Question Number 203716 by professorleiciano last updated on 26/Jan/24 Answered by AST last updated on 26/Jan/24 $${Let}\:{AP}\:{and}\:{DC}\:{meet}\:{at}\:{F},{then}\:\bigtriangleup{BPA}\approx\bigtriangleup{CPF} \\ $$$$\Rightarrow\frac{{BA}}{{CF}}=\frac{{BP}}{{CP}}\Rightarrow\frac{{s}}{{CF}}=\frac{\mathrm{8}}{{s}−\mathrm{8}}\Rightarrow{CF}=\frac{{s}\left({s}−\mathrm{8}\right)}{\mathrm{8}}…\left({i}\right) \\ $$$${in}\:\bigtriangleup{AFD};{AQ}\:{bisects}\:\angle{FAD}\Rightarrow\frac{{AD}}{{DQ}}=\frac{{AF}}{{FQ}} \\ $$$$\Rightarrow\frac{{s}}{\mathrm{9}}=\frac{\sqrt{{s}^{\mathrm{2}} +\left({s}+{CF}\right)^{\mathrm{2}} }}{{CF}+{s}−\mathrm{9}}\Rightarrow\frac{{s}}{\mathrm{9}}=\frac{\sqrt{{s}^{\mathrm{2}}…
Question Number 203712 by Davidtim last updated on 26/Jan/24 $$\mathrm{50}\:{divide}\:{into}\:{to}\:{part}\:{that}\:{the}\:{mini}\: \\ $$$${figure}\:\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:{large}\:{one}\:{is}\:\frac{\mathrm{5}}{\mathrm{7}},\:{and}\:{the}\: \\ $$$${sum}\:{of}\:{them}\:{is}\:\mathrm{21},\:{find}\:{the}\:{tow}\: \\ $$$${figures}? \\ $$ Commented by Davidtim last updated on 30/Jan/24…
Question Number 203676 by 073 last updated on 25/Jan/24 Answered by Frix last updated on 25/Jan/24 $${x}\left({x}+\mathrm{2}\right){x}!=\mathrm{168}{x}^{\mathrm{2}} \\ $$$${x}=\mathrm{0} \\ $$$$\left({x}+\mathrm{2}\right){x}!=\mathrm{168}{x} \\ $$$$\left({x}+\mathrm{2}\right)\left({x}−\mathrm{1}\right)!=\mathrm{168}=\mathrm{2}×\mathrm{3}×\mathrm{4}×\mathrm{7} \\ $$$${x}=\mathrm{5}…
Question Number 203675 by 073 last updated on 25/Jan/24 Answered by Frix last updated on 25/Jan/24 $${x}^{\mathrm{4}} −\mathrm{2}{ax}^{\mathrm{2}} −{x}+{a}^{\mathrm{2}} −{a}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +{x}−{a}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −{x}−{a}\right)=\mathrm{0} \\…
Question Number 203665 by sonukgindia last updated on 25/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203681 by SANOGO last updated on 25/Jan/24 $$\int_{\mathrm{1}} ^{+{oo}} \frac{\mathrm{1}}{{x}\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$ Answered by Frix last updated on 25/Jan/24 $${t}=\frac{\mathrm{2}{x}+\mathrm{1}+\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{\:\sqrt{\mathrm{3}}} \\…
Question Number 203648 by yaslm last updated on 24/Jan/24 Answered by Frix last updated on 24/Jan/24 $${w}\left({x}+\frac{{l}}{\mathrm{2}}\right)\left({x}−\frac{{l}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)\right)\left({x}−\frac{{l}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)\right)=\mathrm{0} \\ $$$${x}=−\frac{{l}}{\mathrm{2}}\vee{x}=\frac{{l}}{\mathrm{2}}\left(\mathrm{1}\pm\mathrm{i}\right) \\ $$ Commented by yaslm last…
Question Number 203650 by Davidtim last updated on 24/Jan/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{2}^{{x}} +\mathrm{3}^{{x}} }{\mathrm{2}}\right)^{\frac{\mathrm{2}}{{x}}} =? \\ $$ Answered by witcher3 last updated on 25/Jan/24 $$\: \\…
Question Number 203651 by Davidtim last updated on 24/Jan/24 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{2}−{x}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}}\right)} =? \\ $$ Answered by Mathspace last updated on 24/Jan/24 $${changement}\:\mathrm{1}−{x}={t}\:{give} \\ $$$${f}\left({x}\right)=\left(\mathrm{2}−{x}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\…
Question Number 203615 by muneer0o0 last updated on 23/Jan/24 $${I}\:=\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:\left({x}\right)}{dx} \\ $$ Answered by witcher3 last updated on 25/Jan/24 $$\mathrm{I}=\mathrm{Re}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…