(1) Construct an example for three distinguish points A, B and C in a 3- space for validating the following inequality: ||AC||² ≤ ||AB||² + ||BC||² Do NOT use examples and exercises from the textbook and Study Guide.

Q: Let f [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

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Q: Not to Scale b Co! = In the diagram OAB is a triangle with vector OA=a and OB=b such that|a|=5, |…

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Q: Let f: [-2,2] → R be defined on [0.2] by f(x)= {2 rove that f is Riemann integral. X≤0 x < 0

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Q: N o q Lor -00 10 The function determining the shapes above is f(x) = a√z. The area shown on the…

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Q: f(X) is a convex function, then ef(x) is also convex function. True

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Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

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Q: Is the function u(x, y) = x² − y² harmonic? If your answer is yes, find a corresponding analytic…

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Q: 4. (a) Find the general solution of the system x₁ = 4x17x2, x2 = 7x1 + 4x₂. (b) Let a and b be real…

A: We solve by eigenvalues and eigenvectors method.

Q: Q1) Determine the halve range odd expansion of the function whose definition is: 0≤x≤1 f(x) = 2-x…

A: Given function is f(x)=1,        0≤x≤12-x,   1≤x≤2 Halve range expansion series is the Fourier sine…

Q: The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t lies in the interval (a)…

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Q: olve by using the method of d'y dx² + 2x dy dx undetermined coeffic + (x2 + 5) y = xe-x

A: Given second order differential equation: d2ydx2+2xdydx+x2+5y=xe-x22

Q: 9. Find inverse Laplace: es S

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Q: Q2:Find out the completion time and the critical activities for the following project: D 20 8 B K 6…

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Q: . Find inverse Laplace:

A: Note: As per Bartleby guidelines, we cannot author handwritten answers, so I am giving type written…

Q: Given the following matrices. Solve for the following: 15 25 58 81 2 14 A= 10 11 5 B = 42 3 -1 -6 42…

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Q: 1. Consider L{y(t)} = Y(s). By solving the equation ty"(t) + 2ty(t)=0 con y(0) = 0 you have to: A)…

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Q: find range of y 1 1 X-2 R/{1,2} O R/{2} O R/{1} O R/{0,1} O 1-

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Q: Using the bisection method, find an approximate root of the equation sin x = 1/x, that lies between…

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Q: Solve by using the method of undetermined coefficients :

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Q: For the function f(x) = 6x-5, construct and simplify the difference quotient The difference quotient…

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Q: 3 y = 4 0.2x +5

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Q: 4. Alton had $725 for Medicare, $3000 for state income tax, and $3100 for Social Security deducted…

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Q: -8s +8 s288 +1 you obtain an equivalent expression given by: s-4 a ~ { ( 2 = ²4 ) ² = 2 ² } + 82 -¹…

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Q: Solve dy dx + y tan x = -y³x sec²(x)

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Q: marks. THE CO igle in 111° 103° 122 polygon all of ning for

A: We know that sum of all angle of pentagon = 540 And 4 angle is given 122, 103, 111,90 and let assume…

Q: 6. The graph of the function y = x¹ is transformed to the graph of the function y=-[2(x+3)]¹ + 1 by…

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Q: 6. What are the advantages and disadvantages of algebraic vectors compared to geometric vectors?

A: Algebraic vectors deals with the properties of vector space, main part of linear algebra. Using…

Q: -49 fy y(u)du = sen (7t) * g(t) for some function g(t). 11. By solving the equation y(t) = = sen…

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Q: Consider the figure below. (Use the rules for working with measurements to give your answers to the…

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Q: 3. Answer the following questions. Show all solution steps: x3 y6 z4 a. Simplify: ÷ 2(x4y7)⁰ xm y2…

A: (a) we have to simplify x2x4y70÷x3y6z4xmy2z-5 also, m=2 Then x2x4y70÷x3y6z4x2y2z-5

Q: transform the given differential equation into an equivalent. system of first-order differential…

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Q: Find the general solution of this ODE: d²y dt² dy + 2 + 17y=11e-3t dt The solution will be of the…

A: The given differential equation is: d2ydt2+2dydt+17y=11e-3t Find the general solution of the…

Q: The question is use the amortization table to determine the payment required to amortize a loan of…

A: Summary of Calculation: Monthly pay = $ 300.30 Total of 30 loan payment = $ 9008.94 Total interest =…

Q: 2: Let f be differentiable function on (a,b) and continuous on[a, b]. Let g be define Rang f. If f…

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Q: Interest (Php) Matu

A: 1) Formula for interest in simple interest: Interest= principal × rate × time Formula for maturity…

Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6).

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Q: Solve using Power Series Centred Around Zero. Xy" + (1-x) y' + 2y=0 2=REZ+

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Q: Use bisection method to find the root of x^3 –x^2 – 3x – 3 with two initial points xl=3 and xr=2 and…

A: The given equation is x3-x2-3x-3=0. To find: the root between 2 and 3 .

Q: Consider an RLC circuit with resistance 2 ohms, inductance 0.05 henrys, capacitance 0.006 farads,…

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Q: Find inverse Laplace: 1 es S

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Q: If u and v are the two solutions of d'y dy dx² + P + Qy = 0 dx uv₂u₂v + P (uv₁u₁v) = 0 (uv₁ - u₁v) =…

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Q: 12. The golden ratio is a famous number/ratio in mathematics that can be traced back to the work of…

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Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Since you have posted multipart question and we can answer three subparts. So answered the first…

Q: Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z =…

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Q: 4. x + 3x = 0 Solve y + 3x + 2y = 0 ż+2y+z=0 transforms. for x(0) = 1, y(0) = 0, z(0) = 1 by using…

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Q: (a) Draw a direction field for the given differential equation. (b) Based on an inspection of the…

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Q: Find the Z-transform of the following sequence/function (with ROC). Show complete solution. 1. x(n)=…

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6).

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Q: d) 2log4128-5

A: Introduction: To make it less hard or difficult; to make it simpler or easier To condense an…