Question Number 182721 by mnjuly1970 last updated on 13/Dec/22 Answered by Acem last updated on 13/Dec/22 $$\:{It}\:{period}:\:{T}=\:\frac{\mathrm{1}}{{a}} \\ $$$$\:{f}\left({x}\right)=\mathrm{1}\:\Rightarrow\:{b}=\mathrm{1} \\ $$$$\underset{{x}\rightarrow\frac{\mathrm{15}^{\:−} }{\mathrm{2}}} {\mathrm{lim}}\:{f}\left({x}\right)=\:−\infty\:\Rightarrow\:\mathrm{cos}\:\pi{ax}=\:\mathrm{cos}\:\frac{\pi^{\:+} }{\mathrm{2}}\:\Rightarrow\:{a}<\mathrm{0} \\…
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Question Number 117172 by zakirullah last updated on 10/Oct/20 Answered by $@y@m last updated on 10/Oct/20 $$\mathrm{21168}=\mathrm{2}×\mathrm{2}×\mathrm{2}×\mathrm{2}×\mathrm{3}×\mathrm{3}×\mathrm{3}×\mathrm{7}×\mathrm{7} \\ $$$$\mathrm{3}\:{has}\:{no}\:{pair}. \\ $$$$\therefore\:\mathrm{21168}\:{must}\:{be}\:{divided}\:{by}\:\mathrm{3} \\ $$$${to}\:{yield}\:{perfect}\:{square}. \\ $$…
Question Number 182704 by HeferH last updated on 13/Dec/22 $${On}\:{a}\:{path}\:{there}\:{was}\:{an}\:{odd}\:{number}\:{of}\:{rocks} \\ $$$$\:{with}\:{a}\:{distance}\:{of}\:\mathrm{10}{m}\:{between}\:{them},\:{we}\: \\ $$$$\:{want}\:{to}\:{put}\:{them}\:{all}\:{where}\:{the}\:{middle}\:{one}\:{is}, \\ $$$$\:{if}\:{we}\:{start}\:{to}\:{collect}\:{from}\:{one}\:{of}\:{the}\:{ends}\:{and} \\ $$$$\:{when}\:{we}\:{finish}\:{we}\:{have}\:{walked}\:\mathrm{3}{km}\:{in}\:{total}, \\ $$$$\:{how}\:{many}\:{rocks}\:{are}\:{there}? \\ $$ Answered by TheSupreme…
Question Number 182705 by HeferH last updated on 13/Dec/22 $${A}\:{father}\:{has}\:\$\mathrm{320}\:{to}\:{go}\:{a}\:{sporting}\:{event}\:{with} \\ $$$$\:{his}\:{children}.\:{If}\:{he}\:{takes}\:{tickets}\:{of}\:\$\mathrm{50}\:{he} \\ $$$$\:{lacks}\:{money},\:{if}\:{he}\:{takes}\:{tickets}\:{of}\:\$\mathrm{40}\:{he} \\ $$$$\:{has}\:{money}\:{left}\:{over}.\:{Find}\:{the}\:{number}\:{of}\: \\ $$$$\:{children}. \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 182702 by CrispyXYZ last updated on 13/Dec/22 $$\mathrm{log}_{\mathrm{2}} \left({x}+\mathrm{1}\right)−{x}>\mathrm{0} \\ $$ Commented by mr W last updated on 13/Dec/22 $${at}\:{x}=\mathrm{0}\:{and}\:{x}=\mathrm{1}:\:\mathrm{log}_{\mathrm{2}} \:\left({x}+\mathrm{1}\right)={x} \\ $$$$\Rightarrow−\mathrm{1}<{x}<\mathrm{0}\:\vee\:\mathrm{1}<{x}<+\infty…
Question Number 182681 by Acem last updated on 12/Dec/22 $$\:{Solve}\:\sqrt{\mathrm{39}−\:\mathrm{10}\:{a}\:−{a}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{9}−{a}^{\mathrm{2}} }\:=\:\mathrm{2}\:\sqrt{\mathrm{14}}\:\:\:;\:{a}\in\:\mathbb{R}^{+\bigstar} \\ $$$$\:@{Mr}.\:{Rasheed},\:{yesterday}\:{i}\:{solved}\:{it}\:{on}\:{a}\:{draft}\:{paper} \\ $$$$\:{When}\:{i}\:{came}\:{today}\:{to}\:{write}\:{it}\:{down}\:{on} \\ $$$$\:{the}\:{notebook}\:{i}\:{got}\:{into}\:{a}\:{maze},\:{do}\:{you}\:{have} \\ $$$$\:{an}\:{easy}\:{way}\:{to}\:{deal}\:{with}?\:“{if}\:{you}\:{have}\:{time}'' \\ $$$$\:{i}\:{lost}\:{that}\:{paper},\:{and}\:{this}\:{formula}\:{makes}\:{me} \\ $$$$\:{laugh}\:{at}\:{myself},\:{it}'{s}\:{for}\:\mathrm{13}\:{y}/{o}\:“{confused}\:{face}''\: \\…
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Question Number 51600 by malwaan last updated on 28/Dec/18 $$\mathrm{solve} \\ $$$$\left(\mathrm{sin}\theta\right)\mathrm{Z}^{\mathrm{2}} −\mathrm{i}\left(\mathrm{cos}\theta\right)\mathrm{Z}+\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{sin}\theta=\mathrm{0} \\ $$ Commented by Abdo msup. last updated on 29/Dec/18 $$\Delta=\left(−{icos}\theta\right)^{\mathrm{2}} −\mathrm{4}{sin}\theta\left(\frac{\mathrm{1}}{\mathrm{4}}{sin}\theta\right)=−{cos}^{\mathrm{2}}…
Question Number 117122 by Ar Brandon last updated on 09/Oct/20 $$\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\mathbb{R}^{\mathrm{3}} \:\mathrm{such}\:\mathrm{that}\:\mathrm{abc}=\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\left(\mathrm{a}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{b}}\right)\left(\mathrm{b}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{c}}\right)\left(\mathrm{c}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{a}}\right)\leqslant\mathrm{1} \\ $$ Commented by MJS_new last updated on 09/Oct/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:\left({a}\mid{b}\mid{c}\right)\in\mathbb{R}^{\mathrm{3}} \\…