Question Number 206805 by BaliramKumar last updated on 26/Apr/24 Answered by A5T last updated on 26/Apr/24 $$\left(\mathrm{225}\right)^{\mathrm{40}} =\mathrm{10}^{{x}} \Rightarrow{x}=\mathrm{40}{log}\mathrm{225}\approx\mathrm{94}.\mathrm{087}<\mathrm{95} \\ $$$$\Rightarrow\mathrm{10}^{\mathrm{94}} <\left(\mathrm{225}\right)^{\mathrm{40}} <\mathrm{10}^{\mathrm{95}} \Rightarrow\mathrm{225}^{\mathrm{40}} \:{has}\:\mathrm{95}\:{digits}…
Question Number 206806 by Frix last updated on 26/Apr/24 $$\mathrm{Given}\:\mathrm{is}\:\mathrm{a}\:\mathrm{square}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length}\:\mathrm{15}. \\ $$$$\mathrm{We}\:\mathrm{need}\:\mathrm{to}\:\mathrm{find}\:\mathrm{exactly}\:\mathrm{17}\:\mathrm{smaller}\:\mathrm{squares} \\ $$$$\mathrm{to}\:\mathrm{fill}\:\mathrm{the}\:\mathrm{big}\:\mathrm{one}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{are} \\ $$$$\mathrm{possible}? \\ $$$$\left(\mathrm{Note}:\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{enough}\:\mathrm{to}\:\mathrm{find}\:\mathrm{squares}\:\mathrm{with}\right. \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{areas}\:\mathrm{being}\:\mathrm{225},\:\mathrm{they}\:\mathrm{must} \\ $$$$\mathrm{fit}\:\mathrm{into}\:\mathrm{the}\:\mathrm{15}×\mathrm{15}\:\mathrm{square}.\:\mathrm{Example}\:\mathrm{with} \\ $$$$\mathrm{3}\:\mathrm{squares}:\:\mathrm{2}×\mathrm{2}+\mathrm{5}×\mathrm{5}+\mathrm{14}×\mathrm{14}=\mathrm{225}\:\mathrm{but} \\…
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Question Number 206783 by BaliramKumar last updated on 25/Apr/24 Commented by BaliramKumar last updated on 25/Apr/24 $$\mathrm{i}\:\mathrm{find}\:\mathrm{20} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 206794 by MaruMaru last updated on 25/Apr/24 $${help}\:{me}… \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left({t}\right)\mathrm{ln}\left({t}\right)}{{t}}{e}^{−{t}} \:{dt} \\ $$ Answered by Berbere last updated on 25/Apr/24 $${let}\:{f}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 206795 by BaliramKumar last updated on 25/Apr/24 Commented by BaliramKumar last updated on 25/Apr/24 $$\mathrm{can}\:\mathrm{be}\:\:\left(\mathrm{a}\right)\:\mathrm{right}??? \\ $$ Commented by A5T last updated on…
Question Number 206804 by mr W last updated on 25/Apr/24 Answered by mr W last updated on 26/Apr/24 Commented by mr W last updated on…
Question Number 206788 by SANOGO last updated on 25/Apr/24 Answered by A5T last updated on 25/Apr/24 $$\mathrm{1}.\:\overline {\left(\frac{{x}}{{y}}\right)}=\frac{\overset{−} {{x}}}{\overset{−} {{y}}}\Rightarrow\overset{} {\left(\frac{\mathrm{1}}{{z}}\right)}=\frac{\overset{−} {\mathrm{1}}}{\overset{−} {{z}}}=\frac{\mathrm{1}}{\overset{−} {{z}}} \\…
Question Number 206789 by BaliramKumar last updated on 25/Apr/24 Answered by A5T last updated on 25/Apr/24 $$\sqrt[{{n}}]{{a}_{\mathrm{1}} {a}_{\mathrm{2}} …{a}_{{n}} }={P} \\ $$$$\sqrt[{\mathrm{2}{n}}]{{a}_{{n}+\mathrm{1}} {a}_{{n}+\mathrm{2}} …{a}_{\mathrm{3}{n}} }={Q}…
Question Number 206791 by akolade last updated on 25/Apr/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\sqrt{\mathrm{x}}}.\mathrm{ln}^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$ Commented by Frix last updated on 25/Apr/24 $$\mathrm{Question}\:\mathrm{206754} \\ $$…