QUESTION 5. Show that if 0 ≤r≤n, then r+2 r r (c) + (+³) + (+³) +- + (*) -(+) n n+ = r (1)...using induction on n. (2) ...using a combinatorial proof.

A: Evaluate the integral  ∫0π​∣cosx∣3dx Since |cos x| is always non-negative, but cos x is positive for…

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A: Step 1. Balancing the EquationAssign oxidation numbers to each element:H2O2: O has an oxidation…

A: We have given, f(x)=3x1​ g(x)=x21​ We need to find, f(121​)−g(51​) =(3×121​1​)−((51​)21​)…

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A: It looks like you're referring to a distance comparison involving Pluto. Based on what you wrote, it…

A: Given Equivalence Relation The relation ∼ on Z is defined as:x ∼ y if and only if x - y is even.This…

A: Here's detailed explanation:part (a): 1. The Problem:We are asked to evaluate the contour…

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A: Part (a) If f and g are injective, then g∘f is injective.Proof:A function is injective (one-to-one)…

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: The problem presented is a second-order linear non-homogeneous differential equation accompanied…

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A: To prove that   SL(n,R) the set of  n×n  real matrices with determinant 1, forms a group under…

A: Step 1: Solve the Characteristic EquationThe characteristic equation for the differential…

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A: We have given, w=⎣⎢⎡​024​⎦⎥⎤​ v1​=⎣⎢⎡​135​⎦⎥⎤​ v2​=⎣⎢⎡​246​⎦⎥⎤​  We need to determine if there exist…

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A: ISA Sea Level Temperature: The ISA defines the standard sea level temperature as +15°C.ISA Lapse…

A: Step 1:Step 2:If you have any further doubt feel free to ask me.

A: We are given the depth of water in a harbour as a function of time: d(t)=5cos(12π​t)+11,0≤t≤24…

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A: We have the two linear systems:x′ = Ax,y′ = By, where:  We need to determine when these two systems…

A: The given differential equation is a second order homogeneous differential equation with constant…

A: The function given is:  f(z)=y2sinx+iy  where z = x + i y, and f(z) = u(x, y) + i v(x, y), with:…

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A: Step 1: Given: h(t)=u(t−4)e2t​ ,    where u(t - 4) is the unit step function. (i).  Applying the…

A: First, let's list down the given probabilities. P(A) = probability that it is made from Aluminum =…

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A: If you have any problem let me know in the comment section thankyou.

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A: Given function, k(x)=54​x−6 Find the inverse function, Replace x with k-1(x) and k(x) with x,…

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A: Given Problem Statement:Step 1:  Given InformationLet me know if you have any doubt.Please upvote if…

A: Check if f(x)  is Even or OddWe check: f(−x)=(−x)sin(−x)=−xsinx. Since f(-x) = f(x), the function is…

A: To determine the exact value of sin(1213π​) using a compound angle formula, we follow these steps:…

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

A: The total number of begonias planted by Lakshmi is 20 and the number of begonias eaten by the dog is…

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A: If you have any questions let me know in the comment box thankyou.

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