Question Number 8466 by FilupSmith last updated on 12/Oct/16 $${t}={n}^{\mathrm{3}} −{n}^{\mathrm{2}} \\ $$$${t}\in\mathbb{E} \\ $$$$\mathrm{Give}\:\mathrm{a}\:\mathrm{general}\:\mathrm{form}\:\mathrm{solving}\:\mathrm{for}\:{n} \\ $$$${i}.{e} \\ $$$${n}^{\mathrm{3}} −{n}^{\mathrm{2}} =\mathrm{2}{k} \\ $$$${n}=? \\ $$…
Question Number 74000 by mhmd last updated on 17/Nov/19 $${if}\:{p}_{{r}} ^{{n}} =\mathrm{840}\:,\:{c}_{{r}} ^{{n}} =\mathrm{35}\:{find}\:{value}\:{of}\:{r}? \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$ Answered by MJS last updated on 17/Nov/19…
Question Number 8465 by tawakalitu last updated on 12/Oct/16 Answered by sandy_suhendra last updated on 12/Oct/16 $$\left.\mathrm{a}\right)\:\mathrm{let}\:\mathrm{r}=\mathrm{7}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{h}=\mathrm{5}\:\mathrm{cm} \\ $$$$\mathrm{the}\:\mathrm{surface}\:\mathrm{area}=\mathrm{2}×\frac{\mathrm{30}}{\mathrm{360}}\:\pi\mathrm{r}^{\mathrm{2}} +\mathrm{2rh}+\frac{\mathrm{30}}{\mathrm{360}}×\mathrm{2}\pi\mathrm{rh} \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{22}}{\mathrm{7}}×\mathrm{7}^{\mathrm{2}} +\mathrm{2}×\mathrm{7}×\mathrm{5}+\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{22}}{\mathrm{7}}×\mathrm{7}×\mathrm{5} \\ $$$$=\mathrm{25}.\mathrm{67}+\mathrm{70}+\mathrm{18}.\mathrm{33}…
Question Number 139532 by mathdanisur last updated on 28/Apr/21 $$\frac{\mathrm{1}}{\mathrm{3}}\:−\:\frac{{x}−\mathrm{3}}{\mathrm{9}}\:+\:\frac{\left({x}−\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{27}}\:+\:…\:=? \\ $$ Commented by mr W last updated on 28/Apr/21 $$=\frac{\mathrm{1}}{{x}} \\ $$ Commented…
Question Number 139530 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{advanced}\:\:{calculus}…… \\ $$$$\:{prove}\:\:{that}:: \\ $$$$\:\:\:{lim}_{{n}\rightarrow\infty} \left\{\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} {n}^{{n}+\mathrm{1}} }{{n}!}\:\frac{{d}^{\:{n}} }{{dx}^{{n}} }\left(\frac{{ln}\left({x}\right)}{{x}}\right)\mid_{{x}={n}} \right\}=\gamma \\ $$$$\:\gamma\::\:\:\:{euler}\:−{mascheroni}\:{constant} \\ $$$$ \\…
Question Number 139525 by TOTTI last updated on 28/Apr/21 Commented by mr W last updated on 29/Apr/21 $$=\mathrm{log}_{\sqrt{{x}}} \:\left(\sqrt{{x}}\right)^{\mathrm{2}} =\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$=\mathrm{2log}_{\sqrt{{x}}} \:\sqrt{{x}}=\mathrm{3}^{\mathrm{1}/\mathrm{3}} \\ $$$$\Rightarrow\mathrm{2}=\mathrm{3}^{\mathrm{1}/\mathrm{3}}…
Question Number 139524 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:……{advanced}\:\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:{i}::\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\mathrm{2}}{e}^{−\mathrm{2}{x}} −\frac{\mathrm{1}}{\mathrm{1}+{e}^{{x}} }\right)\frac{\mathrm{1}}{{x}}\:{dx}={log}\left(\frac{\mathrm{1}}{\:\sqrt{\pi}}\:\right) \\ $$$$\:{ii}::\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{1}+{e}^{−{x}} }\right)\frac{{e}^{−\mathrm{2}{x}} }{{x}}{dx}={log}\left(\frac{\sqrt{\pi}}{\mathrm{2}}\right) \\…
Question Number 8452 by tawakalitu last updated on 11/Oct/16 Commented by 123456 last updated on 12/Oct/16 $$\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${a}=\mathrm{sin}\:{x},{b}=\mathrm{cos}\:{x} \\ $$$${a}+{b}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1}…
Question Number 139521 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:#\:\:\:{nice}\:…\:{calculus}# \\ $$$$\:\:\:\:\:\:\:\:{if}\:\:\:\:\left({pq}\right)^{{sin}^{\mathrm{2}} \left({x}\right)} +\left({pq}\right)^{{cos}^{\mathrm{2}} \left({x}\right)} ={p}+{q} \\ $$$$\:\:\:\:\:\:\:\:\:\:{then}\:\:\:\:{tan}\left({x}\right)=? \\ $$ Answered by qaz last updated…
Question Number 73982 by mhmd last updated on 17/Nov/19 $${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$ Commented by som(math1967) last updated on 17/Nov/19…