Find the least residue of 99! (Mod 101)

Q: find Fourier coefficients

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Q: Chain rule and implicit differentiation Suppose that F(x,y,z) = 0 defines z as a function of a and y…

A: Given that A function Fx,y,z=0 and z as a function of x, y and F is differentiable. differentiate F…

Q: Let f : A → B be a function. Prove that f is surjective if and only if, for every pair of functions…

A: Please comment if you need any clarification. IF you find my answer useful put thumbs up. Thank you.

Q: bound the module of the contour integral (image) where C= { z E C : |z - 1| = 2}}

A: Introduction: Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement…

Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

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Q: Use the Laplace transform to solve the given Ihtegral f(t) f(T) dt = 6 ()

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are…

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Q: Evaluate o(7000).

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Q: A company that manufactures handbags has determined that the dollar cost of producing handbags per…

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Q: Use induction to prove 12 + 22 + · . . + n² n(n+1)(2n+1) 6.

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Q: 8.) Find a matrix P such that PT AP orthogonally diagonalizes A. Verify that P"AP gives the proper…

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Q: 15. Consider a simple dice game in which you roll a single die. If you roll an even number, you lose…

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Q: Find fF(x), the Fourier expansion of the function f(x) = -1 -1 Σ (1+(-1)"+1) cos(nr2) n=1 fF(x) =…

A: Fourier series of the function

Q: Queston2 {e-x, xe-O onlo, c∞) a) shau that q fandamented Set

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Q: Let f(z) = ((z – 3i)² + 9)ez- The Laurent series representation of f(z) in the domain 0 < |z – 3il <…

A: Given function is fz=z−3i2+9e1z−3i. We have to find the Laurent series representation of fz in the…

Q: Advanced Math (a) Use the two step AB method with h = 1 to approximate y' = ty for 0 <t< 3 and y(0)…

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Q: For each of the following: a) Determine the intersection points. b) Draw a sketch of the graph. c)…

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Q: Let A be the matrix of the quadratic form below. It can be shown that the eigenvalues of A are 4, 7,…

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Q: 7. 3 RR Thecross product with one factor kepT a Linear oprator Ti:R3DR°. similarly the c withe one…

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Q: Q3. (a) Use the definition of L{-} to determine L{te="}

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Q: Q12. Identify the correct statement concerning, r the correlation coefficient between X and Y and…

A: We need to see if the given statements are true for the correlation coefficient r and the linear…

Q: 40-45 Special Function Values. Find the values of 40. sin (3 + 4 Ti)

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Q: Prove the soquen enat 2efin ea For n EIN Conv e

A: Introduction: When each term of a sequence is greater than its previous term, the sequence is…

Q: QUESTION TWO A company has three main departments, which are Sales & Marketing, Inventory and…

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Q: 18. A function f(x, y, z) is called harmonic in a region D in space if it satisfies the Laplace…

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Q: Let y = sin(4x). If Ax 0.4 at z 0, use linear approximation to estimate Ay Ay 2 - Find the…

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Q: Let y = 3Ja. Find the change in y, Ay when x = 3 and Ar 0.2 %3D Find the differential dy when x = 3…

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Q: Compute the volume of the solidbounded by the paraboloid z =x+y and the upper hemi sphere 6 -x² -…

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Q: Given the function f(x.y) = In (2 +7y), answer the following questions. a. Find the function's…

A: We will find possible values of x and y to conclude about domain and range of given function

Q: Over the first 4 years, species A has grown more than species B. Over the first 4 years, species B…

A: From the graphs, it can be seen that in first four years, with time, value of both species A and…

Q: (b) If f is a bounded linear functional on a Hilbert space H, show that there is a unique y e H such…

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Q: the Following diFferential equations ave complete then the general Solution was Found dy =0 11

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Q: - the following sys 2z = 1 Bz = 3 az = b

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Q: 2. Solve the differential equation (3x? – x³ + 3y – 3.xy – y°)dx + 3(x + y²)dy = 0, - by determining…

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Q: change 3.6e2i into polar form

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Q: Consider the following Linear Program: max 2x1 + 3x2 +4x3 (1) (2) s.t. X1 + x2 +x3 < 50 X1 + x2 + x3…

A: Given linear programming problem is max    2x1 +3x2 +4x3s.t.   x1 +x2 +x3 ≤50               1…

Q: Write an equation for the function graphed below. The y inte 5+ 4 3.

A: Introduction: Asymptotes are imaginary lines that are very close to the total graph of a function or…

Q: 4. Let R be endowed with its standard topology. a) Find the closures of : i. Q ii. R-Q iii.…

A: This is a problem of topology.

Q: Give 3 examples of fractals, isometries, and patterns, and explain each example.

A: Isometry: An isometry is a one-to-one transformation from one geometric space onto itself which…

Q: Find the equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: 10. Write the binary number (1000110), in decimal and write the decimal number 327 in binary.

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Q: Q13. A department in a small firm has 50 members. The distribution of the number of coffee breaks of…

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Q: ry? V1+ x²

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Q: Find the missing digit in the number 1234x34780 if we know this number is a multiple of 9

A: Introduction: If the remainder is zero, a number is said to be divisible by another number.…

Q: Evaluate the given Laplace transforms. (Write your answer as a function of s.) L{1} %3D L{t} Use…

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Q: Determine the present value P that must be invested to have the future value A at simple interest…

A: The formula for simple interest is SI=PRT100. The formula for amount is A=P+SI. Given R=14.0%, T=6…

Q: The alumni of Athabasca University contribute (C) or do not contribute (NC) to the alumni fund…

A: Solution :-

Q: Find a least-squares solution of Ax = b by (a) constructing the normal equations for x and (b)…

A: Given that A = 1-2-120339 and b = 51-23 . We have to find a least-squares solution of Ax = b by…

Q: 12x5 + 45x4 – 80x – 5 and classify them. Round your Find the critical numbers of the function f(x)…

A: f(x) = 12x5 + 45x4 - 80x3 - 5 =&gt; f'(x) = 60x4 + 180x3 - 240x2                 = 60x2 (x2 + 3x -…

Q: that

A: Given data  G1 is a solid enclosed by  xy-plane, yz- planes x+2y+z=4 and x-y+z=4x+2y+z=4⇒ z=4-x-2y