Question Number 126329 by mnjuly1970 last updated on 19/Dec/20 Answered by Olaf last updated on 19/Dec/20 $${x}^{\mathrm{5}} −\mathrm{5}{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{3}} +\mathrm{10}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{1}\:=\:\mathrm{0} \\ $$$$\left({x}^{\mathrm{5}} −\mathrm{1}\right)−\mathrm{5}\left({x}^{\mathrm{4}} −{x}\right)−\mathrm{10}\left({x}^{\mathrm{3}}…
Question Number 60791 by arcana last updated on 25/May/19 $$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}} }{dx},\:\mathrm{n}\in\mathbb{N} \\ $$ Commented by Forkum Michael Choungong last updated on 25/May/19 $$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}}…
Question Number 191862 by cortano12 last updated on 02/May/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{from}\: \\ $$$$\:\left(\mathrm{2}^{\mathrm{400}} −\mathrm{2}^{\mathrm{320}} \right)\left(\mathrm{2}^{\mathrm{200}} +\mathrm{2}^{\mathrm{160}} \right)\left(\mathrm{2}^{\mathrm{200}} −\mathrm{2}^{\mathrm{160}} \right) \\ $$ Commented by BaliramKumar last updated…
Question Number 60788 by ajfour last updated on 25/May/19 Commented by ajfour last updated on 25/May/19 $${In}\:{terms}\:{of}\:\alpha\:{and}\:{ellipse}\:{parameters} \\ $$$${a}\:{and}\:{b},\:{find}\:{maximum}\:{colored}\:{area}. \\ $$ Answered by mr W…
Question Number 191856 by TUN last updated on 02/May/23 Answered by Subhi last updated on 02/May/23 $$ \\ $$$${put}\:{AD}={y} \\ $$$$\frac{{BD}}{{sin}\left(\mathrm{30}\right)}=\frac{{y}}{{sin}\left(\mathrm{10}\right)} \\ $$$${BD}=\frac{{sin}\left(\mathrm{30}\right)}{{sin}\left(\mathrm{10}\right)}{y}\:\:\:\:\:\:\:{by}\left[{sin}\:{law}\right] \\ $$$$\frac{{CD}}{{sin}\left(\mathrm{50}\right)}=\frac{{y}}{{sin}\left({x}\right)}\:.{hence}\:{CD}=\frac{{sin}\left(\mathrm{50}\right)}{{sin}\left({x}\right)}{y}…
Question Number 126323 by mnjuly1970 last updated on 19/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}\:::: \\ $$$$\:\:\:\:\:\frac{\Gamma\left(\frac{\mathrm{1}−{x}}{\mathrm{2}}\right)\Gamma\left({x}\right)}{\Gamma\left(\frac{{x}}{\mathrm{2}}\right)}\:\overset{???} {=}\:\frac{\mathrm{2}^{{x}−\mathrm{1}} \sqrt{\pi}}{{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 191859 by mathlove last updated on 02/May/23 Commented by mr W last updated on 03/May/23 $${all}\:{are}\:{of}\:{type}\:{y}'+{P}\left({x}\right){y}={Q}\left({x}\right). \\ $$ Answered by qaz last updated…
Question Number 126321 by Ndala last updated on 19/Dec/20 $${if}\:\:{a}+{b}\geqslant{c}>\mathrm{0} \\ $$$$\mathrm{P}{rove}\:{that} \\ $$$$\frac{{a}}{\mathrm{1}+{a}}+\frac{{b}}{\mathrm{1}+{b}}>\frac{{c}}{\mathrm{1}+{c}} \\ $$$$. \\ $$$$\mathrm{I}\:{need}\:{help}… \\ $$ Terms of Service Privacy Policy…
Question Number 126318 by Algoritm last updated on 19/Dec/20 Commented by mr W last updated on 19/Dec/20 371115746176445351701210713361941528546861949073514542015172437236580034634746971244943788132460150776779198800002366059871900041784732217539059306483834977865973576751345853385981719448969027641920 Answered by MJS_new last updated on 19/Dec/20…
Question Number 60783 by aliesam last updated on 25/May/19 $$\underset{−\infty} {\overset{\infty} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 25/May/19 $${let}\:{A}\:=\int_{−\infty}…