For a, b, c, d e R, show the following. (a) If a >b and c> d, then a +c>b+d.

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A: To write: (i) Applications of hamiltonian circuits. (ii) Applications of Graph theory.

Q: · Find fF · dĩ for F = -yi – 4x j+4zk if C is the helix æ = cos t, y = sin t, z = t, for 0 < t < 47

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Q: x3 + xy² + x + i(x²y + y³ – y) x² + y2 F(z)

A: We have to find the derivative of f(z).

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Q: Suppose you are expanding (5x - 2y)°. a) i) How many terms are there in the expansion? ii) State the…

A: In this question, the concept of the Binomial Theorem is applied. Binomial Theorem Using the concept…

Q: 1. Define function f : Z+ → Z such that f(n) = /n. (a) Is f one-to-one? Justify (prove) your answer.

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Q: Question 3. Create proofs to show the following. a) ¬A is provably equivalent to ¬(A ^ A). b) The…

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Q: please answer all the 4 parts, request

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Q: Find a root of: f(x) = -25+82x – 90x² + 44x³ – 8x+ + 0.7x³ Using False Position Method, perform 5…

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Q: Show the differential equation. Choose your answer from the choices below. A. e^x + x²y= Cy B. e^y -…

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Q: 1 (4) s What can be said about the 2 matrices based on your result (d)? -0.5 -1.5

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Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y= f…

A: Introduction: The rectangular form of a function is y=fx. If we introduce another independent…

Q: How many permutations are there of 10 people arranged in a circle? 10 10! - 1! 362,880 3,628,800

A: The number of permutations of n elements in a circle is (n-1)!

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Q: 2. Suppose I wish to define a function g : {0, 1, 2, 3, 4} → Z that takes an input of an equivalence…

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Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: Use the Newton Raphson method to find the second iteration of the root to 5 decimal places of the…

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A: Given that, the light source is directly proportional to the strength of the source and inversely…

Q: X = --6t-1 2 Find all points on the graph of that have either a vertical or horizontal y=- -9t +1 3…

A: Here given x=3t22-6t-1y=t33-9t+1

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Q: (b) Let f(r, y. 2) = (ryz, I +y +2) and g(1.y. 2) = (1, y². 2). Then find (i) fog, if possible.…

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Q: Pachissn Greaty Lae Gogle Trn Thinga to da ELa Gup W 171 Section Wan Lingnal LARCALC11 3.3.037. MY…

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Q: Prove that if a > 0, k > 1, and ak -1 is prime, then a = 2 and k is prime. %3D

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Q: (b) A right-angled triangle has sides of length 3 and æ, and a hypotenuse of length e. Given that (2…

A: Given a right angle triangle has sides of length 3 and x and a Hypotenuse of length l. Given that…

Q: Using secant method, detemine a root of sin Vx - x with initial guesses xo = 0.5 and x, = 1…

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Q: - 2t 2. 4y" + y = e " sin (0.5t) + 6t cos (0.5 t)

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Q: In problems 1 to 3 solve the given differential equations by writing the general solution. Write all…

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Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: 3. Given the equation: Solve the differential equation. Choose your answer from the choices below.…

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