Let x, y and z be real numbers. Show that the distance between a real number x and y is the sum of the distances between x and y and between y and z if and only if y ∈ [x, z]. Illustrate geometrically on the real line

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Q: 69=y"+y = f(t) where: (0)=0, y₁ (0) = 1 0₁ 0≤+ 2π ។ 1 f(t) ] 1 0,

A: We use definition of Heaviside function then solve by Laplace transform.

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A: We know, x∈A∩B ⇔x∈A and x∈B

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Q: Let n E 2, n > Let greatest common divisor of f([aln) = f(bln) whenever la

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A: To find a vector of magnitude 9 in the direction of v=&lt;-3,2&gt; .

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Q: Solve using Euler’s Method. Approximate up to 5 decimal places.

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Q: 5) Examine the characters of the following Series using the Comparison tests. DO a) = 2n²+3n+1 n=1 2…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: f(x) = x2 cosh 3x -

A: Simply, I have used laplace transform formula.

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A: Given,                F=x, yR= x, y: x2+y2≤9

Q: Find the Fourier series of f(x) stion 1 If f(x) = x,-2 ≤x<2

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Q: 2. Using the Fundamental Theorem of Arithmetic, prove that for all a, b, c E Z, if alc, blc and (a,…

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Q: B: Solve the problem of heat transfer through the fin by Finite Differences Method: d²T = -10 x², T…

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Q: Parent Function y = log10x (x, y) VA x = Transformed Function y = -2log10 (x+4)-3 VA x =

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Q: Gauus Jorden's idea is a) Convert the system to an upper or lower trigonometric matrix b) Convert…

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Q: uestions 1. Use Euclidean Algorithm to find the greatest common divisor of 1207 and 569.

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Q: ans. It has 5 acres of pecan Ere each year. The family use

A: The decision variables can be taken for pecan pies (both unshelled and shelled) and cookies.

Q: 6. Find the derivative of y= 2x² (3x - 4). A. 6x³ - 8x² B. 18x² - 16x 7. Find the derivative:…

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Q: the root for the following equation ex -3x, [1.5, 1.6] then f(c4) = 1.50625. O True O False

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: solve using laplace transform ૧ . y"+y = f(t) where: (0)=0, y'(0)=1 1 0, 0≤ t 2π y

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

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Q: the root for the following equation ex - 3x, [1.5, 1.6] then f(c4) = 1.50625.

A: Here follow the python script.

Q: 910

A: 9. Given if the set is the empty set.                           x|x&lt;6 and x&gt;10

Q: 1. Consider the following linear program: Max 3A + 2B s.t. 1A 1B 3A 1B 1A + 2B 10 24 16 A, B ≥ 0 a.…

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Q: 3. Find points at which the mapping defined by f(z) = nz+z^n (n E N) is not conformal.

A: Given :  f(z) = nz+zn,  where  n∈ℕ. To find : The points at which f is not conformal.

Q: Find the orthogonal complement S¹, and find the direct sum S + S¹. 6 -08 S = span 1 1 (a) Find the…

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Q: (HW) Ex. 5 Solve the systems of ODE and the initial value problem (1) V₁ + y₂ = -2cost v₁-v₂ = 2sint…

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