Question Number 205361 by Lambertician last updated on 18/Mar/24 Answered by Berbere last updated on 18/Mar/24 $$=−\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{xln}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}−\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}} \\ $$$$=−\mathrm{4}{a}−{q} \\…
Question Number 205353 by MATHEMATICSAM last updated on 17/Mar/24 $$\mathrm{If}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{had}\:\mathrm{two}\:\mathrm{roots}\:{p}\:\mathrm{and}\:{q} \\ $$$$\mathrm{and}\:{p}^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \:=\:{p}^{\mathrm{3}} \:+\:{q}^{\mathrm{3}} \:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${b}^{\mathrm{3}} \:−\:\mathrm{2}{a}^{\mathrm{2}} {c}\:+\:{ab}^{\mathrm{2}} \:=\:\mathrm{3}{abc}. \\ $$ Answered…
Question Number 205338 by cortano12 last updated on 17/Mar/24 Answered by mr W last updated on 17/Mar/24 $${x}\geqslant−\mathrm{2},\:{y}\geqslant−\mathrm{3} \\ $$$${x}+\mathrm{2}−\mathrm{4}\sqrt{{x}+\mathrm{2}}+\mathrm{4}+{y}+\mathrm{3}−\mathrm{4}\sqrt{{y}+\mathrm{3}}+\mathrm{4}=\mathrm{13} \\ $$$$\left(\sqrt{{x}+\mathrm{2}}−\mathrm{2}\right)^{\mathrm{2}} +\left(\sqrt{{y}+\mathrm{3}}−\mathrm{2}\right)^{\mathrm{2}} =\left(\sqrt{\mathrm{13}}\right)^{\mathrm{2}} \\…
Question Number 205339 by depressiveshrek last updated on 17/Mar/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{tan}\left(\mathrm{tan}{x}\right)}{\mathrm{sin}\left(\mathrm{1}−\mathrm{cos}{x}\right)} \\ $$ Answered by MM42 last updated on 18/Mar/24 $$={lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{tan}\left({x}\right)}{{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} \right)} \\ $$$$={lim}_{{x}\rightarrow\mathrm{0}}…
Question Number 205350 by necx122 last updated on 17/Mar/24 $${A}\:{man}\:{invested}\:{U}\mathrm{24000}.\mathrm{00}\:{in}\:{U}\mathrm{5}.\mathrm{00} \\ $$$${shares}\:{of}\:{a}\:{firm}.\:{After}\:{a}\:{period}\:{of} \\ $$$${time},\:{it}\:{appreciated}\:{to}\:{U}\mathrm{5}.\mathrm{50}\:{per}\:{share}. \\ $$$${How}\:{much}\:{dividend}\:{did}\:{he}\:{receive},\:{if} \\ $$$${the}\:{dividend}\:{declared}\:{is}\:\mathrm{50}{k}\:{per}\:{share}? \\ $$ Commented by A5T last updated…
Question Number 205334 by cortano12 last updated on 17/Mar/24 Commented by Ghisom last updated on 17/Mar/24 $${x}^{\mathrm{2}} −\frac{\mathrm{5}}{\mathrm{2}}{x}^{\mathrm{3}/\mathrm{2}} +\mathrm{2}{x}−\frac{\mathrm{5}}{\mathrm{4}}{x}^{\mathrm{1}/\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{0} \\ $$$$\left({x}−\mathrm{2}{x}^{\mathrm{1}/\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{1}/\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{0} \\…
Question Number 205335 by Lindemann last updated on 17/Mar/24 $$\int\frac{{ax}+{b}}{\left({x}^{\mathrm{2}} −{cx}+{d}\right)^{{n}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205324 by hardmath last updated on 16/Mar/24 $$\mathrm{Compare}: \\ $$$$\mathrm{37}^{\mathrm{37}} \:\:\:\mathrm{and}\:\:\:\mathrm{36}^{\mathrm{38}} \\ $$ Answered by nikif99 last updated on 16/Mar/24 $$\mathrm{37}^{\mathrm{37}} \:\lessgtr\:\mathrm{36}^{\mathrm{38}} \:\Rightarrow…
Question Number 205321 by gopikrishnan last updated on 16/Mar/24 $$\overset{\rightarrow} {{a}}=\hat {{i}}+\mathrm{3}\hat {{j}}+\mathrm{4}\hat {{k}}\:\overset{\rightarrow} {{b}}=\mathrm{2}\hat {{i}}−\mathrm{3}\hat {{j}}+\mathrm{4}\hat {{k}}\:\overset{\rightarrow} {{c}}=\mathrm{5}\hat {{i}}−\mathrm{2}\hat {{j}}+\mathrm{4}\hat {{k}}\:{given}\:{that}\:\overset{\rightarrow} {{p}}×\overset{\rightarrow} {{b}}=\overset{\rightarrow} {{b}}×\overset{\rightarrow}…
Question Number 205323 by liuxinnan last updated on 16/Mar/24 $${If}\:\:\:\:{log}_{\sqrt{\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}}} \frac{{a}+{b}}{{b}}\geqslant{log}_{\sqrt{{ab}}} \frac{\mathrm{2}}{\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}} \\ $$$${when}\:{a}>\mathrm{1}\:{b}>\mathrm{1} \\ $$ Commented by liuxinnan last updated on 17/Mar/24…