Question Number 195948 by Mastermind last updated on 13/Aug/23 $$\mathrm{An}\:\mathrm{object}\:\mathrm{is}\:\mathrm{said}\:\mathrm{to}\:\mathrm{cross}\:\mathrm{a}\:\mathrm{thousand}\: \\ $$$$\mathrm{kilimeters}\:\mathrm{in}\:\mathrm{planks}\:\mathrm{constant}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{times}\:\mathrm{faster}\:\mathrm{is}\:\mathrm{the}\:\mathrm{object}\:\mathrm{to}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{light}.\:\mathrm{plank}'\mathrm{s}\:\mathrm{time}\:=\:\mathrm{10}^{−\mathrm{44}} \mathrm{sec}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 195848 by pete last updated on 11/Aug/23 $$\mathrm{Please}\:\mathrm{how}\:\mathrm{did}\:\mid\mathrm{z}−\mathrm{a}\mid=\mathrm{r}\:\mathrm{became}\: \\ $$$$\mathrm{z}=\:\mathrm{a}\:+\:\mathrm{re}^{\mathrm{i}\theta} ? \\ $$ Answered by Frix last updated on 11/Aug/23 $$\mid{z}−{a}\mid={r}\:\Rightarrow\:{z}−{a}={r}\mathrm{e}^{\mathrm{i}\theta} \\ $$$$\mathrm{This}\:\mathrm{step}\:\mathrm{is}\:\mathrm{always}\:\mathrm{true},\:\mathrm{even}\:\mathrm{for}\:{z}−{a}\in\mathbb{R}…
Question Number 195747 by Mastermind last updated on 09/Aug/23 Commented by AST last updated on 09/Aug/23 $${The}\:{total}\:{amount}\:{spent}\:{does}\:{not}\:{have}\:{to}\:{be} \\ $$$${necessarily}\:{equal}\:{to}\:{the}\:{sum}\:{of}\:{the}\:{remaining} \\ $$$${amount}\:{at}\:{each}\:{step}\:{of}\:{your}\:{spending}.\:{In}\:{fact}, \\ $$$${we}\:{can}\:{make}\:{that}\:{N}\mathrm{51}\:{grow}\:{arbitrarily}\:{large} \\ $$$${by}\:{spending}\:\epsilon\left({such}\:{as}\:\mathrm{0}.\mathrm{000000001}\right)\:{at}\:{every}\:{step}.…
Question Number 195718 by Mastermind last updated on 08/Aug/23 Commented by AST last updated on 08/Aug/23 $$\left(\frac{\mathrm{13}×\mathrm{14}}{\mathrm{2}}−\mathrm{2}\right)+\mathrm{2}=\mathrm{91} \\ $$ Answered by JDamian last updated on…
Question Number 195612 by Mastermind last updated on 05/Aug/23 Answered by a.lgnaoui last updated on 05/Aug/23 $$\mathrm{r}−\mathrm{73}=\pm\mathrm{16} \\ $$$$\begin{cases}{\mathrm{r}−\mathrm{73}=\mathrm{16}\:\:\:\:\:\:\:\:\Rightarrow\:\:\boldsymbol{\mathrm{r}}=\mathrm{89}}\\{\boldsymbol{\mathrm{r}}−\mathrm{73}=−\mathrm{16}\:\:\:\Rightarrow\:\:\boldsymbol{\mathrm{r}}=\mathrm{57}}\end{cases} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{r}}=\left\{\mathrm{57},\mathrm{89}\right\} \\ $$ Terms of…
Question Number 195606 by Mastermind last updated on 05/Aug/23 Commented by mr W last updated on 08/Aug/23 $${do}\:{you}\:{have}\:{the}\:{solution}\:{of}\:{the} \\ $$$${question}? \\ $$ Terms of Service…
Question Number 195557 by Mastermind last updated on 04/Aug/23 Answered by MM42 last updated on 05/Aug/23 $$\mathrm{67} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 195520 by moh777 last updated on 04/Aug/23 $$\: \\ $$$$\:\:\:\:\:{find}\:{domine}\:{and}\:{range}\:{of}\:{function}\: \\ $$$$\:\:\:\:\:{f}\left({x},{y}\right)\:=\:\sqrt{\frac{{x}+{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{4}}} \\ $$$$ \\ $$$$ \\ $$ Answered by…
Question Number 195501 by Mastermind last updated on 03/Aug/23 Answered by MM42 last updated on 03/Aug/23 $$\mathrm{68} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 195412 by Calculusboy last updated on 02/Aug/23 Answered by AST last updated on 02/Aug/23 $${v}_{\mathrm{2}} \left({a}^{\mathrm{2}^{{n}} } −\mathrm{1}\right)={v}_{\mathrm{2}} \left({a}−\mathrm{1}\right)+{n}+{v}_{\mathrm{2}} \left({a}+\mathrm{1}\right)−\mathrm{1}\geqslant{n}+\mathrm{2} \\ $$$$\Rightarrow\mathrm{2}^{{n}+\mathrm{2}} \mid{a}^{\mathrm{2}^{{n}}…