Q4: The volume (V) of liquid in a hollow horizontal cylinder of radius (r) and length (L) is related to the depth of liquid (h) by V = = [r² cos-¹ (=h) - (r-h)√2rh-r²|L Use Newton-Raphson method to find water depth (h) ifr=2, L-5, V=8, starting with h=0.5 as initial value.

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Q: 6. What is the vertical asymptote of f(x)= -3/(x+1)? * O x=1 O x=-1 X=-3 O x=0

A: 6.The given function .The aim is to find the vertical asymptote of the function.Note:  Since you…

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Q: Q1:- Calculate sin(π/4+i)

A: Results:

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Q: Let a, b ∊ R, and suppose that for every ɛ>0 we have a≤b + ɛ. Show that a≤b.

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Q: 6. Let f: Q R be defined by f(x) Show that f is continuous. 0, :{ 1, = if x € (-∞, √2) nQ if x €…

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Q: Suppose that u, v, and w are vectors such that = 3, = -2, = 5, llull Evaluate the following…

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Q: The trace of a square n x n matrix A = (aj) is the sum a₁1 + a22 + ... +ann of the entries on its…

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Q: part (b), why is it equal to 0?

A: We have find  why part b is equal to 0

Q: 92 Solve the PE Eup (Initial value 79₁ 1 O O 01 1 problem) its inco)

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Q: find the general solution by finding the homogeneous solution and a particular solution.

A: 17. Given that the differential equation is                                               To find…

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Q: In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = XI X2 X3 X4…

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Q: Show that for every pair of sets X and Y, the sets X × Y and U {(x, y) | y ≤ Y} xEX are equal.

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Q: 8. Determine the equation of the quadratic function with the zeros 3+√5 and 3-√√5 containing the…

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Q: 1. 2. n−1 4 nh+n-6 7n+1 n² +1

A: We shall divide and using the highest power of n and then find the limit

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Q: 1. Show that there is no monic polynomial p(2) = 2" +an-12-¹+...+ao such that [p(2)| < 1 for all…

A: To show that there is no monic polynomial p(z)=zn+an−1zn−1+…+a0 such that |p(z)|&lt;1 for all z with…

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Q: 10+ 8 6 4 2 -6 -5 -4 3 -2 -1 -2 -4 -6 -8 -10+ 1 2 3 4 5 6 The function graphed above is: Concave up…

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Q: 5. Find all integer solutions to 6s+ 14t+21u = 1.

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Q: Question Given: DE DF, AE LED and CFL FD. Prove: AADE ACDF. Step Statement DE DF AEED CF FD Reason…

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A: (.) Given,

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Q: 4. Let x, y € R. Which of the following inequalities is TRUE? (Circle your answer(s).) • zy ≥ (²+v)…

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Q: 1. Is the affine cipher e(x) = 8x + 5 (mod 75) invertible? Yes or no. If yes, find the inverse…

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Q: In Exercises 21-24, find a basis for N(A) and give the nullity and the rank of A. ·[₁ 21. A = 1 2…

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Q: Question 2. Find the limit lim (x,y) (0,0) 2¹+ y² + ys

A: Q2: we have to find out  if exists.we claim that Now using A.MG.M  , so we get  ,but So we get Now…