Question Number 198067 by necx122 last updated on 09/Oct/23 $${A}\:{father}\:{reduced}\:{the}\:{quantity}\:{of}\:{food} \\ $$$${bought}\:{for}\:{the}\:{family}\:{by}\:\mathrm{10\%}\:{when}\:{he} \\ $$$${found}\:{that}\:{the}\:{cost}\:{of}\:{living}\:{had} \\ $$$${increased}\:{by}\:\mathrm{15\%}.\:{What}\:{is}\:{the}\:{fractional} \\ $$$${increase}\:{in}\:{the}\:{family}\:{food}\:{bill}? \\ $$ Answered by yogamulyadi last updated…
Question Number 197961 by cherokeesay last updated on 06/Oct/23 $$ \\ $$A cylindrical container is designed to contain bees. At exactly 12:00pm, there are 2…
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Question Number 197772 by Erico last updated on 28/Sep/23 $$\mathrm{Can}\:\mathrm{anyone}\:\mathrm{do}\:\mathrm{this}? \\ $$$$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \frac{\mathrm{t}−\mathrm{1}}{\left(\mathrm{1}+\mathrm{t}\right)^{\mathrm{3}} \:\mathrm{lnt}}\mathrm{dt} \\ $$ Commented by witcher3 last updated on 28/Sep/23 $$\mathrm{we}\:\mathrm{can}\:\mathrm{Give}\:…
Question Number 197475 by mnjuly1970 last updated on 19/Sep/23 $$ \\ $$$$\:\:\:\:\:\:{x}\:,\:{y}\:\in\:\mathbb{R}\:\:\:, \\ $$$$\:\:\:\:{x}^{\:\mathrm{2}} \:+\:{xy}\:=\:\mathrm{12} \\ $$$$\:\:\:\:\:{y}^{\:\mathrm{2}} \:+\:\mathrm{2}{xy}\:=\:\mathrm{7}\: \\ $$$$\:\:\:\:−−−−−\:\:\:{x}\:,\:{y}\:=? \\ $$ Answered by Sutrisno…
Question Number 197323 by Erico last updated on 13/Sep/23 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\:\mathrm{and}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{f}\left(\mathrm{k}\pi+\frac{\pi}{\alpha}\right)+\mathrm{f}\left(\mathrm{k}\pi−\frac{\pi}{\alpha}\right)\right]\:\:\:\:\left(\alpha>\mathrm{1}\right) \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{n}\rightarrow+\infty} {\:\mathrm{lim}}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\mathrm{1}−\mathrm{f}\left(\frac{\pi}{\alpha}\right) \\ $$ Answered by witcher3 last updated on…
Question Number 197247 by Erico last updated on 11/Sep/23 $$\mathrm{calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{{ln}\left({cht}\right)}{{sh}\left({t}\right)}{dt} \\ $$ Answered by witcher3 last updated on 11/Sep/23 $$=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{ch}\left(\mathrm{t}\right)\right)\mathrm{sh}\left(\mathrm{t}\right)}{\mathrm{1}−\mathrm{ch}^{\mathrm{2}} \left(\mathrm{x}\right)}…
Question Number 196971 by dimentri last updated on 05/Sep/23 $$\:\:{solve}\:\begin{cases}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{9}{y}=\mathrm{1}}\\{\mathrm{3}{y}^{\mathrm{2}} −\mathrm{9}{x}=\mathrm{0}}\end{cases} \\ $$ Answered by Frix last updated on 05/Sep/23 $${y}=\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{9}} \\ $$$${x}^{\mathrm{4}}…
Question Number 196880 by subheenoy last updated on 02/Sep/23 $$\mathrm{1}.\:{A}\:{container}\:{of}\:{milk}\:{is}\:\frac{\mathrm{4}}{\mathrm{5}}\:{full}.\:{When}\:\mathrm{10}{L}\:{of}\:{milk}\:{is}\:{poured}\:{into}\:{it}\:{the}\:{container}\:{becomes}\:\:\frac{\mathrm{9}}{\mathrm{10}}\:{full}.\:{What}\:{is}\:{the}\:{capacity}\:{of}\:{the}\:{container}? \\ $$ Answered by Frix last updated on 02/Sep/23 $$\frac{\mathrm{4}}{\mathrm{5}}{x}+\mathrm{10}=\frac{\mathrm{9}}{\mathrm{10}}{x} \\ $$$$\mathrm{10}=\left(\frac{\mathrm{9}}{\mathrm{10}}−\frac{\mathrm{4}}{\mathrm{5}}\right){x}=\left(\frac{\mathrm{9}−\mathrm{8}}{\mathrm{10}}\right){x}=\frac{\mathrm{1}}{\mathrm{10}}{x} \\ $$$${x}=\mathrm{100} \\…
Question Number 196638 by mr W last updated on 28/Aug/23 $${find}\:{the}\:{sum}\:{of}\:{the}\:{all}\:\mathrm{168}\:{prime} \\ $$$${numbers}\:{from}\:\mathrm{1}\:{to}\:\mathrm{1000}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{13245} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{52788} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{76127} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{86344} \\ $$ Commented by…