4. Prove that cos x cos y ≤ x - y for any x, y.

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Q: A game is called zero-sum if Vi, j : R(dį, dj) + S(di, &j) = c O a. True O b. False

A: True.True .

Q: What type of graph is this?

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Q: 2. Given the following functions f(t), use the formulas to find the Laplace transform c) f(t)=(e²¹ -…

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Q: C. Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

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Q: lowing values. ㅏ t) = 2t e 20et 35et x(0) = + 18- -t e [] eAt 3 4e2t-e-t 4e2t - 4e-t - e

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Q: Solve and extraneous reject any roots log 5√2²-21x = orth 2

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Q: Let fcilien be a collection of path components of a topological space X then c; =X. it

A: To prove that , we need to show two inclusions:1. : This follows directly from the definition of the…

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A: Given information:The electric field is given as .The surface is a part of the cylinder defined by…

Q: 1. Prove that (a) ▼ × (▼ƒ) = 0 for any C² function ƒ : U → R;

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Q: 4. Suppose K is a finite field, and let : (Z.+.0) → (K. +.0k) be the unique group homomorphism with…

A: The objective of this question is to prove several properties of a finite field K and a group…

Q: The set B = {4- 2x², 12 + 3x − 6x², 18x² - (35 + 6x)} is a basis for P₂. Find the coordinates of…

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Q: =ider some specific examples of the influence of e heated plate. The differential equation is Eq.…

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Q: 4. (i) Show that 2 is a primitive root mod 112 = 121. Hint: Use the criterion given by Lemma 6.4 and…

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Q: If is a solution of the differential equation then its coefficients C are related by the equation…

A: Here we have to find the coefficient cn related to the equation.

Q: Calculate P(FIE), if P(E|F) = 0.1 P(E) = 0.92 P(F) = 0.19 Round your answer to five decimals.

A: We have to calculate .

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Q: when values of theta are small approximations are sometimes used for trig functions sin theta, cos…

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Q: can both parts be written on paper please, if you can only do one then let it be part

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Q: acteristic polynomials is referred to in Exercises -11 p(t) = (t - A = ^-[-3-2]. -1 p(t) = (t - 3)(t…

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Q: You purchased 500 shares of stock six years ago at $21.25 and incurred brokerage fees of $345.  You…

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Q: The Center for Business Analytics is considering a refund policy for no-shows. No refund would be…

A: “Since you have asked multiple questions and due to the time constraint & complexity, we will…

Q: Look at some decimal expressions of fractions such as 2,3 25¹ 8 15 20 14¹ 50 12 7 9 16 71 50 54,30…

A: We need to analyse the given fractions to make a conjecture. Let us insert them into a table with…

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A: Given Information:Tesla has dealerships in Fresno and Walnut Creek.Manufacturing facilities are in…

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: Find the general solutions of the system. 6-90 x' = 1 1 1 12 0 x 39

A: Given Information:a) The system is given as b) The system is given as To find:The solution to the…

Q: 4. (i) Show that 2 is a primitive root mod 11² = 121. Hint: Use the criterion given by Lemma 6.4 and…

A: Basic facts on primitive roots will be used.

Q: Solve Cauchy problem for the non-homogeneous equation: y" - 5y' + 4y = x-2, y(0) = -1, y'(0) = 1…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

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Q: .,Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace…

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Q: 6. Find the inverse Laplace transform of the following: (assuming that inverse transform exists): 8…

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Q: [39] (a) u(t-3)(t-8) +2u(t-7) cos(xt) (b) (i-8 t-8+2 cos(xt) t<3, 3<t<7, 127.

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Q: Using the data in the table below, compute the latest finish time for activity E. Activity A B C D E…

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Q: Numerical analysis Find an interval [a,b] that contains the root of the function f(x)=x^3-4x-9?

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Q: can this be written on paper

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Q: 2. Function: 4. Function:

A: This graph is composition of two graphs.

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Q: 1. For the lamina in figure #1 compute the moment of Inertia about the x-axis. The density is p(x,…

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Q: 12. Consider the vectors x(¹) (t) = and x(2) (t) - (2) a. compute the Wronskian of x(¹) and x(2). b.…

A: Note that : Since you have posted a question with multiple sub parts, we will provide the solution…

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Q: Problem 4.4a. Produce a BVP for the Laplace equation, describing the equilibrium heat distribution…

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Q: Q5. (a) (b) Let P1 and P2 be distinct odd primes such that (p₁ − 1) | (p2 − 1). Let m = P1P2. Prove…

A: If gcd(a,p)=1 then ap−1≡1(modp)

Q: Let D be the region between the circles C₁ and C₂ centered at the origin of radius 1 and 4,…

A: Let C be the positively oriented, smooth, and simple closed curve in a plane, and D be the region…