Question Number 161403 by akolade last updated on 17/Dec/21 $$\mathrm{Two}\:\mathrm{force}\:\mathrm{f1}\:\mathrm{act}\:\mathrm{on}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{f1}\:\mathrm{has}\:\mathrm{aa} \\ $$$$\mathrm{mgnitude}\:\mathrm{of}\:\mathrm{5n}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{30}\:\mathrm{andf} \\ $$$$\mathrm{2}\:\mathrm{has}\:\mathrm{a}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{8n}\:\mathrm{in}\:\mathrm{then} \\ $$$$\mathrm{directio}\:\mathrm{of}\:\mathrm{90}\:\mathrm{fine}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{andi} \\ $$$$\mathrm{drection}\:\mathrm{of}\:\mathrm{their}\:\mathrm{resultant} \\ $$ Terms of Service Privacy Policy…
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Question Number 161282 by byaw last updated on 15/Dec/21 Answered by alephzero last updated on 16/Dec/21 $$\boldsymbol{{First}}\:\boldsymbol{{method}}. \\ $$$$\frac{{u}}{\mathrm{2}}\:\rightarrow\:{u}\:\rightarrow\:\mathrm{3}.\mathrm{14}{u} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{3}\:\rightarrow\:\mathrm{6}\:\rightarrow\:\mathrm{3}.\mathrm{14}{u}\:=\:? \\ $$$${u}\:=\:\mathrm{6}\:\Rightarrow\:\mathrm{3}.\mathrm{14}\left(\mathrm{6}\right)\:=\:\mathrm{18}.\mathrm{84}\: \\ $$$$\left(\mathrm{2}\right)\:\frac{{u}}{\mathrm{2}}\:\rightarrow\:\mathrm{10}\:\rightarrow\:\mathrm{50}.\mathrm{24}…
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Question Number 161156 by LEKOUMA last updated on 13/Dec/21 $${Calculate} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\mathrm{ln}\:\left(\mathrm{1}+{e}^{−{x}} \right)\right)^{\frac{\mathrm{1}}{{x}}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}}{\mathrm{2}+\mathrm{sin}\:\frac{\mathrm{1}}{{x}}}\right) \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{a}^{{x}} +{b}^{{x}} }{\mathrm{2}}\right)^{\frac{\mathrm{1}}{{x}}} \\ $$ Answered…
Question Number 95604 by 174 last updated on 26/May/20 Commented by MJS last updated on 26/May/20 $${x}^{\mathrm{5}} +\mathrm{1}=\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right) \\ $$$$\mathrm{decompose}\:\mathrm{and}\:\mathrm{solve}. \\ $$ Commented…
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Question Number 30017 by jonah last updated on 15/Feb/18 $$\mathrm{find}\:\mathrm{the}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}\:\mathrm{given}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation} \\ $$$$\mathrm{1}.\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{25}}+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{1} \\ $$$$\mathrm{2}.\mathrm{x}^{\mathrm{2}} +\mathrm{9y}^{\mathrm{2}} =\mathrm{9} \\ $$ Answered by ajfour last updated…
Question Number 95473 by aurpeyz last updated on 25/May/20 Answered by EmericGent last updated on 25/May/20 $${regroup}\:{every}\:{two}\:{terms} \\ $$$$\mathrm{1}-\:\frac{\mathrm{1}}{\mathrm{2}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${and}\:{then}\:\forall{n}\:\in\:\mathbb{N}\ast \\ $$$$\frac{\mathrm{1}}{{n}}\:−\:\frac{\mathrm{1}}{{n}+\mathrm{1}}\:=\:\frac{{n}+\mathrm{1}−{n}}{{n}\left({n}+\mathrm{1}\right)}\:=\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)} \\ $$$${since}\:{n}\left({n}+\mathrm{1}\right)\:{is}\:{a}\:{non}\:{zero}\:{positive}\:…
Question Number 160993 by gbanda95 last updated on 10/Dec/21 Answered by mathmax by abdo last updated on 10/Dec/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{x}^{\mathrm{3}} \mathrm{sinx}\:\mathrm{dx}\:=\mathrm{I}_{\mathrm{3}} =\mathrm{3}\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2}} −\mathrm{3}\left(\mathrm{3}−\mathrm{1}\right)\mathrm{I}_{\mathrm{1}} =\frac{\mathrm{3}\pi^{\mathrm{2}}…