF o dr where F(x,y,z) = x²zi + xy²j + z²k and C is C the curve…

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Q: Question Using the Method for Variation of Parameters, u₁ is evaluated by the following expression:…

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Q: Let there be set of a, b, c. Prove A×(B∩C) = (A∩B)×(B∩C)

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Q: Find a function f such that F(x, y, z) = evaluate F. dr along the curve C given by r(t) = (t²…

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Q: Graph the function f(x)=x²-1 over the interval [0, 2] Partition the interval into four subintervals…

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Q: Find the remainder term R, in the nth order Taylor polynomial centered at a for the given function.…

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Q: In a game of dice, a pair thrown in the table, what is the probability of getting a total sum of 10…

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Q: Determine the Laplace transform of the function. a) [4+sin(31)+5e²]- b) Z[6r'+2t’e" +sinh(4)].

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Q: Which of the following letters has a nontrivial (that is, the angle of rotation is not equal to 0°…

A: The correct answer is determined as shown in the next step.

Q: The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been…

A: Markov Chain: A Markov Chain is a random process describing a sequence of possible events in which…

Q: Find the transition matrix from B to B'. B = {(1, 1, 3), (0, 0, 4), (-1, -2, -3)}, B' = {(1, 0, 0),…

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Q: What isometries can be found in the following frieze pattern? O half-turn O glide reflection O…

A: The above is the Case of Glide Reflection. There are 7 cases of Frieze Patterns: 1. Translation 2.…

Q: The set of all 2 x 2 matrices of the form - 1 0 [19] 0 I2x2 Select one: O True - where x is any real…

A: Given: The set of all 2×2 matrices of the form I2×2--100x where x is any real number, is a subspace…