Question Number 201214 by mr W last updated on 02/Dec/23 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{function}\:{z}={xy}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:{xy}−\mathrm{plane}\:\mathrm{where}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{will} \\ $$$$\mathrm{touch}\:\mathrm{it}. \\ $$$$ \\ $$$$\left({an}\:{unsolved}\:{old}\:{question}\:{Q}\mathrm{200929}\right) \\ $$ Answered by…
Question Number 201209 by sonukgindia last updated on 02/Dec/23 Commented by ajfour last updated on 02/Dec/23 should it converge ? Commented by mr W last updated on 02/Dec/23…
Question Number 201266 by Mathspace last updated on 02/Dec/23 $${calculate}\:\int_{\mathrm{1}} ^{\infty} \frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }} \\ $$ Answered by witcher3 last updated on 03/Dec/23 $$\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }=\mathrm{y} \\…
Question Number 201267 by Mathspace last updated on 02/Dec/23 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\left(\mathrm{1}+{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\left({x}−\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$ Commented by Frix last updated on 02/Dec/23 $$\mathrm{Question}\:\mathrm{201110} \\…
Question Number 201263 by mnjuly1970 last updated on 02/Dec/23 $$ \\ $$$$\:\:\:\:{Q}:\:{the}\:{equation}\:,\:{sin}^{\:\mathrm{2}} \left({x}\right)−{sin}\left({mx}\right){cos}\:^{\mathrm{2}} \left({x}\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:{has}\:\:{four}\:{distinct}\:{roots} \\ $$$$\:\:\:\:\:\:\:{in}\:\left(\:\mathrm{0}\:,\:\mathrm{2}\pi\:\right)\:\:{find}\:{the}\:{values} \\ $$$$\:\:\:\:\:\:\:\:{of}\:\:,\:\:\:{m}\:\:\:.\:\:\left({m}\:\in\:\mathbb{N}\:\right) \\ $$$$ \\ $$ Answered…
Question Number 201257 by BaliramKumar last updated on 02/Dec/23 $$\mathrm{Biggest}\:\mathrm{prime}\:\mathrm{factor}\:\mathrm{of}\:\left(\mathrm{3}^{\mathrm{14}} \:+\:\mathrm{3}^{\mathrm{13}} \:−\:\mathrm{12}\right)\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 02/Dec/23 $$\mathrm{Biggest}\:\mathrm{prime}\:\mathrm{factor}\:\mathrm{of}\:\left(\mathrm{3}^{\mathrm{14}} \:+\:\mathrm{3}^{\mathrm{13}} \:−\:\mathrm{12}\right)\:=\:? \\…
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Question Number 201253 by mathlove last updated on 02/Dec/23 $${find}\:{the}\:{sum}\:{of}\:{n}\:{terms}\:{of}\:{the}\:{serice} \\ $$$${s}_{{n}} =\mathrm{5}+\mathrm{11}+\mathrm{19}+\mathrm{29}+\mathrm{41}+………. \\ $$ Answered by Rasheed.Sindhi last updated on 02/Dec/23 $$\left(\mathrm{4}+\mathrm{1}\right)+\left(\mathrm{9}+\mathrm{2}\right)+\left(\mathrm{16}+\mathrm{3}\right)+\left(\mathrm{25}+\mathrm{4}\right)+.. \\ $$$$\left(\mathrm{2}^{\mathrm{2}}…
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Question Number 201237 by mnjuly1970 last updated on 02/Dec/23 $$ \\ $$$$\:\:\:\:{If}\:\:,\:\:\:{a}\:\mid\:\mathrm{5}{b}^{\:\mathrm{2}} −\mathrm{10}{b}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\Rightarrow\:\:\:\left[\:{a}\:\:,\:\mathrm{5}{b}\:\right]_{\mathrm{lc}{m}} \:=\:\:?\: \\ $$$$ \\ $$$$ \\ $$ Commented by AST…