Find the remainder of 5^1521/13

Q: Given the following graph of the function y = f(x) and n = 6, answer the following questions about…

A: For trapezoidal rule, a =0 b= 6

Q: Determine the y-coordinate of the centroid of the shaded area shown. 13" Parabolic. 5" I 5" -x

A: We know that centroid coordinate y (y-)=∫05xf(x)dx∫05f(x)dx let equation of parabola is f(x)=…

Q: (d) How large should we take n in order to guarantee that the Simpson's Rule approximation for 1¹6…

A: The error bound in composite Simpson's 1/3rd rule for approximating ∫abf(x)dx is given by h4180(b-a)…

Q: Problem 2. a) If y₁ is a known nonvanishing solution to y" +p(t)y' + q(t)y = 0, show that a second…

A: Note : Here student wants to get solutions of the problem 2 only . So i solved only all parts of…

Q: 8. Find the square roots of 1-√3i and express in rectangular coordinates. 9. Write the function f…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Convent Cartesian equation to Parametric a) x² - y² = 4 b) y= ex et

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Q: #solve the following IVP x= -10x+4y y² = - 8x-2y x(0)=-2 y(0) = 4 Then find y(0.25) to at least the…

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Q: Which point of the cube is i + j? Which point is the vector sum of i = (1, 0, 0) and j = (0, 1 , 0)…

A: Cube: A solid three dimensional shape which has six square faces, eight vertices and twelve edges is…

Q: Suppose 16 blackberry plants started growing in a yard. Absent constraint, the blackberry plants…

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Q: A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held…

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Q: A coincidence is defined as a striking occurrence of two or more events at one time apparently by…

A: It is given that neither person is born in a leap year. It is required to find the probability that…

Q: 43.75 A system is given in the s domain by F(s): s(s3+5.5s2+8.5s+46.75) tain the associated time…

A: As per the question we are given the Laplace Transform of a time domain system f(t) as : F(s) =…

Q: 2 4 2 [²√² (1 – xy²) dady − -1 0

A: To Find: ∫-12∫041-xy2dxdy using Riemann sums.

Q: Convert the decimal number 43 into a binary number.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis…

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Q: The ratio of rock music to total CD's that Ella owns is 25/40.Paolo has 50 rock music CD's.The ratio…

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Q: Draw the cuts in A (2 by 3) and B (3 by 4) and AB to show how each of the four multiplication rules…

A: Consider two matrices A2x3, B3x4. To Show: Each multiplication gives AB using block multiplication.…

Q: x-2y Which method would you use to evaluate the limit lim (x,y) → (2.1) 4y-x² 3 and what conclusion…

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Q: Let a, b, n E Z. Prove: If an and bln with gcd(a, b) = 1, then abln.

A: If g(a,b)=d then there exist r and s such that ar+bs=d. If a|c then it means there exists x such…

Q: Solve the following Initial Value Problem: ex e2x + 1 y': = y, y = y(x),y(0) = 1

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Q: 5 The manager of a garden store wants to build a rectangular enclosure on the store's parking lot…

A: Check the optimal using second derivative

Q: Find the maximum rate of increase of f at (-2,1), and the direction in which this occurs.

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Q: Can anyone please help me to solve this problem? I am stuck!

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Q: Prove if this is true of false. We know |x| = x if x ≥ 0, and |x| = -x, if x < 0. Then, for all…

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Q: 1. A Markov chain has state space {0, 1, 2} and transition probability matrix .1 .5 .4 P = 0 0 1 .2…

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Q: 3.2 Evaluate the value of e²dz using Simpson's rule.

A: Now, ∫abfxdx=∆x3fx0+4fx1+2fx2+4fx3+....+4fxn-1+fxn. Here ∆x=b-an. Let n=4.   To evaluate ∫02e2xdx.…

Q: Solve the equation. dy 3x² csc(y²) dx y a)

A: A differential equation can be solved using the variable separation method. In this method, the…

Q: Which of the following functions is not differentiable on all of its domain? Select one alternative:…

A: The function which is not differentiable on all of its domain is determined as shown in the next…

Q: Let code C be Up to how many errors can the code C detect? 2 1 C= {01011010, 11000001, 01010101}. 3

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Q: Find a counterexample to show that the statement is false. (Select all that apply.) 1 X x>- Ox>2…

A: Given x&gt;1x. This can be written as: x&gt;1x⇒x2&gt;1 Consider the equality x2=1. Solving this:…

Q: Which of the following is the solution to the linear system given by the matrix below? [1 0 3 -1] 0…

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Q: Suppose that a subgroup H of S5 contains a 5-cycle and a 2-cycle.Show that H = S5.

A: It is given that, H be a subgroup of S5 which contains a 5-cycle and a 2-cycle. We have to show…

Q: For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many…

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Q: 7-14 Sketch the curve with the given vector equation. Indicate with an arrow the direction in which…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: The table below shows the educational attainment of a country's population, aged 25 and over. Use…

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Q: Write the function f (z) = z³ + z + 1 in the form f (z) = u(x, y) + iv(x, y).

A: Since you have asked multiple question we will solve first question for you. If you want any…

Q: Let E be an extension field of the field F. Show that the automorphismgroup of E fixing F is indeed…

A: It is given that, E be an extension field of the field F. We have to show that, the automorphism…

Q: Copy the graph paper given below. Given, F(x, y) = -yi+xj, sketch the vector field ♬ by drawing…

A: Given: The vector field F→ is given by:                                             F→x,y=-yi^+xj^

Q: Using the Gram-Schmidt orthonormalization associated with the following set of vectors. e₁[1 -1 6…

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Q: ((x + 1)5 + 3y)dx − (x + 1)dy = 0

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Q: Construct a truth table using tva model for the following wff. A → [B → (CAA)]

A: The main objective is to construct the truth table.

Q: Write the addition and multiplication table for R={0,2,4,6,8} under addition and multiplication…

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Q: (a) Use Newton's method to find the critical numbers of the function f(x) = x6 − x4 + 2x³ − 3x…

A: The critical points of a function fx is defined as the points that satisfy the condition f'x=0. In…

Q: The point x = 0 is a regular singular point of the given differential equation. 3x²y" - xy + (x² +…

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Q: should the exponential of W = 4∠60°  not be 4ej1.05 rather than W=4ej60°

A: Actually the are the same, as the both give nearly same value. The explanation is provided in the…

Q: Given the surface 2x² + y² = 3+z², (a) find the points on the surface where the tangent plane is…

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Q: Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using…

A: Given : sn , tn are sequences such that sn=tn except for finitely many values of n and Limn→∞sn=s.We…

Q: Determine all solutions of the following Diophantine equations: 1335x801y = 534. Further, find all…

A: Applying Euclidean algorithm GCD1335,-801 -801 = (-1)×1335 + 534   1335 = 2×534 + 267    534 = 2×267…

Q: Problem 4. Polynomials p₁(x) = 1, p₂(x) = x and p3(x) = r² form a basis for the vector space P3.…

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Q: Which of the following is the field that is aimed at the construction error-correcting codes? O…

A: This is a problem of coding theory.