Question Number 6174 by madscientist last updated on 17/Jun/16 $${prove}\:{the}\:{identity} \\ $$$$\int_{\partial{D}} \phi\bigtriangledown\phi\centerdot{nds}=\int\int_{{D}} \left(\phi\bigtriangledown^{\mathrm{2}\:} \phi+\bigtriangledown\phi\centerdot\bigtriangledown\phi\right){dA} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6169 by sanusihammed last updated on 17/Jun/16 $${A}\:{telephone}\:{wire}\:{hangs}\:{from}\:{two}\:{points}\:{P},\:{Q}\:\:\mathrm{60}{m}\:{apart} \\ $$$${P},\:{Q}\:\:{are}\:{on}\:{the}\:{same}\:{level}\:.\:{the}\:{mid}\:{point}\:{of}\:{the}\:{telephone} \\ $$$${wire}\:{is}\:\:\mathrm{3}{m}\:\:{below}\:{the}\:{level}\:{of}\:{P},\:{Q}.\:{Assuming}\:{that}\:{it}\:{hangs}\:{in}\: \\ $$$${form}\:{of}\:{a}\:{curve}\:,\:\:{find}\:{it}\:{equation}. \\ $$$$ \\ $$$${please}\:{help}.\:{thanks}\:{for}\:{your}\:{time}. \\ $$ Answered by Yozzii…
Question Number 6166 by sanusihammed last updated on 16/Jun/16 $${If}\:{the}\:{sum}\:{of}\:{the}\:{first}\:{nth}\:{terms}\:{of}\:{a}\:{sequence}\:{is}\:{given}\:{by}\: \\ $$$${S}_{{n}\:} \:=\:\:\mathrm{9}\left(\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{3}^{{n}} \:}\right) \\ $$$$\left({a}\right)\:{find}\:{the}\:{first}\:{and}\:{the}\:{second}\:{term}\:{of}\:{the}\:{sequence} \\ $$$$\left({b}\right)\:{find}\:{the}\:{nth}\:{term}\:{of}\:{the}\:{sequence} \\ $$$$\left({c}\right)\:{show}\:{that}\:{the}\:{sequence}\:{is}\:{a}\:{GP}\:{and}\:{find}\:{it}\:{common}\:{ratio} \\ $$$$ \\ $$$${please}\:{help}. \\…
Question Number 6164 by sanusihammed last updated on 16/Jun/16 $${A}\:{stone}\:{is}\:{thrown}\:{vertically}\:{upwards}\:{with}\:{velocity}\:\mathrm{20}{m}/{s}. \\ $$$${at}\:{the}\:{same}\:{time}\:,\:{and}\:\mathrm{20}{m}\:{vertically}\:{above}\:.\:{a}\:{second}\:{stone}\:{is} \\ $$$${allowed}\:{to}\:{fall}.\:{After}\:{whst}\:{time}\:{and}\:{at}\:{what}\:{height}\:{do}\:{they}\: \\ $$$${collide}\:?. \\ $$$${take}\:\:{g}\:=\:\mathrm{10}{m}/{s}^{\mathrm{2}} \\ $$ Commented by prakash jain last…
Question Number 71698 by TawaTawa last updated on 18/Oct/19 Commented by MJS last updated on 19/Oct/19 $$\mathrm{we}\:\mathrm{had}\:\mathrm{a}\:\mathrm{similar}\:\mathrm{example}\:\mathrm{a}\:\mathrm{few}\:\mathrm{weeks}\:\mathrm{ago} \\ $$ Commented by TawaTawa last updated on…
Question Number 71696 by TawaTawa last updated on 18/Oct/19 $$\mathrm{The}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{measured}\:\mathrm{to}\:\mathrm{be}\:\:\mathrm{12cm}\:\mathrm{long}\:\mathrm{cofrect} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\:\mathrm{cm}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{absolute}\:\mathrm{error} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{percentage}\:\mathrm{error}\:\mathrm{for} \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\:\:\:\:\left(\mathrm{Answer}:\:\:\mathrm{0}.\mathrm{5cm},\:\:\mathrm{4}.\mathrm{17\%}\right) \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\:\:\:\:\:\left(\mathrm{Answer}:\:\:\:\:\mathrm{12}.\mathrm{25cm},\:\:\:\mathrm{8}.\mathrm{5\%}\right) \\ $$ Answered by MJS last updated…
Question Number 71695 by peter frank last updated on 18/Oct/19 Answered by MJS last updated on 19/Oct/19 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\sqrt{\mathrm{tan}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{\mathrm{tan}\:{x}}\mathrm{cos}^{\mathrm{2}} \:{x}\:{dt}=\frac{\mathrm{2}{t}}{{t}^{\mathrm{4}} +\mathrm{1}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}} }{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{4}}…
Question Number 6158 by enigmeyou last updated on 16/Jun/16 $$\frac{−\mathrm{1}}{\mathrm{1048576}}=\frac{\mathrm{1}}{\mathrm{8}}×\left(\frac{−\mathrm{1}}{\mathrm{2}}\right)^{{n}} \\ $$$${find}\:{n}\:? \\ $$ Answered by Rasheed Soomro last updated on 16/Jun/16 $$\frac{−\mathrm{1}}{\mathrm{1048576}}=\frac{\mathrm{1}}{\mathrm{8}}×\left(\frac{−\mathrm{1}}{\mathrm{2}}\right)^{{n}} \\ $$$$\frac{−\mathrm{8}}{\mathrm{1048576}}=\left(\frac{−\mathrm{1}}{\mathrm{2}}\right)^{{n}}…
Question Number 6157 by Rasheed Soomro last updated on 16/Jun/16 Answered by Yozzii last updated on 16/Jun/16 $$\mid{BC}\mid=\mid{CD}\mid=\mid{DA}\mid=\mid{AB}\mid={x}\:{units}>\mathrm{0} \\ $$$${Form}\:{the}\:{triangle}\:\bigtriangleup{GBH}\:{where}\:\angle{GBH}=\mathrm{90}° \\ $$$${and}\angle{GHB}=\theta\:\left(\mathrm{0}<\theta<\mathrm{90}°\right).\:{Let}\:\mid{GH}\mid={r}>\mathrm{0}.\:{Since} \\ $$$${H}\:{is}\:{the}\:{centre}\:{of}\:{arc}\:{GE},\:{then}\:\mid{EH}\mid=\mid{GH}\mid={r}. \\…
Question Number 71693 by TawaTawa last updated on 18/Oct/19 Answered by MJS last updated on 19/Oct/19 $$\mathrm{the}\:\mathrm{discs}\:\mathrm{are}\:\mathrm{cylinders} \\ $$$${V}=\pi{r}^{\mathrm{2}} {h} \\ $$$${V}=\pi×\mathrm{1}^{\mathrm{2}} ×\mathrm{1}+\pi×\mathrm{2}^{\mathrm{2}} ×\mathrm{1}+\pi×\mathrm{3}^{\mathrm{2}} ×\mathrm{1}=\mathrm{14}\pi…