Recall that if p> 5 is prime, then the decimal expansion of 1/p has period e equal to the order of 10 mod p. Show that as p grows, e tends to infinity. (Hint: show that e≥ log10(p).)

Q: Find the order of z=0 for the following function:

A: 7Explanation:The order of a function at a point is the order of the zero at that point. It's the…

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Q: 3 b) please

A: f(z) = (z−zi​)31​ + 8 z−(i−3)z−(i−3)​ + 6ez-iExplanation:Here's the justification:a. Pole of order 3…

Q: Part 1: Think about a business you are working in, hope to develop, or plan on joining after you…

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Q: Show that the σ-algebra B of Borel sets contains all closed sets

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A: We will use bounds of error in approximation using trapezoidal rule and Simpsons rule

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: final answer = approximately zeroExplanation:In this article, we present the Brazilian Portuguese…

Q: 4. This question is about linear transformations and subspaces. Let L: R4 R³ be a linear…

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Q: need help

A: (a)No, N is "not reflexive".is not equal to,False, is not. (b)Yes, N is symmetric.is not equal to,is…

Q: Let k = N. Let g: NZ be defined by g(0) = 1 and g(n) = kg(n - 1) + k − 1 for n≥k - 1. Write an…

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Q: Let f(x, y) = 4/x+5/y+ 6x + 7y in the region R where x, y > 0. Explain why must have a global…

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A: Given that an investment of $10,000 earns interest at an annual rate of 6.7%…

Q: 6. (Basis and Dimension.) Say P3(R) = {f: R → R | f(x) = ax³ + bx²+cx+d for some a, b, c, d = R}…

A: The objective of the question is to determine which of the two collections of functions, W₁ and W₂,…

Q: Determine the local stability of equilibrium of the predator prey model d x(t)=x-0.5xy dt d y(t) =…

A: Given system of differential equation:

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A: I can answer only one question according to Q&A guidelines. So I answered part (a).

Q: Classify the following functions with respect to concavity and convexity. Please explain as detailed…

A: The given question is discussed in the explanation section.Explanation:Answer:Let's classify the…

Q: Sketch the curve given in parametric form by r = ti+ sin tj + cos tk, 0 < t < 2π, and write down an…

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Q: Let the universal set R, the set of real numbers. Let A= {x = R| 1≤x6 } {xЄR|x6} O {x ER 1≤x≤6} ○…

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Q: Find the solution of the given initial value problem 40y" + 13y" + y' = 0, y(0) = -1; y'(0) = −6,…

A: We will find the solution of the given differential equations.

Q: Here are two new definitions about graphs. The distance between two vertices in a graph is the…

A: The diameter of a graph is the greatest distance between any pair of vertices in the graph.We have…

Q: Solve the differential equation below using the Laplace transform:

A: The required solution is    y(t)=sintExplanation:Step 1: Given  :…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: ∂t∂z​=540 when s=−3,t=3.Explanation:

Q: 8y" +32y+8y = 3x a) What is the general solution for homogenous ODE (yn) b) What is the particular…

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Q: SHOW ALL YOUR WORK! 1. Let sets X, Y, and Z be subsets of the universal set U. Using Venn diagrams,…

A: The objective of this question is to determine the conditions that must hold for the union of a set…

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: (3) Consider the following LPP where a, b = R: maximize ax1 + bx2 subject to 4x1 + 3x2 ≥ 12 x1, x20…

A: The objective of this question is to solve the given Linear Programming Problem (LPP) graphically.…

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A: The commission rate is calculated by calculating the difference between the purchase rate and the…

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Q: 2. The context of this question is linear transformations on the plane R². Let T: R2 R² be the…

A: is a function defined by first rotating the vector counter-clockwise by an angle of  and then…

Q: Skis are listed by a manufacturer for $860, less trade discounts of 30% and 18%. What further rate…

A: 9.043%Explanation:

Q: 1. This question is about subspaces and bases. Let H₁R be the hyperplane defined in normal form by…

A:

Q: 5. Use the Laplace transform to solve the value problem Initials y" + y = d(t − 2), y(0) = 0, y'(0)…

A: We have to use Laplace transform to solve the following IVPWe know that

Q: Combine the two equation and make Eeq the subject , no value need just one equation

A: The combined equation for (Eeq​) is:…

Q: - Find R 7(x + y) sin(x − y) dA, where R is the triangular region whose verticies are (-5, 5), (5,5)…

A: Given, a triangular region with vertices , and .Change of variables  and Integrating function It…

Q: let n be a positive integer. prove that (X nY) nZ = X n(Y nZ) for all x,y,z E Z

A: You can prove the statement that (X∩Y)∩Z=X∩(Y∩Z) for all sets X, Y, and Z by using the distributive…

Q: 1. Suppose V is a finite-dimensional vector space with dim(V) = n, and that T € L(V) has n distinct…

A: Proof are in explanation sectionExplanation:Step 1:

Q: Determine the local stability of equilibrium of the ODE d dt x(t) = x(1−xy) dt³ (t) = y=x².

A: Given, a system of ordinary differential equations:It is required to find the local stability of the…

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: We need 45 minutes past hour to complete the evaluation of the given scripts.Explanation:Step 1:

Q: 4. Sketch the solid whose volume is given by the iterated integral. 1 1-x 2-2z dy dz dx 0 2 2-y (b)…

A: We have to sketch the solid whose volume is given in the iterated integral.Note: According to the…

Q: (10) Find the general solution of y" − x²y' + xy = x - if a solution of homogeneous part is y₁(x)

A: i have attached the solution image. please check it.Explanation:

Q: Write the function f(x,y) = xcosh(x)cos(y) - ysinh(x)sin(y) + i(xsinh(x)sin(y) + ycosh(x)sin(y)) in…

A: f(z)=Re(z)cosh(Re(z))cos(Im(z))−Im(z)sinh(Re(z))sin(Im(z))+i(Re(z)sinh(Re(z))sin(Im(z))+Im(z)cosh(Re…

Q: 2.- Using the parameter variation method, solve the following equation 4 - y = x

A: Answer y(x)=c1​e−x/2+c2​ex/2+8ex/2x2​−4ex/2x​    Explanation:Step 1: We have to solve the…

Q: need help

A: R is only symmetric relation.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: In this question, we discuss the concepts of range, nullspace, and row space of a matrix. Write a…

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Q: The net price of an item after trade discounts of 30.00%, 11.00%, and 5.50% is $2,300.00. a.…

A: A. Regular selling price of the goods: $3906.68B. Equivalent discount rate of the series of discount…

Q: 2) a) A table of values of a function g is given. Use Simpson's Rule to estimate f₁1.6 g(x)dx. x…

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Q: Convert the following Volterra integral equation into an initial value problem  y(x) =  integral of…

A: Let ϕ(x)=∫a(x)b(x)f(x,t)dtWhere both a(x),b(x) are differentiable functions.Then the derivative…

Q: Good afternoon, Unsure how to approach this.

A: detJ=p^2sin(phi)V=4/3(pi)p^3Explanation:Step 1: Step 2: Step 3: Step 4: