Question Number 206332 by MATHEMATICSAM last updated on 12/Apr/24 $$\mathrm{If}\:\mathrm{log}\left({a}\:+\:{b}\:+\:{c}\right)\:=\:\mathrm{log}{a}\:+\:\mathrm{log}{b}\:+\:\mathrm{log}{c}\: \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{log}\left(\frac{\mathrm{2}{a}}{\mathrm{1}\:−\:{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{2}{b}}{\mathrm{1}\:−\:{b}^{\mathrm{2}} }\:+\:\frac{\mathrm{2}{c}}{\mathrm{1}\:−\:{c}^{\mathrm{2}} }\right)\:=\: \\ $$$$\mathrm{log}\left(\frac{\mathrm{2}{a}}{\mathrm{1}\:−\:{a}^{\mathrm{2}} }\right)\:+\:\mathrm{log}\left(\frac{\mathrm{2}{b}}{\mathrm{1}\:−\:{b}^{\mathrm{2}} }\right)\:+\:\mathrm{log}\left(\frac{\mathrm{2}{c}}{\mathrm{1}\:−\:{c}^{\mathrm{2}} }\right). \\ $$ Answered…
Question Number 206365 by hardmath last updated on 12/Apr/24 $$\mathrm{Number}\:\mathrm{series}: \\ $$$$\mathrm{a}_{\mathrm{3}} \:=\:\mathrm{2a}\:+\:\mathrm{b}\:−\:\mathrm{6} \\ $$$$\mathrm{a}_{\mathrm{9}} \:=\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{5} \\ $$$$\mathrm{a}_{\mathrm{15}} \:=\:\mathrm{3a}\:+\:\mathrm{b}\:−\:\mathrm{7} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}\:=\:? \\ $$ Commented by…
Question Number 206367 by hardmath last updated on 12/Apr/24 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{6}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{24}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{60}}\:\:+\:…\:+\:…\:\:\frac{\mathrm{1}}{\mathrm{720}}\:=\:? \\ $$ Commented by TheHoneyCat last updated on 12/Apr/24 Can you please explain what the "..." are? Commented by TonyCWX08…
Question Number 206328 by mnjuly1970 last updated on 12/Apr/24 $$ \\ $$$$\:\:\:\:\:\:\:{f}\left({x}\right)=\:\lfloor\:\frac{\:\mathrm{1}+\:{x}\:+{x}^{\mathrm{2}} }{{x}+\:{x}^{\:\mathrm{2}} }\:\rfloor\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:\Rightarrow\begin{cases}{\:\:{D}_{{f}} \:=\:?\:\left({domain}\:\right)}\\{\:\:\:{R}_{\:{f}} \:=\:?\left(\:{range}\right)}\end{cases} \\ $$$$ \\ $$ Answered by TheHoneyCat…
Question Number 206362 by MATHEMATICSAM last updated on 12/Apr/24 $$\mathrm{sin}\frac{\pi}{\mathrm{7}}\:×\:\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{7}}\:×\:\mathrm{sin}\frac{\mathrm{3}\pi}{\mathrm{7}}\:=\:? \\ $$ Answered by Skabetix last updated on 12/Apr/24 $$=\frac{\sqrt{\mathrm{7}}}{\mathrm{8}} \\ $$ Answered by Berbere…
Question Number 206363 by hardmath last updated on 12/Apr/24 $$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}<\mathrm{1} \\ $$$$\mathrm{Compare}: \\ $$$$\frac{\mathrm{1}}{\mathrm{a}−\mathrm{1}}\:\:,\:\:\frac{\mathrm{a}}{\mathrm{a}−\mathrm{1}}\:\:,\:\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{a}}\:\:,\:\:\frac{\mathrm{a}}{\mathrm{1}−\mathrm{a}}\:\:,\:\:\frac{\mathrm{a}}{\mathrm{2a}} \\ $$ Commented by TheHoneyCat last updated on 12/Apr/24 Commented by…
Question Number 206357 by hardmath last updated on 12/Apr/24 $$\mathrm{Find}: \\ $$$$\mathrm{1}\:+\:\mathrm{cos444}°\:−\:\mathrm{cos84}°\:+\:\mathrm{cot45}°\:=\:? \\ $$ Answered by MM42 last updated on 12/Apr/24 $$\mathrm{2}\:\checkmark \\ $$ Commented…
Question Number 206353 by BaliramKumar last updated on 12/Apr/24 Commented by Rasheed.Sindhi last updated on 15/Apr/24 $${I}\:{think}\:\mathrm{15}\:{is}\:{wrong}\:{here},\:{it}\:{should} \\ $$$${be}\:\mathrm{14}\:{or}\:{otherwise}\:{the}\:{answer}\:{is} \\ $$$${not}\:{correct}. \\ $$ Commented by…
Question Number 206321 by cortano21 last updated on 12/Apr/24 Answered by TonyCWX08 last updated on 12/Apr/24 $${By}\:\Delta{BCD}\:\backsim\:\Delta{CDE} \\ $$$$\frac{{x}}{\:\sqrt{\mathrm{14}}}=\frac{\mathrm{7}\sqrt{\mathrm{14}}}{{x}} \\ $$$${x}^{\mathrm{2}} =\mathrm{98} \\ $$$$ \\…
Question Number 206322 by MATHEMATICSAM last updated on 12/Apr/24 $$\mathrm{If}\:{abc}\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{a}\:+\:{b}^{−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{b}\:+\:{c}^{−\mathrm{1}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{c}\:+\:{a}^{−\mathrm{1}} }\:=\:\mathrm{1} \\ $$ Commented by Rasheed.Sindhi last updated on 12/Apr/24 $${For}\:{similar}\:{question}\:{see}…