Question Number 205430 by hardmath last updated on 21/Mar/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\frac{\mathrm{1}}{\mathrm{sinA}}\:+\:\frac{\mathrm{1}}{\mathrm{sinB}}\:+\:\frac{\mathrm{1}}{\mathrm{sinC}}\:\leqslant\:\frac{\mathrm{2}}{\mathrm{3}}\:\left(\mathrm{cot}\frac{\mathrm{A}}{\mathrm{2}}\:+\:\mathrm{cot}\frac{\mathrm{B}}{\mathrm{2}}\:+\:\mathrm{cot}\frac{\mathrm{C}}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205431 by hardmath last updated on 21/Mar/24 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\frac{\mathrm{cotA}\:\mathrm{cotB}\:\mathrm{cotC}}{\mathrm{sinA}\:\mathrm{sinB}\:\mathrm{sinC}}\:\leqslant\:\frac{\mathrm{8}}{\mathrm{27}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205456 by BaliramKumar last updated on 21/Mar/24 Answered by Rasheed.Sindhi last updated on 21/Mar/24 $${First}\:{digit}\:{can}\:{be}\:{occuied}\:{in}\:\mathrm{5}\:{ways} \\ $$$${Second}\:{digit}\:{can}\:{be}\:{occuied}\:{in}\:\mathrm{4}\:{ways} \\ $$$${Third}\:{digit}\:{can}\:{be}\:{occuied}\:{in}\:\mathrm{3}\:{ways}. \\ $$$${Total}\:{ways}:\:\mathrm{5}×\mathrm{4}×\mathrm{3}=\mathrm{60} \\ $$$$\left({d}\right)\:{is}\:{correct}.…
Question Number 205457 by BaliramKumar last updated on 21/Mar/24 Answered by Rasheed.Sindhi last updated on 21/Mar/24 $${x}+\mathrm{log}_{\mathrm{15}} \left(\mathrm{1}+\mathrm{3}^{{x}} \right)={x}\mathrm{log}_{\mathrm{15}} \mathrm{5}+\mathrm{log}_{\mathrm{15}} \mathrm{12} \\ $$$$\mathrm{log}_{\mathrm{15}} \mathrm{15}^{{x}} +\mathrm{log}_{\mathrm{15}}…
Question Number 205448 by mathlove last updated on 21/Mar/24 $${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinx}}{{x}^{\mathrm{3}} }=? \\ $$ Answered by namphamduc last updated on 21/Mar/24 $${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left({x}\right)}{{x}^{\mathrm{3}} }=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}\right)}{{x}}.{x}^{\mathrm{4}}…
Question Number 205451 by MrGHK last updated on 21/Mar/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{{x}} \frac{{dt}}{{e}^{\mathrm{2}{t}} {t}} \\ $$ Answered by Berbere last updated on 21/Mar/24 $$\left.{x}\overset{{f}} {\rightarrow}{e}^{−\mathrm{2}{x}}…
Question Number 205446 by 073 last updated on 21/Mar/24 Answered by namphamduc last updated on 21/Mar/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205472 by SANOGO last updated on 21/Mar/24 Answered by TheHoneyCat last updated on 01/Apr/24 $$\mathrm{This}\:\mathrm{will}\:\mathrm{be}\:\mathrm{true}\:\mathrm{if}\:\left(\mathrm{and}\:\mathrm{only}\:\mathrm{if}\right)\:\mathrm{the}\:{A}_{{n}} \:\mathrm{are}\:\mathrm{all} \\ $$$$\mathrm{disjoint}. \\ $$$$\mathrm{If}\:\mathrm{they}\:\mathrm{are}\:\mathrm{not},\:\mathrm{take}\:{x}\in{A}_{{i}} \cap{A}_{{k}} \:\left(\mathrm{with}\:{k}\neq{i}\right) \\…
Question Number 205420 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$$\mathrm{Then}: \\ $$$$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:\geqslant\:\mathrm{2} \\ $$ Answered…
Question Number 205421 by hardmath last updated on 20/Mar/24 $$\mathrm{If} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{abc}=\mathrm{1} \\ $$$$\mathrm{Then}: \\ $$$$\frac{\mathrm{a}}{\mathrm{b}^{\mathrm{2024}} }\:+\:\frac{\mathrm{b}}{\mathrm{c}^{\mathrm{2024}} }\:+\:\frac{\mathrm{c}}{\mathrm{a}^{\mathrm{2024}} }\:\geqslant\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c} \\ $$ Terms of Service Privacy…