Question Number 5425 by love math last updated on 14/May/16 $$\int_{\mathrm{1}} ^{\mathrm{3}} {ln}\left(\mathrm{3}{x}−\mathrm{2}\right){dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$\left[{xln}\left(\mathrm{3}{x}−\mathrm{2}\right)\right]_{\mathrm{1}} ^{\mathrm{3}} −\mathrm{3}\int_{\mathrm{1}}…
Question Number 5422 by love math last updated on 14/May/16 $$\int_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} \left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$=\left[\frac{\mathrm{3}}{\mathrm{8}}\left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right]_{\mathrm{0}}…
Question Number 5421 by love math last updated on 14/May/16 $$\int_{\mathrm{0}} ^{\mathrm{2}} \:{xe}^{{x}^{\mathrm{2}} } {dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$=\left[\frac{\mathrm{1}}{\mathrm{2}}{e}^{{x}^{\mathrm{2}}…
Question Number 136494 by liberty last updated on 22/Mar/21 $$\mathrm{5}\left(\sqrt{\mathrm{1}−{x}}\:+\sqrt{\mathrm{1}+{x}}\:\right)=\:\mathrm{6}{x}\:+\:\mathrm{8}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\: \\ $$ Answered by MJS_new last updated on 22/Mar/21 $$\mathrm{I}\:\mathrm{get}\:\mathrm{2}\:\mathrm{solutions} \\ $$$${x}_{\mathrm{1}} =\frac{\mathrm{24}}{\mathrm{25}} \\…
Question Number 136489 by liberty last updated on 22/Mar/21 $$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{6}}{\mathrm{16}}+\frac{\mathrm{11}}{\mathrm{32}}+\frac{\mathrm{20}}{\mathrm{64}}+\frac{\mathrm{37}}{\mathrm{128}}+…\:=? \\ $$ Answered by Olaf last updated on 22/Mar/21 $$\mathrm{Tribonacci}\:\mathrm{numbers}\:: \\ $$$$\mathrm{T}_{\mathrm{0}} \:=\:\mathrm{0},\:\mathrm{T}_{\mathrm{1}} \:=\:\mathrm{1},\:\mathrm{T}_{\mathrm{2}} \:=\:\mathrm{0}…
Question Number 5417 by FilupSmith last updated on 14/May/16 $$\mathrm{Prove},\:\mathrm{or}\:\mathrm{disprove},\:\mathrm{that}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{has}\:\mathrm{the}\:\mathrm{largest}\:{Perimiter}\:\mathrm{over}\:\mathrm{all} \\ $$$$\mathrm{natural}\:\mathrm{shapes}\:\mathrm{that}\:\mathrm{have}\:\mathrm{area}\:{A} \\ $$ Commented by Rasheed Soomro last updated on 14/May/16 $$\mathrm{I}\:\mathrm{think}\:\mathrm{that}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{has}\:\mathrm{the}\:\mathrm{smallest}…
Question Number 5414 by FilupSmith last updated on 14/May/16 $$\mathrm{How}\:\mathrm{do}\:\mathrm{we}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}/\mathrm{rectangle} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{its}\:\mathrm{maximum}\:\mathrm{when}\:\mathrm{both}\:\mathrm{sides}\:\mathrm{are}\:\mathrm{equal}. \\ $$$$ \\ $$$$\mathrm{So},\:\mathrm{if}\:\mathrm{we}\:\mathrm{have}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{of}\:\mathrm{sides}\:{a}\:\mathrm{and}\:{b}, \\ $$$$\mathrm{how}\:\mathrm{do}\:\mathrm{we}\:\mathrm{show}\:\mathrm{its}\:\mathrm{maximized}\:\mathrm{when}\:{a}={b}? \\ $$ Answered by 123456 last updated…
Question Number 136487 by physicstutes last updated on 22/Mar/21 Commented by physicstutes last updated on 22/Mar/21 $$\mathrm{The}\:\mathrm{figure}\:\mathrm{above}\:\mathrm{shows}\:\mathrm{a}\:\mathrm{system}\:\mathrm{of}\:\mathrm{two}\:\mathrm{slaps}\:\mathrm{with}\:\mathrm{a}\:\mathrm{space}\:\mathrm{inbetween}\:\mathrm{them} \\ $$$$,\mathrm{given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{respective}\:\mathrm{thermal}\:\mathrm{conductivities}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slap}−\mathrm{space}−\mathrm{slap}\:\mathrm{system} \\ $$$$\mathrm{is}\:{k}_{\mathrm{1}} ,{k}_{\mathrm{2}} \:\mathrm{and}\:{k}_{\mathrm{3}} .\:\mathrm{and}\:\mathrm{thier}\:\mathrm{lenght}\:\left(\mathrm{or}\:\mathrm{thickness}\right)\:\mathrm{are}\:{y}_{\mathrm{1}} ,{y}_{\mathrm{2}}…
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Question Number 70949 by ajfour last updated on 10/Oct/19 Commented by ajfour last updated on 10/Oct/19 $${For}\:{coordinate}\:{geometry}\:{experts}! \\ $$ Commented by ajfour last updated on…