Question Number 217871 by hardmath last updated on 22/Mar/25 $$\mathrm{n}\:\geqslant\:\mathrm{2} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\prod}}\:\mathrm{tg}\:\left[\:\frac{\pi}{\mathrm{3}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{3}^{\boldsymbol{\mathrm{k}}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}} \:−\:\mathrm{1}}\right)\right]\:=\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\prod}}\:\mathrm{ctg}\:\left[\:\frac{\pi}{\mathrm{3}}\:\left(\mathrm{1}\:−\:\frac{\mathrm{3}^{\boldsymbol{\mathrm{k}}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}} \:−\:\mathrm{1}}\right)\right] \\ $$ Answered…
Question Number 217857 by hardmath last updated on 22/Mar/25 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos20}°}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{cos80}°}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{cos160}°}\:=\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{3}\:\centerdot\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\mathrm{6}}{\mathrm{2}}} \\ $$ Answered by Frix last updated on 22/Mar/25 $$\mathrm{Staying}\:\mathrm{in}\:\mathbb{R}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{20}°}=−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{160}°}\:\Rightarrow \\ $$$$\mathrm{cos}\:\mathrm{80}°\:=\frac{\mathrm{3}}{\mathrm{2}}\sqrt[{\mathrm{3}}]{\mathrm{9}}−\mathrm{3}\approx.\mathrm{12} \\…
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Question Number 217789 by hardmath last updated on 21/Mar/25 Commented by mr W last updated on 21/Mar/25 $$?=\sqrt{\left(\mathrm{27}+\mathrm{12}+\mathrm{15}\right)^{\mathrm{2}} −\mathrm{4}×\mathrm{27}×\mathrm{15}}=\mathrm{36} \\ $$ Commented by mr W…
Question Number 217822 by Ari last updated on 21/Mar/25 Answered by mr W last updated on 22/Mar/25 $$\left.{a}\right) \\ $$$$\mathrm{0}.\mathrm{10}×\mathrm{0}.\mathrm{05}=\mathrm{0}.\mathrm{5\%} \\ $$$$\left.{b}\right) \\ $$$${can}\:{not}\:{be}\:{determined},\:{but}\:{at}\:{least} \\…
Question Number 217818 by chidera last updated on 21/Mar/25 Answered by mr W last updated on 22/Mar/25 $${a}.\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${b}.\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${c}.\:\frac{\mathrm{5}}{\mathrm{8}} \\ $$ Commented…
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Question Number 217813 by Wuji last updated on 21/Mar/25 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\left[\left({xp}\left(\mathrm{2}+{x}\right)\right]^{−\mathrm{1}} {dx}\:\:\:\right. \\ $$$${p}\in\mathbb{R} \\ $$ Answered by mr W last updated on 22/Mar/25…
Question Number 217814 by Rasheed.Sindhi last updated on 21/Mar/25 $${Tinku}\:{Tara}\:{sir}, \\ $$$${Why}\:{can}\:{I}\:{not}\:{sign}\:{in}\:{with}\:{my} \\ $$$${existing}\:{credentials}\:{on}\:{my} \\ $$$${other}\:{device}\left({tablet}\right)\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com