Question Number 56500 by kelly33 last updated on 17/Mar/19 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{X}}_{\mathrm{0}} \:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{x}}\:\boldsymbol{{variable}}\:\boldsymbol{{with}}\:\boldsymbol{{which}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{function}}\:\boldsymbol{{assumes}}\:\boldsymbol{{the}}\:\boldsymbol{{lower}}\:\boldsymbol{{value}}. \\ $$$$ \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{7}+{sin}\left(\pi{x}\right) \\ $$ Commented by kelly33 last updated…
Question Number 56498 by kelly33 last updated on 17/Mar/19 $${It}\:{is}\:{known}\:{that}\:\mathrm{5}\pi<\alpha<\frac{\mathrm{13}\pi}{\mathrm{2}}.\:\:{cos}\alpha=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${calculate}\:\:{sin}\mathrm{2}\alpha \\ $$$$ \\ $$ Commented by kelly33 last updated on 17/Mar/19 $${please}\:{help}\:{me} \\…
Question Number 56481 by Gulay last updated on 17/Mar/19 Commented by Gulay last updated on 17/Mar/19 $$\mathrm{sir}\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 56477 by problem solverd last updated on 17/Mar/19 $$\mathrm{let}\:{x}\:\mathrm{and}\:{y}\:\mathrm{be}\:\mathrm{two}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{if}\:{x}+{y}\leqslant\mathrm{10}\:\mathrm{prove} \\ $$$$\mathrm{ln}\left({x}+\mathrm{1}\right)+\mathrm{ln}\left({y}+\mathrm{1}\right)\leqslant\mathrm{2ln6} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19 $${x}+{y}\leqslant\mathrm{10}…
Question Number 187546 by yaslm last updated on 18/Feb/23 Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $${S}=\frac{\mathrm{1}×\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{2}×\mathrm{3}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{3}×\mathrm{4}}{\mathrm{3}^{\mathrm{3}} }+\frac{\mathrm{4}×\mathrm{5}}{\mathrm{3}^{\mathrm{4}} }+\centerdot\centerdot\centerdot\:\:\left({i}\right) \\ $$$$\mathrm{3}{S}=\mathrm{1}×\mathrm{2}+\frac{\mathrm{2}×\mathrm{3}}{\mathrm{3}}+\frac{\mathrm{3}×\mathrm{4}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{4}×\mathrm{5}}{\mathrm{3}^{\mathrm{3}} }+\centerdot\centerdot\centerdot\:\:\left({ii}\right) \\…
Question Number 56471 by harish 12@g last updated on 17/Mar/19 Answered by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19 $$\int_{\mathrm{0}} ^{\pi} \frac{{xdx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}} {x}+{b}^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}{dx}={I} \\…
Question Number 122007 by ZiYangLee last updated on 13/Nov/20 $$\mathrm{i}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{3}{A}=\mathrm{3sin}\:{A}−\mathrm{4sin}^{\mathrm{3}} {A}. \\ $$$$\mathrm{ii}.\mathrm{Show}\:\mathrm{that}\:\theta=\mathrm{54}°\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:\mathrm{3}\theta=−\mathrm{cos}\:\mathrm{2}\theta.\:\mathrm{Hence}\:\mathrm{or}\:\mathrm{otherwise},\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{54}°. \\ $$ Answered by TANMAY PANACEA last updated…
Question Number 187525 by sciencestudentW last updated on 18/Feb/23 $$\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\frac{{dx}}{\:\sqrt{\mid{x}−\mathrm{1}\mid}}=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 18/Feb/23 $$=\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{{dx}}{\:\sqrt{\mathrm{1}−{x}}}+\int_{\mathrm{1}} ^{\mathrm{2}}…
Question Number 121989 by mlj5 last updated on 13/Nov/20 $${determiner}\:{le}\:{plus}\:{grand}\:{entier}\:{de}\:{n}\:{tel}\:{que} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{1}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}+\sqrt{\mathrm{3}}}+…\frac{\mathrm{1}}{\:\sqrt{{n}+\mathrm{1}}+\sqrt{{n}}}\leqslant\mathrm{9} \\ $$ Answered by Ar Brandon last updated on 13/Nov/20 $$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}}…
Question Number 56426 by Hassen_Timol last updated on 16/Mar/19 $${Let}\:{consider}\:{the}\:{following}\:{sequence}\:: \\ $$$$ \\ $$$$\mathrm{1}\:,\:\mathrm{3}\:,\:\sqrt{\mathrm{17}}\:,\:\mathrm{5}\:,\:\sqrt{\mathrm{33}}\:,\:\sqrt{\mathrm{41}}\:,\:…\: \\ $$$$ \\ $$$${What}\:{may}\:{be}\:{the}\:{explicit}\:{formula}\:{that} \\ $$$${can}\:{gives}\:{this}\:{sequence}\:{of}\:{number}\:? \\ $$$$ \\ $$$${Thank}\:{you} \\…