Why is /(x2 – x1)² + (y2 – Y1)² equal to V(x1 – x2)² + (y1 – Y2)² when subtraction is NOT commutative?

Q: 1. Let f: Z/4Z → Z/2Z × Z/2Z be defined by f([0]) = ([0], [0]), ƒ([1]) = ([1], [1]), f([2]) = ([0],…

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Q: 2 Use the inverse of A = 3 125 60 80 30 45 19 26 3 to decode the following 85 120 6 8 10 15 84 117…

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Q: A researcher is analyzing the relationship between various variables in housing data for 32 cities:…

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Q: A bin contains 5 red and 5 green balls. 2 balls are chosen at random, without replacement. Let the…

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Q: 2. Consider the following labeling scheme for the set of rational numbers Q = {†, where a E I, and…

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Q: 1. Write the following permutations in cycle notation. (1bd from 5.4) (1 2 3 4 5 (1 2 3 4 5 4 3 2 5/…

A: To find- Write the following permutations in cycle notation. 1234542513 1234514325

Q: 2. Prove that a 2 x 2 matrix A with entries in Z26 is invertible if and only if gcd(det(A), 26) = 1.

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Q: 2. Give an example of an unbounded sequence {an} of negative terms such that an does not diverge to…

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Q: Find the following.

A: Given: I=∫5x2-6x+3dx We know that ∫xndx=xn+1n+1+c…

Q: 1. Find all x € ZZ satisfying each of the following equations. [from # 1, 3.5] a) 5x + 1 = 13 (mod…

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Q: Show {5, 10, 15, 20, - - ·} is countable. (Hint: Use the function f(n) and onto). = 5n and show it…

A: 4 Given set is 5,10,15,20,....... We have to show that the set 5,10,15,20,...... is countable. Let a…

Q: Let S = R\{-1} and define a binary operation on S by a*b = a + b + ab. Prove that (S, *) is an…

A: 2) S=R∖-1 binary operation defined by a*b=a+b+ab

Q: • Write 2.4020202 -.. as a fraction of two integers. • Can the number 3.73747879710711 -.. be…

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Q: Prove that P(Ø) = 0. Hint: Let A, = Ø for all i in equation (1.3.3).

A: Consider that

Q: 4. Let a1 = v2 and let an for n > 2 be defined recursively by the formula = Ip V2+ van. an+1 = Prove…

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Q: Find an equation for the sine graph, f(x): fx 3 2 -360° -180° 180° 360° -1 -2 -3 -4 Write your…

A: first observe vertical and horizontal shift then see the changes

Q: In a study of government financial aid for college students, it becomes necessary to estimate the…

A: Solution: From the given information, confidence level is 0.99 and E=0.05.

Q: 0 500 soft ( + ( ① so) & cu!ss) d + ) (cose) dr

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Q: (a) Find the connected components of each graph. (i) G = (V, E). V = {a, b, c, d, e}. E = Ø (ii) G =…

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Q: Sales records indicate that if Blu-ray players are priced at $240, then a large store sells an…

A: If the price is $240, then the store can sell 6 units per day  If the price is $120, then the store…

Q: Calculate by changing to polar coordinates. 5e (+y) dæ dy -4 а) -10те + 107 b) e* 2 -4 е c) 2 2 d) O…

A: The given integral is ∫-22∫-4-y24-y25e-(x2+y2)dxdy. Here, the limit of x varies from -4-y2  to 4-y2…

Q: In the circle below, IK is a diameter and IL is tangent at I. Suppose m IJ = 66°. Find the…

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Q: Use the MVT to show • Prove that the derivative of f(x) = k, on [a, b], where k is constant, is…

A: We know that the mean value theorem states that: If f is a continuous function on a,b, f is…

Q: 1. In the Cantor construction of the Cantor st K, remove the middle fifth instead of the middle…

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Q: Give an example of a nonzero continuous function f on [0,1] such that f f(x) dx = 0.

A: We will be solving Q2(i) as asked. We have to give an example of a nonzero continuous function f  on…