For the following logarithms, either write the correct value, or explain why the expression does not exist. Don't use calculators, since you don't need them. (a) log9 81 (b) log(-10) (c) log 0.001

Q: nd r'(t), r"(t), and r'(t) · r"(t). r(t) = 4 cos(t)i + 3 sin(t)j a) r'(t) b) r"(t)

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Q: Solve the following initial value problems using Laplace transform: 1. y" – 4y' + 3y = 0, y(0) = 3,…

A: The given initial value problem is                                      y''-4y'+3y=0,   y(0)=3,…

Q: An island is 3 mi from the nearest point on a straight shoreline; that point is 16 mi from a power…

A: To solve this problem, we have to determine an equation of the length of the pipe using the value of…

Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: Find the eigenvalues 11 < 12 < 13 and corresponding eigenvectors of the matrix

A: Given,          A=-5-201400-130005

Q: d) TO e στοτ. OTO tionc of R?

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Q: 2 In C, (x, y) = xAy* is an inner product, where A = i ). Compute (x, y) -i 3 for r = (1+ i, 3i) and…

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Q: Find all eigenvalues and eigenfunctions of the following eigenvalue problem: X"+AX = 0. X (0) =…

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Q: A cylindrical water tank 6 meters high with a radius of 2 meters is buried so that the top of the…

A: The work done  in moving an object from one point to other is given by the product of weight of the…

Q: Solve the equation. dy dx dx -- dy %3D

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Q: 1- Estimate f(1.72) from the giving data using; a- Newton's forward formula. b- Newton's backward…

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Q: 8. Let V be the volume of the region inside the sphere r2 + y? + z? = 6 that lies above the…

A: We will find range of value for z then draw figure and find its component on xy plane to get range…

Q: (xj, Y;) AA, whe i = 1 Approximate the integral f(x, y) dA by dividing the rectangle R with vertices…

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: Find the characteristic polynomial of the matrix 3 -4 A = -4 -3 4

A: Characteristics polynomial of the matrix

Q: 2. For each of the following polynomials find its factor and its roots. (х3 — Зх2 + 5х — 6) b. (x3 +…

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Q: Using high-accuracy central difference formula, determine the derivative of the function F(x) =…

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Q: 1. Using the British Railway metric on R2, which of the following is the distance between the points…

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Q: Find all eigenvalues and eigenfunctions of the

A: Given,         X''+λX=0, X0=X'2=0

Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

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Q: Let -4 -4 4 A = |-4 -4 -4 4 -4 -4 Find an orthogonal matrix P and a diagonal matrix D such that D =…

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Q: Sunrise Records Ltd. manufactures and replicates CDs for software and music recording companies.…

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Q: Let f be Continuous on [a,b] and diffrentiable on (a, b), Prave that if azo, then there are Xi, Xz,…

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Q: 12 Three forces act on an object of mass 5 kg. These forces are represented by the vectors 9i – 2j,…

A: To solve this problem we use the following  ∑ F→=ma→  where m is the mass of the object and  F→ is…

Q: A. Solve the following and show your solution. 1. Use the definition of Fibonacci numbers to find…

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Q: Evaluate the double integral f(r, 0) dA. 3 cos(0) r dr de Sketch the region R. T/2 л/2 2 2 -1 1 -4…

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Q: The integral represents the volume of a solid of revolution. 2n x dx (a) Identify the plane region…

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Q: 4. An airplane uses a radio beacon transmitting from an airport to determine how far off course it…

A: We have to find how far away is the beacon, and hence the airport, at the time of the second reading…

Q: Evaluate the double integral f(r, 0) dA. ' π/2 re dr de

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Q: OA. C1 J(5/9) (x) + c2J_(5/9) (x) B. Cį J(5/9) (x) + c2 Y(5/9) (x) OC. c J9/5) (x) + c2J_(9/5)(x) D.…

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Q: The matrix. -9 2 A = -8 -1 has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector v.…

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Q: Find the volume of the solid generated when the region enclosed by y = Vx, y = 6 – x, and y = 0 is…

A: The volume of revolution of the area bounded by the curve f(x) and the x-axis between the limits x=a…

Q: For a confidence level of 99%, the level of significance is: O 0.01 O 0.10 O 0.005 O 0.05 O 0.99

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Q: We know that f(x, y, z)= x³- 9x² + y² + z² +24x-4z +20. Determine the optimum value of the function…

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Q: (1) [4+4 points] Determine whether the following series converge or diverge: k! (a) Σ 2.4.6... (2k)…

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Q: 04: Find the distance between the parllel lines L, and L2 where L1: x = 2 - t, y = 2t, z = 1+t L2: x…

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Q: Construct and evaluate definite integrals representing the area of the region enclosed by y = 2x and…

A: We have evaluate the area of the region R, where the region R is bounded by the lines y=2x, x=6 and…

Q: Let E be the 3 x 3 matrix that corresponds to the row operation R3 = R3 – 3R1 (a) Find E 1. E 1= 26…

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Q: 4.1 Consider the three permutations in S6: 1 2 3 4 5 6 4 5 6 2) 3 1 1 2 3 4 5 136 5 2 4 1 2 3 4 5 S…

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Q: 12. x Ct) = cosh 3t Sin 3t te

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Q: E real matrix with an eigenvalue A = 5 + 3i and corresponding eigenvector -1+ v = i nental set…

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Q: Question 4: Let T be defined as T (v1, v2, v3) = (vl1-v2+v3, v2-v3, v1+v2) a) Find the image of (1,…

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Q: Find the area of the region outside the cardioid r = 2 – 2 cos 0 and %3D inside the circler = 4.…

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Q: R: square with vertices (0, 0), (2, 0), (0,

A: Given,         f(x, y)=19+3x-3y         R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2).

Q: Analyze the stability of the zero solution for the system dx = -y + y(x² +y² dt dy = x – x(x² + y²)…

A: To analysing  the stability of the zero solution for such a non linear system of ordinary…

Q: Using high-accuracy central difference formula, determine the derivative of the funct F(x) = x + 2x²…

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Q: 3. Let F(n) = 9F(n − 1) − 24F(n − 2) + 20F(n − 3) with initial conditions F(0) = 1, F(1) = 5 and…

A: To solve this problem first we find the generating / characteristic function and the find roots of…

Q: 43. Let {rn}-1 be a bounded sequence and {y„}=1 be a sequence tending to 0. Pro that x„yn → 0.

A: We have given that , xn be a bounded sequence. Also , yn be sequence tending to 0. We need to prove…

Q: OLet W, X, Y, and Z be invertible square matrices. Show that if WY = YW, then det Y det(W Z –YX)

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Q: 2 (1– ¡)(3 + i) | 15. V3 +i (1 – i)(/3 – i 16. (1– iX1– 2i)(1+ 2i) 17. 1- 2i 2+i 18. 3+ 4i 5i |1+ il

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Q: The fixed point of g(x) = In(e2* – 3e* + 3) +x on [0,1]: In (2)

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