Question Number 164814 by mr W last updated on 22/Jan/22 $${does}\:{the}\:{forum}\:{support}\:{animated} \\ $$$${images}\:{in}\:{gif}\:{format}? \\ $$ Commented by Rasheed.Sindhi last updated on 22/Jan/22 $${I}\:{think}\:{animation}\:{not}\:{supported}\:\boldsymbol{{sir}}. \\ $$$$\left({I}'{ve}\:{tried}\right)…
Question Number 164810 by tabata last updated on 22/Jan/22 $${find}\:{n}^{{th}} \:{terms}\:{of}\:<\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{0},….> \\ $$ Commented by mr W last updated on 22/Jan/22 $${a}_{{n}} ={n}\:\left({mod}\:\mathrm{2}\right) \\ $$$${a}_{{n}}…
Question Number 33724 by mondodotto@gmail.com last updated on 22/Apr/18 $$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{persons}}\:\boldsymbol{\mathrm{selected}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{random}} \\ $$$$\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{stopped}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{street}},\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{probability}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{born}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{friday}}? \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{born}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{friday}}\:\boldsymbol{\mathrm{and}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{others}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{thursday}}? \\ $$$$\left(\boldsymbol{\mathrm{iii}}\right)\boldsymbol{\mathrm{none}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{born}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{friday}} \\ $$$$ \\…
Question Number 99259 by DGmichael last updated on 19/Jun/20 Answered by abdomathmax last updated on 19/Jun/20 $$\mathrm{A}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\mathrm{k}\:\mathrm{2}^{\mathrm{k}−\mathrm{1}} \:\mathrm{let}\:\mathrm{p}\left(\mathrm{x}\right)\:=\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\mathrm{x}^{\mathrm{k}} \:\Rightarrow \\…
Question Number 164793 by bekzodjumayev last updated on 22/Jan/22 Commented by bekzodjumayev last updated on 22/Jan/22 $${Help} \\ $$ Commented by mr W last updated…
Question Number 164783 by mkam last updated on 21/Jan/22 Answered by Mathspace last updated on 21/Jan/22 $$={lim}_{{x}\rightarrow\mathrm{3}} \frac{{f}\left({x}\right)−{f}\left(\mathrm{3}\right)}{{x}−\mathrm{3}}×\frac{{x}−\mathrm{3}}{\left({x}−\mathrm{3}\right)\left({x}+\mathrm{3}\right)} \\ $$$$={lim}_{{x}\rightarrow\mathrm{3}} \frac{{f}\left({x}\right)−{f}\left(\mathrm{3}\right)}{{x}−\mathrm{3}}×{lim}_{{x}\rightarrow\mathrm{3}} \frac{\mathrm{1}}{{x}+\mathrm{3}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}{f}^{'} \left(\mathrm{3}\right)…
Question Number 99232 by otchereabdullai@gmail.com last updated on 19/Jun/20 $$\mathrm{In}\:\mathrm{a}\:\mathrm{class}\:\mathrm{of}\:\:\mathrm{70}\:\mathrm{students},\:\mathrm{6}\:\mathrm{offer}\: \\ $$$$\mathrm{economices}\:\mathrm{only},\:\mathrm{18}\:\mathrm{offer}\:\mathrm{economics}\: \\ $$$$\mathrm{but}\:\mathrm{not}\:\mathrm{mathematics},\:\mathrm{36}\:\mathrm{offer}\: \\ $$$$\mathrm{economics}\:\mathrm{and}\:\mathrm{geography},\:\mathrm{53}\:\mathrm{offer}\: \\ $$$$\mathrm{economics},\:\mathrm{50}\:\mathrm{offer}\:\mathrm{Geography}\:\mathrm{and}\:\mathrm{34} \\ $$$$\mathrm{offer}\:\mathrm{mathematics}\:\mathrm{and}\:\mathrm{geography},\:\mathrm{all}\: \\ $$$$\mathrm{students}\:\mathrm{off}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{subject}. \\ $$$$\left.\mathrm{a}\right)\:\mathrm{illustrate}\:\mathrm{the}\:\mathrm{information}\:\mathrm{on}\:\mathrm{a}\:\mathrm{venn} \\…
Question Number 99227 by Algoritm last updated on 19/Jun/20 Commented by Algoritm last updated on 19/Jun/20 $$\mathrm{thank}\:\mathrm{you} \\ $$ Commented by MJS last updated on…
Question Number 33690 by mondodotto@gmail.com last updated on 22/Apr/18 $$\int\frac{\boldsymbol{\mathrm{dx}}}{\:\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{x}}}+\sqrt{\boldsymbol{\mathrm{x}}}} \\ $$ Answered by math1967 last updated on 22/Apr/18 $${let}\:{x}={z}^{\mathrm{6}} \:\:\therefore{dx}=\mathrm{6}{z}^{\mathrm{5}} {dz} \\ $$$$\mathrm{6}\int\frac{{z}^{\mathrm{5}} {dz}}{{z}^{\mathrm{2}}…
Question Number 33688 by mondodotto@gmail.com last updated on 22/Apr/18 $$\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{10}^{\boldsymbol{{x}}} +\mathrm{10}^{−\boldsymbol{{x}}} \right)\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)=\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)+\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 22/Apr/18…