Question Number 10114 by JAZAR last updated on 24/Jan/17 $${how}\:{can}\:{demontred} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}\underset{\:\:\:\:\:\:\:\:\:} {=}\frac{\mathrm{3}{tanx}−{tan}^{\mathrm{3}} {x}}{\underset{} {\mathrm{1}}−\mathrm{3}{tan}^{\mathrm{2}} {x}} \\ $$$${pleace}\:{help}\:{me} \\ $$ Answered by mrW1 last updated…
Question Number 75648 by Rio Michael last updated on 14/Dec/19 $$\:{A}\:{student}\:{seals}\:\mathrm{200}{g}\:{of}\:{ice}−{cold}\:{water}\:{in}\:{a}\:{glass}\:{vacuum} \\ $$$$\left({thermos}\right)\:{flask}\:{and}\:{finds}\:{that}\:{it}\:{warms}\:{up}\:{by}\:\mathrm{3}.\mathrm{5}\:{K}\:{in}\:{one}\:{hour} \\ $$$${SHC}\:{of}\:{water}\:=\mathrm{2400}\:{Jkg}^{−\mathrm{1}} {K}^{−\mathrm{1}} \\ $$$$\left.{a}\right)\:{Calculate}\:{the}\:{average}\:{rate}\:{of}\:{heat}\:{flow}\:{in}\:{the}\:{flask}\:{in}\:{watts}. \\ $$$${To}\:{check}\:{this}\:{result}\:{over}\:{a}\:{longer}\:{period},{the}\:{student}\:{fills}\:{the}\:{flask}\:{with} \\ $$$${equal}\:{amounts}\:{of}\:{ice}\:{and}\:{water}\:{all}\:{at}\:\mathrm{0}°{C},\:{and}\:{leaves}\:{it}\:{for}\: \\ $$$$\mathrm{4}\:{hours}.\:{the}\:{specific}\:{latent}\:{heat}\left({enthalpy}\right)\:{of}\:{fusion}\:{of}\:{ice}\:{is}\:\mathrm{0}.\mathrm{33}{MJg}^{−\mathrm{1}} \\…
Question Number 141186 by SLVR last updated on 16/May/21 Commented by SLVR last updated on 16/May/21 $${Good}\:{evening}\:{sir}..\:{Mr}.{Dwaipayan}.. \\ $$$${i}\:{forgotten}\:{to}\:{write}\:{your}\:{explanation} \\ $$ Commented by SLVR last…
Question Number 10108 by ridwan balatif last updated on 24/Jan/17 Answered by nume1114 last updated on 24/Jan/17 $${from}\:{Vieta}'{s}\:{fomula}: \\ $$$$\begin{cases}{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} =\mathrm{2}}\\{{x}_{\mathrm{1}} {x}_{\mathrm{2}} =−\mathrm{5}}\end{cases} \\…
Question Number 75641 by aliesam last updated on 14/Dec/19 Commented by vishalbhardwaj last updated on 15/Dec/19 $$\mathrm{Hypergeometric}\:\mathrm{Function}\::\: \\ $$$$\mathrm{2F1}\:\left({a},{b};{c};{z}\right)\:=\:\mathrm{1}+\frac{{ab}}{\mathrm{1}!\:{c}}\:{z}+\frac{{a}\left({a}+\mathrm{1}\right){b}\left({b}+\mathrm{1}\right)}{\mathrm{2}!\:{c}\left({c}+\mathrm{1}\right)}\:{z}^{\mathrm{2}} +\frac{{a}\left({a}+\mathrm{1}\right)\left({a}+\mathrm{2}\right){b}\left({b}+\mathrm{1}\right)\left({b}+\mathrm{2}\right)}{\mathrm{3}!\:{c}\left({c}+\mathrm{1}\right)\left({c}+\mathrm{2}\right)}\:{z}^{\mathrm{3}} +\:.\:.\:. \\ $$ Answered by…
Question Number 10104 by konen last updated on 23/Jan/17 $$\frac{\mathrm{a}}{\mathrm{2}}=\frac{\mathrm{b}}{\mathrm{5}}\:,\sqrt{\mathrm{5a}}\:+\sqrt{\mathrm{2b}}\:=\mathrm{16} \\ $$$$\Rightarrow\frac{\mathrm{5a}}{\mathrm{2}}+\mathrm{b}=\overset{} {?} \\ $$ Answered by arge last updated on 23/Jan/17 $$\mathrm{5}{a}=\mathrm{2}{b},\sqrt{\mathrm{2}{b}}\:+\sqrt{\mathrm{2}{b}}\:=\mathrm{16} \\ $$$$\mathrm{2}\sqrt{\mathrm{2}{b}}\:=\mathrm{16}…
Question Number 75639 by aliesam last updated on 14/Dec/19 Answered by $@ty@m123 last updated on 14/Dec/19 $${x}={y}\mathrm{cos}\:{y}\:….\left(\mathrm{1}\right) \\ $$$${Differentiating}\:{w}.{r}.{t}.\:{x}, \\ $$$$\mathrm{1}=\left\{{y}\left(−\mathrm{sin}\:{y}\right)+\mathrm{cos}\:{y}\right\}{y}' \\ $$$$\frac{\mathrm{1}}{{y}'}=\mathrm{cos}\:{y}−{y}\mathrm{sin}\:{y}\:….\left(\mathrm{2}\right) \\ $$$${Multiplying}\:\left(\mathrm{2}\right)\:{by}\:{y},…
Question Number 10102 by konen last updated on 23/Jan/17 $$\mathrm{a}−\mathrm{b}=\frac{\mathrm{a}+\mathrm{b}}{\mathrm{7}}=\frac{\mathrm{a}×\mathrm{b}}{\mathrm{24}}\:\Rightarrow\mathrm{a}−\mathrm{b}=? \\ $$ Answered by mrW1 last updated on 23/Jan/17 $$\mathrm{a}−\mathrm{b}=\frac{\mathrm{a}+\mathrm{b}}{\mathrm{7}}=\frac{\mathrm{a}×\mathrm{b}}{\mathrm{24}}={u} \\ $$$${a}−{b}={u} \\ $$$${a}+{b}=\mathrm{7}{u} \\…
Question Number 10101 by Tawakalitu ayo mi last updated on 23/Jan/17 $$\int\:\frac{\mathrm{z}\:+\:\mathrm{2}}{\mathrm{10z}\:+\:\mathrm{28}}\:\mathrm{dz} \\ $$ Commented by prakash jain last updated on 24/Jan/17 $$=\frac{\mathrm{1}}{\mathrm{10}}\int\frac{\mathrm{10}{z}+\mathrm{28}−\mathrm{8}}{\mathrm{10}{z}+\mathrm{28}}{dz} \\ $$$$=\frac{\mathrm{1}}{\mathrm{10}}\int\left[\mathrm{1}−\frac{\mathrm{8}}{\mathrm{10}{z}+\mathrm{28}}\right]{dz}…
Question Number 141171 by iloveisrael last updated on 16/May/21 Commented by iloveisrael last updated on 16/May/21 $$\:{insteresting}\:{question} \\ $$ Commented by mr W last updated…