Question Number 204595 by SEKRET last updated on 22/Feb/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\:=\:\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:−\:\mathrm{16}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:−\:\mathrm{57}\boldsymbol{\mathrm{x}}\:+\mathrm{1}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{a}}\right)=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{b}}\right)=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{c}}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{a}}}\:+\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{b}}\:}\:+\:\sqrt[{\mathrm{5}}]{\boldsymbol{\mathrm{c}}\:}\:=\:? \\ $$ Answered by mr W last updated on…
Question Number 204541 by necx122 last updated on 21/Feb/24 $${In}\:{a}\:{regular}\:{pentagon}\:{PQRST}\:,\:{PR} \\ $$$${intersects}\:{QS}\:{at}\:{O}.\:{Calculate}\:{ROS}? \\ $$ Commented by som(math1967) last updated on 21/Feb/24 $$\measuredangle{ROS}=\mathrm{72}° \\ $$ Commented…
Question Number 204558 by universe last updated on 22/Feb/24 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}^{−\mathrm{3}/\mathrm{2}} \left[\left(\mathrm{n}+\mathrm{1}\right)^{\left(\mathrm{n}+\mathrm{1}\right)} \left(\mathrm{n}+\mathrm{2}\right)^{\left(\mathrm{n}+\mathrm{2}\right)} …\left(\mathrm{2n}\right)^{\mathrm{2n}} \right]^{\mathrm{1}/\mathrm{n}^{\mathrm{2}} } \:=\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 204568 by pticantor last updated on 21/Feb/24 $$\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{convert}}\:\mathrm{31230}\:\boldsymbol{{in}}\:\boldsymbol{{base}}\:\mathrm{60}? \\ $$$$\boldsymbol{{pls}}\:\boldsymbol{{help}} \\ $$ Answered by A5T last updated on 22/Feb/24 $$\mathrm{31230}=\mathrm{520}×\mathrm{60}+\mathrm{30}=\left(\mathrm{8}×\mathrm{60}+\mathrm{40}\right)×\mathrm{60}+\mathrm{30} \\ $$$$=\mathrm{8}×\mathrm{60}^{\mathrm{2}} +\mathrm{40}×\mathrm{60}+\mathrm{30}=\mathrm{8}{eU}_{\mathrm{60}}…
Question Number 204569 by pticantor last updated on 21/Feb/24 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\: \\ $$$$\boldsymbol{{I}}=\int_{\mathrm{0}} ^{+\infty} \boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{e}}^{−\boldsymbol{{x}}} \right)\boldsymbol{{dx}}\:\boldsymbol{{nowing}}\:\boldsymbol{{that}}\: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\mathrm{1}}{\boldsymbol{{n}}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$ Answered by…
Question Number 204550 by Rasheed.Sindhi last updated on 21/Feb/24 $${Where}'{s}\:{sir}\:{AST}? \\ $$$${Why}\:{his}\:{posts}\:{are}\:{now}\:{by} \\ $$$$'{deleteduser}\mathrm{1}'\:! \\ $$$${Did}\:{he}\:{delete}\:{his}\:{account}? \\ $$$$\mathcal{T}{here}'{s}\:{no}\:{post}\:{by}\:{name}\:\:'{AST}\:\:' \\ $$ Commented by A5T last updated…
Question Number 204560 by mr W last updated on 21/Feb/24 Commented by mr W last updated on 21/Feb/24 $${AC}={BD} \\ $$$${find}\:\angle{B}=? \\ $$ Answered by…
Question Number 204544 by hardmath last updated on 21/Feb/24 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{3}} }\:\:+\:\:…\:\:+\:\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} }\:\:<\:\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$ Answered by mr W last updated on 21/Feb/24…
Question Number 204545 by hardmath last updated on 21/Feb/24 $$\mathrm{If} \\ $$$$\mathrm{a}\:=\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\:\:+\:\:…\:\:+\:\:\frac{\mathrm{1}}{\mathrm{100}^{\mathrm{2}} } \\ $$$$\mathrm{b}\:=\:\mathrm{0},\mathrm{99} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{a}\:<\:\mathrm{b} \\ $$ Answered by…
Question Number 204510 by Ghisom last updated on 20/Feb/24 $$\mathrm{solve}\:\mathrm{for}\:{x}\neq{y}\wedge{y}\neq{z}\wedge{z}\neq{x} \\ $$$$\left(\mathrm{exact}\:\mathrm{solutions}\:\mathrm{required}\right) \\ $$$$\sqrt{\left(−\mathrm{3}+\mathrm{4i}\right){x}}={y} \\ $$$$\sqrt{\left(−\mathrm{3}+\mathrm{4i}\right){y}}={z} \\ $$$$\sqrt{\left(−\mathrm{3}+\mathrm{4i}\right){z}}={x} \\ $$ Answered by Frix last updated…