Question Number 5809 by Apoorva last updated on 28/May/16 Commented by Apoorva last updated on 28/May/16 $${please}\:{solve}\:{this}\:{limit} \\ $$ Answered by Yozzii last updated on…
Question Number 71198 by Rio Michael last updated on 13/Oct/19 $${A}\:{particle}\:{P}\:{is}\:{projected}\:{from}\:\:{a}\:{point}\:{O}\:{at}\:\:{the}\:{edge}\:{of}\:{a}\:{cliff}\:\mathrm{60}{m} \\ $$$${from}\:{the}\:{sea}\:{with}\:{a}\:{velocity}\:{of}\:\mathrm{30}{ms}^{−\mathrm{1}} .\:{When}\:{P}\:{is}\:{at}\:{a}\:{point}\:{B} \\ $$$${where}\:{OB}\:{is}\:{a}\:{horizontal},\:{another}\:{particle}\:{Qsuch}\:{that}\: \\ $$$${P}\:{and}\:{Q}\:{hit}\:{the}\:{sea}\:{simultaneously}\:{at}\:{thesame}\:{point}\:{A}.\:{Gven}\:{that}\:{they} \\ $$$${strike}\:{the}\:{sea}\:\mathrm{6}{seconds}\:{after}\:{P}\:{was}\:{fired}\bar {\:}\:{calculate} \\ $$$$\left.{a}\right)\:{the}\:{sine}\:{of}\:{the}\:{angle}\:{of}\:{elevation}\:{of}\:{projection}. \\ $$$$\left.{b}\right)\:{the}\:{distance}\:{from}\:{A}\:{to}\:{O}.…
Question Number 5466 by 3 last updated on 15/May/16 $$\sqrt{\mathrm{8}} \\ $$ Answered by FilupSmith last updated on 15/May/16 $$\sqrt{\mathrm{8}}=\sqrt{\mathrm{4}×\mathrm{2}} \\ $$$$=\sqrt{\mathrm{4}}\sqrt{\mathrm{2}} \\ $$$$\therefore\sqrt{\mathrm{8}}=\mathrm{2}\sqrt{\mathrm{2}} \\…
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Question Number 5452 by 3 last updated on 15/May/16 $$\mathrm{5}×\mathrm{6} \\ $$ Answered by FilupSmith last updated on 15/May/16 $$=\mathrm{5}×\mathrm{3}×\mathrm{2} \\ $$$$=\mathrm{15}×\mathrm{2} \\ $$$$=\mathrm{30} \\…
Question Number 70876 by Fakhar last updated on 09/Oct/19 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{The}\:\mathrm{necessary}\:\mathrm{and}\:\mathrm{sufficient}\:\mathrm{condition} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{be}\:\mathrm{plane}\:\left(\mathrm{curve}\right)\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{r}}',\boldsymbol{\mathrm{r}}'',\boldsymbol{\mathrm{r}}'''\right]=\mathrm{0}. \\ $$$$\:\mathrm{OR}\:\:\:\: \\ $$$$\mathrm{A}\:\mathrm{curve}\:\mathrm{is}\:\mathrm{plane}\:\mathrm{curve}\:\mathrm{iff}\:\tau=\mathrm{0}. \\ $$ Terms of Service…
Question Number 5153 by 1771727373 last updated on 23/Apr/16 $${proof}\:\:\:\:{e}^{{i}\Theta} ={cos}\left(\Theta\right)+{isin}\left(\Theta\right) \\ $$ Answered by 123456 last updated on 23/Apr/16 $$\mathrm{lets}\:{f}\left(\theta\right)=\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta,{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\frac{\partial{f}}{\partial\theta}=−\mathrm{sin}\:\theta+{i}\mathrm{cos}\:\theta={i}\left(\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta\right)={if} \\ $$$$\frac{{df}}{{f}}={id}\theta…
Question Number 5115 by Yozzii last updated on 14/Apr/16 $${Given}\:{the}\:{space}\:{curve}\:\boldsymbol{{r}}=\boldsymbol{{r}}\left({t}\right),\:{show} \\ $$$${that}\:{its}\:{torsion}\:\tau\:{is}\:{given}\:{by} \\ $$$$\tau=\frac{\overset{.} {\boldsymbol{{r}}}\bullet\overset{..} {\boldsymbol{{r}}}×\overset{…} {\boldsymbol{{r}}}}{\mid\overset{.} {\boldsymbol{{r}}}×\overset{..} {\boldsymbol{{r}}}\mid^{\mathrm{2}} }.\:{It}\:{may}\:{help}\:{to}\:{know}\:{that}\:{its} \\ $$$${curvature}\:{is}\:{numerically}\:{given}\:{by}\:\kappa=\frac{\mid\overset{.} {\boldsymbol{{r}}}×\overset{..} {\boldsymbol{{r}}}\mid}{\mid\overset{.} {\boldsymbol{{r}}}\mid^{\mathrm{3}}…
Question Number 135933 by Engr_Jidda last updated on 17/Mar/21 $${Locate}\:{the}\:{critical}\:{points}\:{of}\:{the}\:{following} \\ $$$${functions}\:{and}\:{state}\:{the}\:{nature}\:{of}\:{each}. \\ $$$$\left(\mathrm{1}\right)\:{f}\left({x},{y}\right)=\mathrm{3}{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}−{x}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{y}+\mathrm{15} \\ $$$$\left(\mathrm{2}\right)\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} −\mathrm{4}{xy}+{y}^{\mathrm{2}} \\ $$ Answered by dhgt…