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Question-69098

Question Number 69098 by rajesh4661kumar@gmail.com last updated on 20/Sep/19 Commented by Kunal12588 last updated on 20/Sep/19 $${its}\:{really}\:{easy}\:{just}\:{construct}\:{a}\:{line}\:{through} \\ $$$${F}\:{parallel}\:{to}\:{AB}\:\&\:{CD}.\:{and}\:{remember}\:{the} \\ $$$${property}\:{of}\:{alternate}\:{interior}\:{angles}\:{and} \\ $$$${consectutive}\:{interior}\:{angles} \\ $$…

To-Tinku-Tara-The-Developer-Sir-You-re-going-to-update-this-useful-in-real-sense-precious-app-Taking-advantage-of-this-opportunity-I-suggest-some-revolutionary-changes-if-they-re-possib

Question Number 69010 by Rasheed.Sindhi last updated on 17/Sep/19 $${To}\:{Tinku}\:{Tara},\:{The}\:{Developer} \\ $$$${Sir}, \\ $$$$\:\:\:\:\:\:\:\:\:{You}'{re}\:{going}\:{to}\:{update}\:{this}, \\ $$$$\boldsymbol{{useful}}\:\boldsymbol{{in}}\:\boldsymbol{{real}}\:\boldsymbol{{sense}},\:{precious}\:{app}. \\ $$$${Taking}\:{advantage}\:{of}\:{this}\:{opportunity} \\ $$$${I}\:{suggest}\:{some}\:{revolutionary}\: \\ $$$${changes}\:{if}\:{they}'{re}\:{possible}\:{for}\:{you}. \\ $$$$\bullet{HIDE}/{UNHIDE}\:{DETALS}. \\…

The-speed-of-a-train-is-reduced-from-80km-hr-to-40km-hr-in-a-distance-of-500m-on-applying-the-brakes-i-How-much-further-will-the-train-travels-before-coming-to-rest-ii-Assuming-the-retar

Question Number 134530 by I want to learn more last updated on 04/Mar/21 $$\mathrm{The}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{a}\:\mathrm{train}\:\mathrm{is}\:\mathrm{reduced}\:\mathrm{from}\:\:\mathrm{80km}/\mathrm{hr}\:\:\mathrm{to}\:\:\mathrm{40km}/\mathrm{hr}\:\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{distance}\:\mathrm{of}\:\:\mathrm{500m}\:\:\mathrm{on}\:\mathrm{applying}\:\mathrm{the}\:\mathrm{brakes}. \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{How}\:\mathrm{much}\:\mathrm{further}\:\mathrm{will}\:\mathrm{the}\:\mathrm{train}\:\mathrm{travels}\:\mathrm{before}\:\mathrm{coming}\:\mathrm{to}\:\mathrm{rest}. \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{Assuming}\:\mathrm{the}\:\mathrm{retardation}\:\mathrm{remains}\:\mathrm{constant},\:\mathrm{how}\:\mathrm{long}\:\mathrm{will}\:\mathrm{it} \\ $$$$\mathrm{take}\:\mathrm{to}\:\mathrm{bring}\:\mathrm{the}\:\mathrm{train}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{after}\:\mathrm{the}\:\mathrm{application}\:\mathrm{of}\:\mathrm{the}\:\mathrm{brakes}? \\ $$ Answered…

lets-u-v-w-C-3-such-that-uvw-0-proof-that-or-give-a-counter-example-v-u-w-v-u-v-w-u-w-u-v-w-0-

Question Number 3410 by 123456 last updated on 13/Dec/15 $$\mathrm{lets}\:\left({u},{v},{w}\right)\in\mathbb{C}^{\mathrm{3}} \:\mathrm{such}\:\mathrm{that}\:{uvw}\neq\mathrm{0},\:\mathrm{proof} \\ $$$$\mathrm{that}\:\left(\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\right) \\ $$$$\frac{{v}}{{u}}=\frac{{w}}{{v}}\wedge\mid{u}\mid=\mid{v}\mid=\mid{w}\mid\wedge{u}\neq{w}\Rightarrow{u}+{v}+{w}=\mathrm{0} \\ $$ Commented by RasheedSindhi last updated on 13/Dec/15 $$\mathcal{W}{hat}\:{is}\:{meant}\:{by}\:{u},{v},{w}\in\mathbb{C}^{\mathrm{3}}…

sin1-sin2-2-sin3-3-sin4-4-1-2-

Question Number 134439 by Dwaipayan Shikari last updated on 03/Mar/21 $${sin}\mathrm{1}−\frac{{sin}\mathrm{2}}{\mathrm{2}}+\frac{{sin}\mathrm{3}}{\mathrm{3}}−\frac{{sin}\mathrm{4}}{\mathrm{4}}+…=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mnjuly1970 last updated on 03/Mar/21 $$\:\:\:\boldsymbol{\Omega}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {sin}\left({nx}\right)}{{n}}=\:\:\: \\…