Question Number 192936 by Abdullahrussell last updated on 31/May/23 Answered by Frix last updated on 31/May/23 $$\mathrm{Obviously}\:{x}^{\mathrm{2}} =\mathrm{3}\vee{x}^{\mathrm{2}} =\mathrm{4}\:\Rightarrow \\ $$$${x}=\pm\sqrt{\mathrm{3}}\vee{x}=\pm\mathrm{2} \\ $$$$\mathrm{If}\:\mathrm{we}\:\mathrm{use}\:\sqrt[{\mathrm{3}}]{−{z}}=−\sqrt[{\mathrm{3}}]{{z}}\:\mathrm{also}\:{x}^{\mathrm{2}} =\mathrm{12}\:\Rightarrow\:{x}=\pm\mathrm{2}\sqrt{\mathrm{3}} \\…
Question Number 127400 by mohammad17 last updated on 29/Dec/20 $${prove}\:{that}\::\mid\mid{z}_{\mathrm{1}} \mid−\mid{z}_{\mathrm{2}} \mid\mid\leqslant\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid \\ $$ Commented by mohammad17 last updated on 29/Dec/20 $$? \\…
Question Number 61864 by Tawa1 last updated on 10/Jun/19 Commented by MJS last updated on 10/Jun/19 $$\mathrm{I}\:\mathrm{cannot}\:\mathrm{read}\:\mathrm{the}\:\mathrm{fraction}.\:\mathrm{Is}\:\mathrm{it}\:\frac{\mathrm{3}}{\mathrm{2}}{k}? \\ $$ Commented by Tawa1 last updated on…
Question Number 192933 by mnjuly1970 last updated on 31/May/23 Answered by MM42 last updated on 01/Jun/23 $${ln}\left(\mathrm{1}−{x}\right)={u}\Rightarrow\frac{−\mathrm{1}}{\mathrm{1}−{x}}{dx}={du}\:\:\&{i}\:{x}^{{n}−\mathrm{1}} {dx}={dv}\Rightarrow\frac{{x}^{{n}} }{{n}}={v} \\ $$$$\Rightarrow{I}_{{n}} =\int{x}^{{n}−\mathrm{1}} {ln}\left(\mathrm{1}−{x}\right){dx}=\frac{{x}^{{n}} {ln}\left(\mathrm{1}−{x}\right)}{{n}}\:+\frac{\mathrm{1}}{{n}}\int\:\frac{{x}^{{n}} }{\mathrm{1}−{x}}{dx}…
Question Number 61861 by mr W last updated on 10/Jun/19 Commented by mr W last updated on 10/Jun/19 $${H}\:{is}\:{the}\:{orthocenter}\:{of}\:{triangle}\:{ABC}. \\ $$$${Its}\:{distance}\:{to}\:{the}\:{vertexes}\:{is}\:\alpha,\:\beta,\:\gamma \\ $$$${respectively}. \\ $$$${Find}\:{the}\:{side}\:{lengthes}\:{a},\:{b},\:{c}\:{of}\:{the}…
Question Number 61860 by Tawa1 last updated on 10/Jun/19 $$\mathrm{simplify}:\:\:\:\:\overset{\mathrm{n}\:+\:\mathrm{1}} {\:}\mathrm{C}_{\mathrm{r}} \:−\:\overset{\mathrm{n}\:−\:\mathrm{1}} {\:}\mathrm{C}_{\mathrm{r}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 192928 by BaliramKumar last updated on 31/May/23 $$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}+{k}\:=\:\mathrm{0}\:{where}\:{k}<\mathrm{0}\: \\ $$$$\left(\frac{\alpha}{\beta}\:+\:\frac{\beta}{\alpha}\right)_{\mathrm{max}} \:=\:? \\ $$ Answered by MM42 last updated on 31/May/23 $${s}=\mathrm{3}\:\:\&\:\:{p}=\frac{{k}}{\mathrm{2}} \\…
Question Number 61856 by mr W last updated on 10/Jun/19 Commented by mr W last updated on 10/Jun/19 $${point}\:{P}\:{is}\:{randomly}\:{selected}\:{in}\:{a} \\ $$$${triangle}\:{with}\:{side}\:{lengthes}\:{a},{b},{c}. \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{average}\:{value}\:{of}\:{the}\:{sum} \\ $$$${of}\:{distances}\:{from}\:{P}\:{to}\:{the}\:{vertexes}.…
Question Number 192925 by Shrinava last updated on 31/May/23 $$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\mathrm{2}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:+\:\mathrm{0},\mathrm{5}^{\boldsymbol{\mathrm{x}}−\mathrm{2}} \:=\:\mathrm{9} \\ $$$$\mathrm{2}.\:\mathrm{4}^{\mathrm{3}\boldsymbol{\mathrm{x}}} \:=\:\mathrm{12} \\ $$$$\mathrm{3}.\:\mathrm{6}^{\boldsymbol{\mathrm{x}}+\mathrm{2}} \:=\:\mathrm{18} \\ $$ Answered by MM42…
Question Number 61855 by aliesam last updated on 10/Jun/19 $$\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx} \\ $$ Answered by MJS last updated on 10/Jun/19 $$\frac{\mathrm{3}{x}^{\mathrm{3}}…