Question Number 105388 by mohammad17 last updated on 28/Jul/20 Answered by john santu last updated on 28/Jul/20 $${let}\:{u}\:=\:\mathrm{log}\:_{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{1}\right) \\ $$$$\frac{{du}}{{dx}}\:=\:\frac{\mathrm{3}{x}^{\mathrm{2}} \:}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)\mathrm{ln}\:\mathrm{2}} \\…
Question Number 170926 by Tawa11 last updated on 04/Jun/22 $$\int\:\frac{\mathrm{dx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\:\:\:−\:\:\:\mathrm{6sin}\left(\mathrm{x}\right)\:\:\:\:+\:\:\:\:\mathrm{5}} \\ $$ Answered by thfchristopher last updated on 04/Jun/22 $$\int\frac{{dx}}{\mathrm{sin}^{\mathrm{2}} {x}−\mathrm{6sin}\:{x}+\mathrm{5}} \\ $$$$\mathrm{Let}\:{t}=\mathrm{tan}\frac{{x}}{\mathrm{2}}\:\Rightarrow\:\mathrm{sin}\:{x}=\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }…
Question Number 170912 by MathsFan last updated on 03/Jun/22 $$\boldsymbol{\mathrm{In}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{{QRS}},\:\boldsymbol{{QR}}=\mathrm{14}\boldsymbol{{cm}},\:\boldsymbol{{RS}}=\mathrm{12}\boldsymbol{{cm}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{{SQ}}=\mathrm{9}\boldsymbol{{cm}}.\:\boldsymbol{\mathrm{An}}\:\boldsymbol{\mathrm{incircle}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{drawn}}\:\boldsymbol{\mathrm{to}} \\ $$$$\boldsymbol{\mathrm{touch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{sides}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{{X}},\boldsymbol{{Y}},\boldsymbol{{Z}}\:\boldsymbol{\mathrm{respectively}}.\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{lenghts}} \\ $$$$\boldsymbol{{QX}},\:\boldsymbol{{RY}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{{SZ}}. \\ $$ Answered by som(math1967) last updated…
Question Number 170911 by MathsFan last updated on 03/Jun/22 $$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{manufacturing}}\:\boldsymbol{\mathrm{company}}\:\boldsymbol{\mathrm{produces}} \\ $$$$\boldsymbol{\mathrm{containers}}\left(\boldsymbol{\mathrm{jugs}}\right)\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{kind}}.\:\boldsymbol{\mathrm{Two}} \\ $$$$\boldsymbol{\mathrm{similar}}\:\boldsymbol{\mathrm{containers}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{height}}\:\mathrm{1}.\mathrm{5}\boldsymbol{\mathrm{cm}} \\ $$$$\boldsymbol{\mathrm{and}}\:\mathrm{8}\boldsymbol{\mathrm{cm}}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{selected}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{filled}}\:\boldsymbol{\mathrm{with}} \\ $$$$\boldsymbol{\mathrm{orange}}\:\boldsymbol{\mathrm{juice}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{some}}\:\boldsymbol{\mathrm{athletes}}.\:\boldsymbol{\mathrm{Determine}} \\ $$$$\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{quantity}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{orange}}\:\boldsymbol{\mathrm{juice}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{smaller}}\:\boldsymbol{\mathrm{container}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{bigger}}\:\boldsymbol{\mathrm{one}} \\ $$$$\:\boldsymbol{\mathrm{contained}}\:\mathrm{7}\boldsymbol{\mathrm{liters}}. \\…
Question Number 105370 by mohammad17 last updated on 28/Jul/20 Answered by Ar Brandon last updated on 28/Jul/20 $$\mathrm{Q1}/\mathrm{A}/ \\ $$$$\left(\mathrm{1}\right)\:\mathrm{f}\left({x},{y}\right)={e}^{−\mathrm{2}{y}} \mathrm{cos}\left(\mathrm{3}{x}\right) \\ $$$$\:\:\frac{\delta\mathrm{f}}{\delta{x}}=−\mathrm{3}{e}^{−\mathrm{2}{y}} \mathrm{sin}\left(\mathrm{3}{x}\right)\Rightarrow\frac{\delta^{\mathrm{2}} \mathrm{f}}{\delta{x}^{\mathrm{2}}…
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Question Number 170889 by 0731619 last updated on 02/Jun/22 Commented by Tawa11 last updated on 03/Jun/22 $$\mathrm{Great}\:\mathrm{sir} \\ $$ Answered by mr W last updated…
Question Number 170891 by 0731619 last updated on 02/Jun/22 Commented by mr W last updated on 02/Jun/22 $${x}=\sqrt{−\frac{\mathrm{3}}{\mathrm{2}}{W}\left(−\frac{\mathrm{2}}{\mathrm{3}{e}^{\frac{\mathrm{2}}{\mathrm{3}}} }\right)} \\ $$ Terms of Service Privacy…
Question Number 170878 by 0731619 last updated on 02/Jun/22 Answered by thfchristopher last updated on 02/Jun/22 $$\int{e}^{\mathrm{2}{x}} \mathrm{sin}\:\mathrm{3}{xdx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{sin}\:\mathrm{3}{xd}\left({e}^{\mathrm{2}{x}} \right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}{e}^{\mathrm{2}{x}} \mathrm{sin}\:\mathrm{3}{x}−\frac{\mathrm{1}}{\mathrm{2}}\int{e}^{\mathrm{2}{x}} {d}\left(\mathrm{sin}\:\mathrm{3}{x}\right)…