In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class did not complete the homework? Completed the homework Did not complete the homework Passed the Failed the test test 11 2 7 3

Q: 2. (a) Find the linear approximation to f(x) = 60x¹/³ around x = 27. (b) Find the quadratic…

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A: The solid is generated by revolving the region bounded by the curve x=y and the line y=2x about…

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Q: li) 8 x³ + 2x² - 4x - 8 r³+2x² J dr

A: ∫8x3+2x2-4x-8dx We have to evaluate the integral using partial fractions.

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Q: Consider the matrix A = 2 0 1 010 02 a) Diagonalize the symmetric matrix A = SAST, i.e. compute the…

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Q: (a) Using the Ratio Test, or otherwise, determine the radius of convergence of the power series nn –…

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Q: 7. Y = 2x²+x-7 x²+x-56 Find the horizontal and vertical asymptotes of the curve.

A: Horizontal Asymptote: To find the horizontal asymptote, we examine the limit of the given function…

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A: Lines :r→=3, 1+t-3, 5, t∈ℝx=-6+2s and y=3-2s, s∈ℝ

Q: Using the Residue Theorem, or otherwise, compute 2-7 +z-2 dz, where C is the positively oriented…

A: Let  fz = z-7z2+z-2                consider  z2+z-2 = 0…

Q: (b) Using the Residue Theorem, or otherwise, compute z-7 -z-2 dz, where C is the positively oriented…

A: Useful result:

Q: only the question B please Solve the following problems by using the inverse of the matrix involved.…

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A: 1)Residue of f(z) about z=a is, The coefficient of (z-a)-1 in the Laurent series of f(z) about z=a2)…

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Q: 16. A region V is defined by the quatersphere x² + y² + z² = 16, z ≥ 0, y ≥ 0 and the planes z = 0,…

A: Given: A region V is defined by the quatersphere x2+y2+z2=16, z≥0, y≥0 and the planes z=0, y=0. A…

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A: Here, fz=z2, then find  1) If z≠0, then f'z not exits. 2) If z=0,then find f'z.

Q: Using the Residue Theorem, or otherwise, compute Sezz dz, z-7 z²+z-2 where C is the positively…

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Q: 13. Which of the following ranges for x and y would be better to show the rational function below?…

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Q: u (x, y) = -ey sin x − 2e¯º sin y. —

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Q: Consider the matrix A = a) Compute the eigenvalue decomposition (eigenvalues A and eigenvectors S)…

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Q: Differentiate between measurable sets and Borel sets by illustrating an example.

A: Measurable sets and borel sets are both concepts related to the field of measure theory.

Q: Section C: Polynomial and Rational Functions 11. If x > 1, then complete the triple…

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Q: Q1(A): 19 Marks] Two vectors A and B are located at Pi(2,2,2) and P2(2,-2,-2). Write vector notation…

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Q: Let a,b,c,d, and e be integers with a not equal to 0. if (ab,ac)=e and (b,c)=d, then e divides ad.…

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Q: (b) Using the Residue Theorem, or otherwise, compute Sezz z-7 -22²-22-2 dz, where C is the…

A: We shall first split the integral into partial fractions and then use Cauchys integral formula

Q: Using the Residue Theorem, or otherwise, compute z-7 Sezzzzzz dz, z²+z-2 where C is the positively…

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A: The profit function is given by        P = R – C          = (4500Q – 36Q2) – (2Q3 – 6Q2 + 900Q +…

Q: Express Log (34) 3+4i in Cartesian form (x+iy). Justify all of your steps.

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Q: Evaluate the integral [(6-2²) dz where C is the anticlockwise square contour with vertices at 1 + i,…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: This has to be done the matrices way not calculus.   Can the vector [1 2] be written as a linear…

A: In this question we will write the given vector to the linear combination of the vector.

Q: (b) Using the Residue Theorem, or otherwise, compute z-7 -z-2 dz, where C is the positively oriented…

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Q: The table gives the increase or decrease in the number of donors to a college athletics support…

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Q: Question 1. Show that if S,TEL(V, W), then M(S+T)= M(S) + M(T).

A: Given: S, T∈LV, W We need to prove that, MS+T=MS+MT.