Find the integer a such that 0 < a < 113 and 10270 + 1 = a³7 (mod 113).

Q: Let p> 0 be a rational number. Prove that zº is periodic.

A: Consider the given complex function, fz=zp It is required to prove that if p&gt;0 be a rational…

Q: TASK 1: INTEGRATION Another application of integration is in probability. This task applies your…

A: Explanation of the answer is as follows

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f(1) = 1, ƒ(2) = 1, and f(3) = 0.

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Q: The x- and y coordinates of a moving particle are given by the parametric equations below. Find the…

A: Given- The parametric equations are: x = 4t, y = 4 - t, t = 2 To find-  The magnitude and direction…

Q: unction be + about y

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Q: Determine the following estimate without using a calculator. Then use a calculator to perform the…

A: Given- You lease a car at $603 per month for 6 years. To find- Estimate the total cost of the lease…

Q: A. Suppose that the economy is characterized by the following behavioral equations: C = 160+ 0.6 Yd…

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Q: Solve the following problems with the second parti a) Find the points on the surface x²y²z = 1 cl…

A: We have to solve the problems by the Lagrange's multipliers and the second partial derivative test.…

Q: Approximate fƒ(1, 3) using the contour diagram of f(x, y) shown below

A: Here, in the question, it is been discussed about contour diagram. We have to approximate the…

Q: Let P be an odd prime. Then for all nЄN, we have () = n²¹ (mod p). Р

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Q: U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz)…

A: Given, U=ℝ3 with standard vector addition but with scalar multiplication given by r(x, y, x)=(r2x,…

Q: Find the differential of ƒ(x, y) = √√x³ + y² at the point (3,2). df = Then use the differential to…

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Q: Prove each of the following statements a) Use the direct method to prove that if a < 0, b < 0,c< a,…

A: We have given that a&lt;0 , b &lt;0 , c&lt;a and d &lt;bIf we multiply by negative number then…

Q: A function F(x,y) is said to be homogeneous of degree n if F(yx, yy) = y"F(x,y) Determine which of…

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Q: a) What is the voter population in District 4 ? ________________ b) How many potential voters do…

A: Distribution of voters is drawn is tabulated below: District  percentage of voters  Number of…

Q: Find the Inverse Fourier transform of e) e 2 cw-4Jj 4- C4-wJj

A: Given: In this question, the given details are Here, the given expression is, e2(ω-4)j4-(4-ω)j To…

Q: Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of…

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Q: let p be am odd prime, legen. dre symbol completely multiplicate function of an

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Q: Let S = {(2,0) = R² : 2 = R}. If lim f(x, y) = 0 then (2.9)-(0,0) f(x, y) = 0. lim (z.g)-(0,0)(8…

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Q: Find the exact value that the sequencesin" 1 converges to. (Note 1-0 that as usual, sin" a means…

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Q: Suppose Sally’s current salary is $62,000 per year, and she is planning to retire 25 years from now.…

A: in order to find  in her account at the time of her retirement , we calculate thethe effective…

Q: If n(A) =7, n(B)= 8, and n(A intersection B)= 6 what is n(A Union B)?

A: Sol:- Givenn(A) =7n(B)= 8n(A intersection B)= 6

Q: 2.15 For what values of n is (n) odd?

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Q: It’s about 1500. The pope needs the roof of a big cathedral chapel painted. It’s 400 square meters.…

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Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

A: Given: f(x)=7-x3, a=0, b=2 and n=10 To find: The value of integral ∫027-x3dx using (a) the…

Q: #5 Discuss the convergence. of the secre สะ (enn) Jn h={

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Q: Simplify the following. Write the answer as a simplified fraction. 1 1 1 4(3y-1) 28(2y-3)…

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Q: 1. Determine a general solution of the differential equation: y" + 4y + 5y = 200 sin t

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Q: A function F (x,y) is said to be homogeneous of degree n if F(yx, yy) = y"F(x,y) Determine which of…

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Q: Suppose that a package courier service promises to deliver to customers at 10:00 am on the morning…

A: -   The company should allow for a maximum delivery time of 1 hour after the promised delivery…

Q: Problem 10. Suppose that f~g and h~ g. Which of the following are true? Briefly explain your answer.…

A: We have to check which of the given condition about functions are true .

Q: Solve the following using variation of parameters show complete solution: 1. (D²3D + 2)y: = 2x 1+ex

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Q: 2.30 Compute the last two digits of 345. Please include steps

A: Given : 345 To Find : last two digit

Q: The approximate heights of two of the world's tallest mountains are given. Determine which is the…

A: Remark: Since the required height is in meters unit, we need to convert all the units in meters. We…

Q: Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of…

A: This follows from basics of set theory. We give all the details in step 2.

Q: 10x + 3y -7z = 3 -7x - y -z = 12 -2x + 4y +10z = 6

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Q: 1. Consider the hyperbola with foci (-6, 1) and (-6, -9), and a vertex at (-6, -1). a. Give the…

A: Given- Foci of the hyperbola: -6, 1 and -6, -9. Vertex of the hyperbola: -6, -1. To find-…

Q: how to use Bolzano Weierstrass Theorem to prove that every bounded infinite subset has at least one…

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Q: Consider four lines, labeled L1, L2, L3, and L4. The following information is known. o Line L1 goes…

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Q: Safelite guaranteed an $11 hourly wage when it rolled out performance pay, so it paid installers $20…

A: Given that, Safelite company     Guaranteed pay: Hourly wage : $11  Paid: Installers $20 per…

Q: 1. Roland's Boat Tours sells deluxe and economy seats for each tour it conducts. In order to…

A: Note: As per your requirement I solved here both the questions.

Q: Prove Σ'() - ΑΣΘ n2"-1

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Q: If diesel fuel averaged $2.97 in the Summer of 2019 and it averages $2.05 in the Summer of 2020,…

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Q: 16 in. 20 in. r = 38 in. X

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Q: Find the principle solution of sin(3-4x) = -√3 2 x= If there is a distinct solution from the other…

A: Sin is negative in 3rd and quadrent. Also, cos is negative in 3rd quadrent. I have used this concept…

Q: (1) Find the stationary points of y = (x² – 2x³)e²¹. Note: you must give exact values - do not…

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Q: Devise formulas for the nth pentagonal number and the nth hexagonal number.

A: We find the formula with the help of  graph drawing take as n=1,2,3.... So by observation we find…

Q: Use the table, along with dimensional analysis, to convert the given square unit to the square unit…

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Q: A clerk must use the elevator to move boxes of paper. The elevator's maximum weight limit is 1441…

A: We can solve the following problem as follows. Let x be the number of boxes she can move at a time.…

Q: In a population of 100,000 people, 40,000 are infected with a virus. After a person becomes infected…

A: Given data:The population is 100,000 people.In that 40,000 are infected wit a virus.3% will die each…