Use the PBH test to prove or disapprove that, for any a E R, the controllability of (A, B) implies the controllability of (A² + aI, B).

Q: ∞ For r < 1, n(n-1)² = 2² +6³ +12r²¹ +….. the power series for f(x) = 21² (1+z)³ 27² (1-r)³ 1 Use…

A: Given that for r&lt;1,∑n=0∞n(n-1)rn=2r2+6r3+12r4+ . . . =2r2(1-r)3. By using this to find the power…

Q: Solve the DE shown below using the Exponential Shift (m = 2 & n = 5) y" + 2y' + y = menx

A: The given differential equation y''+2y'+y=menx, m=2 &amp; n=5 We have to find the solution of the…

Q: Three large tanks contain brine, as shown in the figure below. pure water 4 gal/min dx₂ dt dx3 dt…

A: Let x1(t), x2(t), x3(t)  be the amount of salt in tank A, tank B, and tank C. Now The rate of change…

Q: Let m, n 1 be integers. We have m 1 Sm(n): ₁ Σ(−1)² (m + ¹) B₁nm-k+1 1) m+1 k =

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Q: Solve the differential equation (6D² +13D+7)y = e¯6x — 11x².

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Q: The parametric equations for a line L₂ are as follows: x = 2+6t y = -4-6t z=-1+2t Let L₂ be the line…

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Q: n=1 (4)n-1 gn

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Q: Use the given transformation to evaluate the integral. 4y² dA, where R is the region bounded by the…

A: To Evaluate: ∬R4y2dA, where R is the region bounded by xy=1, xy=3, xy2=3 , xy2=7.

Q: (x + ) 2 + 125 (475) 2 46 21

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Q: 4. Consider the group A4, a group with twelve elements. Note that the positive divisors of 12 are 2,…

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Q: Σlogp pa P = xlogx + O(x).

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Q: Determine whether the set, together with the standard operations, is a vector space. If it is not,…

A: A matrix of order m×n contains m rows and n columns. We have to identify whether the set M4,6 is a…

Q: Find a function that models the simple harmonic motion having the given properties. Assume that the…

A: We know that the cosine function: y=cos t is maximum for t=0 and the sine function: y=sin t is…

Q: 3. A 200-liter tank initially contains 100 liters of brine solution containing 25kg of salt. A brine…

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Q: Samas (:])-[-] - (M)-[:] L (1) a) why do you know as compute given. {0.00} solve using system…

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

Q: Convert the point (x, y, z) = (1, 4, − 1) to spherical coordinates. Give answers as positive values,…

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Q: a) Consider the following game matrix: Use the Simplex method to find optimal solutions to each…

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Q: Theorem 7.6. Suppose that both f and fare in L¹(R). Suppose there exist co 2 such that Then we have…

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Q: Suppose A is a 5x5 singular matrix. What is the value of det (2A) ?

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Q: A force of 39 N is needed to keep a spring with a 8 kg mass stretched 0.75 m beyond its natural…

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Q: Q2 Use the method of undetermiend coefficients to find the general solution of y(3) - 3y" - y =…

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Q: Consider the following. the volume of the solid that lies within both the cylinder x² + y² = 9 and…

A: We will convert all equation into cylindrical form by using  relation between cartesian and…

Q: 20. In three weeks, six workers can assemble 32 products. Working at the same rate, how many workers…

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Q: Recall that C¹(0, 1) is the vector space of continuous real-valued functions on the open interval…

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Q: Fill in the missing value to make a valid probability distribution. 6 9 0.14 0.23 X P(x) 3 0.05 What…

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Q: Let A(p², -p), B(q, q), C(², - r) be the vertices o ABC. A parallelogram AFDE is drawn with D, E,…

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Q: Find the maximum value of F. dr. where F= 2xy²1+ (22-6xy²)j + (4y - 2x2y) k and C is a simple closed…

A: Given: F→=2xy2i+2z-6xy2j+4y-2x2yk and c is a simple closed curve in the plane 3x+y+z=6 oriented…

Q: Consider the series ∞ Σ(cos 0.9)* k=1 Determine whether the series converges, and if it converges,…

A: The given problem is to check whether the series is converges or diverges and also to find the value…

Q: ● C. The following data represent the average monthly temperatures for Washington, D.C. Month, x…

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Q: Please do Exercise 17.3.3 part B, C, and D and please show step by step and explain Hint for B: You…

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Q: Convert the point (x, y, z) = (2, 1, — 4) to cylindrical coordinates. Give answers either as…

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Q: A company produces and sells 211, 600 boxes of t-shirts each year. Each production run has a fixed…

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Q: 4) Veejay works as a car salesman. His monthly commission forms an arithmetic sequence. In the tenth…

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Q: Find the values of x so that the series below converges. Give your answer in interval notation. 8…

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Q: ) Let VC Rn be a subspace. Let F: V→V and G: V→V be invertible linear transformations. Denote by…

A: We have, V⊂ℝn is a subspace. F : V→V and G : V→V are invertible linear transformations, denoted by,…

Q: Part A  Parallelogram STUV is reflected about the y-axis. Which quadrants will contain the vertices…

A: From the given diagram We can say that the vertices are S,T,U,V. The vertex S is in the second…

Q: Convert the equation x² + y² = 36 to spherical coordinates and write in standard form, solving for…

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Q: Let f (u, v) = (tan(u — 1) — eº, 8u² – 7v²) and g(x, y) = (e⁹(x−y), 9 (x - y)). Calculate f . g.…

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Q: For the experiment described below, let x determine a random variable, and use your knowledge of…

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Q: 3 Consider the integral dx with n = 4. X 1 a. Find the trapezoid rule approximations to the integral…

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Q: Elimination Tournaments In an elimination tournament the teams are arranged in opponent pairs for…

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Q: Light travels at 186,283 miles every second. How many feet per hour does light travel? Round your…

A: Light travels 186283 miles per second. We have to find the value in feet per hour.

Q: 9. Solve the system { 3x-7y = 0 5x + y = 2 using Cramer's Rule.

A: The given problem is solve the system of linear equations by using the method of Cramer's rule.

Q: 4. Evaluate these complex numbers: (a) (40/50° + 20/-30°)¹/2

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: Let each matrix in Exercises 1-6 am on C². Find the eigenvalues and a basis for each eigenspace in…

A: Let us consider the matrix A. To find the eigenvalue and eigenvectors  Determine the characteristic…

Q: Consider the group S9, a group with 9! = 362, 880 = 27.34.5 7 elements. (a) Find a subgroup with 7…

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Q: The sum of 2 resistances is 84 2. Twice the smaller resistance decreased by the larger resistance is…

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Q: If my goal is to determine whether vectors dent or independent, I will solve the system (Do not…

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Q: Let E be the region bounded cone z = z = x² + y² + z². Provide an answer accurate to at least 4…

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Q: Integrate counterclockwise f²+2 dz, C: 12-11 = 4 Soz-2

A: The given integral ∮Cz+4z-2dz, C:z-1=4. We have to find the value of the integral.