Question Number 66937 by Cmr 237 last updated on 20/Aug/19 Answered by mr W last updated on 21/Aug/19 $${let}\:{t}=\mathrm{81}^{\mathrm{sin}^{\mathrm{2}} \:{x}} \\ $$$$\mathrm{81}^{\mathrm{cos}^{\mathrm{2}} \:{x}} =\mathrm{81}^{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}…
Question Number 132469 by Algoritm last updated on 14/Feb/21 Answered by Olaf last updated on 15/Feb/21 $$\mathrm{Let}\:\Omega_{{i}} \:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}_{{i}} \left(\mathrm{1}−\mathrm{ln}{x}_{{i}} \right)}{dx}_{{i}} \\ $$$$\mathrm{Let}\:{u}_{{i}} \:=\:\mathrm{1}−\mathrm{ln}{x}_{{i}}…
Question Number 66932 by Tinkutara@ last updated on 20/Aug/19 $${which}\:{of}\:{the}\:{sequences}\:{converges}\:? \\ $$$$\left.\mathrm{1}\right)\:{a}_{{n}} =\:{n}−\frac{\mathrm{1}}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{a}_{{n}} =\:\left(\left(−\mathrm{1}\right)^{{n}} +\mathrm{1}\right)\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$ Answered by turbo msup by abdo…
Question Number 1397 by 314159 last updated on 28/Jul/15 $${Arrange}\:\mathrm{8}\:{coins}\:{in}\:{one}\:{line}\:{on}\:{a}\:{table} \\ $$$${such}\:{that}\:{the}\:{head}\:{or}\:{tail}\:{will}\:{be}\:{facing} \\ $$$${upward}.{Try}\:{to}\:{flip}\:{two}\:{neighboring}\:{coins}\: \\ $$$${that}\:{are}\:{not}\:{with}\:{identical}\:{face}\:{upside}\:{down}.{After}\: \\ $$$${several}\:{operations}\:,\:{how}\:{many}\:{different}\: \\ $$$${ways}\:{can}\:{the}\:{heads}\:{and}\:{tails}\:{be}\:{arranged} \\ $$$${in}\:{one}\:{line}\:{on}\:{the}\:{table}. \\ $$ Commented…
Question Number 132470 by physicstutes last updated on 14/Feb/21 $$\int\:\mathrm{tan}^{\mathrm{3}} {x}\:{dx} \\ $$ Answered by mindispower last updated on 14/Feb/21 $$\int{tg}\left({x}\right)\left(\mathrm{1}+{tg}^{\mathrm{2}} \left({x}\right)\right){dx}−\int{tg}\left({x}\right){dx} \\ $$$$=\frac{{tg}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}}+{ln}\mid{cos}\left({x}\right)\mid+{c}…
Question Number 1395 by Rasheed Soomro last updated on 28/Jul/15 $$\:\:\:\:\:\:\:\:\:\:\mathrm{C}{onsider}\:\boldsymbol{\mathrm{quadrilateral}}\:\boldsymbol{\mathrm{ABCD}}\:\:{same}\:{as}\:{in}\:{Q}\:\mathrm{1378}\:{with}\: \\ $$$${same}\:{conditions}/{restrictions}\:\left({Pl}\:\:{refer}\:\:{the}\:{Question}\:{again}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\bullet\:{What}\:{could}\:{be}\:{possible}\:\boldsymbol{\mathrm{minimum}}\:{and}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}} \\ $$$${of}\:{the}\:{quadrilateral}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\bullet{When}\:{qusdrilateral}\:{has}\:\boldsymbol{\mathrm{minimum}}\:\boldsymbol{\mathrm{area}}\:{what}\:{is}\:{the}\:{value}/{s} \\ $$$${of}\:\boldsymbol{{m}}\angle\boldsymbol{\mathrm{A}}?\:{Similarly}\:{what}\:{is}\:{value}/{s}\:\:{of}\:\boldsymbol{{m}}\angle\boldsymbol{\mathrm{A}}\:{in}\:{case}\:{of} \\ $$$$\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}}? \\ $$$$…
Question Number 66928 by mr mondo last updated on 20/Aug/19 $$\frac{\mathrm{3}^{\mathrm{120}} }{\mathrm{6}^{\mathrm{60}} } \\ $$$$\mathrm{express}\:\mathrm{in}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in} \\ $$$$\mathrm{3}\:\mathrm{significant}\:\mathrm{figure} \\ $$ Answered by mr W last updated…
Question Number 66927 by Cmr 237 last updated on 21/Aug/19 $${calcul}\:{la}\:{limite}\:{suivante}: \\ $$$${lim}\:\:\:\:\:\:\:\left(\frac{\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\mathrm{3}^{{x}} +……+{n}^{{x}} }{{n}}\right)^{\frac{\mathrm{1}}{{x}}} =\mathrm{A} \\ $$$${x}\rightarrow\mathrm{0} \\ $$$$\mathrm{trouve}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\boldsymbol{\mathrm{A}} \\ $$$$\mathrm{trouve}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\boldsymbol{\mathrm{P}}\:\mathrm{definir}\:\mathrm{par}: \\…
Question Number 132463 by EDWIN88 last updated on 14/Feb/21 $$\:\mathrm{Given}\:\int_{{a}} ^{\:{b}} \:\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}}{\mid{x}−\mathrm{3}\mid}\:\mathrm{dx}\:=\:\frac{\mathrm{11}}{\mathrm{2}}\:\mathrm{where}\:\begin{cases}{{a}<\mathrm{3}<{b}}\\{{a}+\mathrm{2}{b}=\mathrm{8}}\end{cases} \\ $$$$\:\mathrm{Find}\:\int_{{a}} ^{{b}} \:\mid{x}\mid\:\mathrm{dx}.\: \\ $$ Answered by bemath last updated on…
Question Number 66922 by paro123 last updated on 20/Aug/19 Commented by paro123 last updated on 20/Aug/19 $$\mathrm{No}.\mathrm{8} \\ $$ Terms of Service Privacy Policy Contact:…