Question Number 200691 by sonukgindia last updated on 22/Nov/23 Commented by aleks041103 last updated on 22/Nov/23 $${a},{b}\in\mathbb{Z}? \\ $$$${or}\:{just}\:{a},{b}\in\mathbb{R} \\ $$ Answered by witcher3 last…
Question Number 200748 by Rupesh123 last updated on 22/Nov/23 Answered by MM42 last updated on 22/Nov/23 $$\left.{s}=\mathrm{4}\int_{\mathrm{0}} ^{{c}} \left({c}^{\mathrm{2}} −{x}^{\mathrm{2}} \right){dx}=\mathrm{4}\left({c}^{\mathrm{2}} {x}−\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} \right)\right]_{\mathrm{0}} ^{{c}} \\…
Question Number 200750 by arif1234567890 last updated on 22/Nov/23 $$\mathrm{5}×\mathrm{5} \\ $$$$ \\ $$ Answered by Frix last updated on 22/Nov/23 $$\sqrt{\mathrm{625}} \\ $$ Terms…
Question Number 200746 by sonukgindia last updated on 22/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 200747 by Rupesh123 last updated on 22/Nov/23 Answered by MM42 last updated on 22/Nov/23 $$\left.{lnx}={u}\Rightarrow\int_{\mathrm{1}} ^{\infty} \:\frac{{du}}{{u}^{\mathrm{2}} }\:=−\frac{\mathrm{1}}{{u}}\right]_{\mathrm{1}} ^{\infty} =\mathrm{1}\:\checkmark \\ $$ Commented…
Question Number 200741 by Rydel last updated on 22/Nov/23 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{a}\mathrm{sin}\:{x}−{x}\mathrm{sin}\:{a}}{{x}−{a}} \\ $$ Commented by JDamian last updated on 22/Nov/23 really? Answered by JDamian last…
Question Number 200736 by Calculusboy last updated on 22/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{A}}\:\boldsymbol{{particle}}\:\boldsymbol{{moves}}\:\boldsymbol{{along}}\:\boldsymbol{{the}}\:\boldsymbol{{space}} \\ $$$$\boldsymbol{{curve}}\:\underset{−} {\boldsymbol{{r}}}=\left(\boldsymbol{{t}}^{\mathrm{2}} +\boldsymbol{{t}}\right)\boldsymbol{{i}}+\left(\mathrm{3}\boldsymbol{{t}}−\mathrm{2}\right)\boldsymbol{{j}}+\left(\mathrm{2}\boldsymbol{{t}}^{\mathrm{3}} −\mathrm{4}\boldsymbol{{t}}^{\mathrm{2}} \right)\boldsymbol{{k}}. \\ $$$$\boldsymbol{{find}} \\ $$$$\left(\boldsymbol{{a}}\right)\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{b}}\right)\boldsymbol{{speed}}\:\boldsymbol{{or}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{of}}\:\boldsymbol{{velocity}} \\ $$$$\left(\boldsymbol{{c}}\right)\boldsymbol{{acceleration}} \\…
Question Number 200737 by Calculusboy last updated on 22/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{The}}\:\boldsymbol{{position}}\:\boldsymbol{{vector}}\:\boldsymbol{{of}}\:\boldsymbol{{a}}\:\boldsymbol{{particle}}\:\boldsymbol{{at}}\:\boldsymbol{{any}}\:\boldsymbol{{time}}\:\boldsymbol{{t}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{given}}\:\boldsymbol{{by}}\:\:\underset{−} {\boldsymbol{{r}}}=\left(\boldsymbol{{acoswt}}\right)\boldsymbol{{i}}+\left(\boldsymbol{{asinwt}}\right)\boldsymbol{{j}}+\boldsymbol{{bt}}^{\mathrm{2}} \boldsymbol{{k}} \\ $$$$\left(\boldsymbol{{a}}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}},\boldsymbol{{although}}\:\boldsymbol{{the}}\:\boldsymbol{{speed}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{particle}} \\ $$$$\boldsymbol{{increases}}\:\boldsymbol{{with}}\:\boldsymbol{{time}},\boldsymbol{{the}}\:\boldsymbol{{magnitude}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{acceleration}}\:\boldsymbol{{is}}\:\boldsymbol{{always}}\:\boldsymbol{{constant}} \\ $$$$\left(\boldsymbol{{b}}\right)\:\boldsymbol{{describe}}\:\boldsymbol{{the}}\:\boldsymbol{{motion}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{particle}}\:\boldsymbol{{geometrically}} \\ $$ Terms…
Question Number 200738 by Calculusboy last updated on 22/Nov/23 $$\boldsymbol{{Solve}}:\:\boldsymbol{{A}}\:\boldsymbol{{smooth}}\:\boldsymbol{{sphere}}\:\boldsymbol{{A}},\boldsymbol{{of}}\:\boldsymbol{{mass}}\:\mathrm{2}\boldsymbol{{kg}}\:\boldsymbol{{and}} \\ $$$$\boldsymbol{{moving}}\:\boldsymbol{{with}}\:\boldsymbol{{speed}}\:\mathrm{6}\boldsymbol{{ms}}^{−\mathrm{1}} \boldsymbol{{collides}}\:\boldsymbol{{obliquely}}\: \\ $$$$\boldsymbol{{with}}\:\boldsymbol{{a}}\:\boldsymbol{{smooth}}\:\boldsymbol{{sphere}}\:\boldsymbol{{B}}\:\boldsymbol{{of}}\:\boldsymbol{{mass}}\:\mathrm{4}\boldsymbol{{kg}}.\:\boldsymbol{{just}}\:\boldsymbol{{before}}\:\boldsymbol{{the}}\:\boldsymbol{{impact}}\:\boldsymbol{{B}}\:\boldsymbol{{is}} \\ $$$$\boldsymbol{{stationary}}\:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{velocity}}\:\boldsymbol{{of}}\:\boldsymbol{{A}}\:\boldsymbol{{makes}} \\ $$$$\boldsymbol{{an}}\:\boldsymbol{{angle}}\:\boldsymbol{{of}}\:\mathrm{10}°\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{lines}}\:\boldsymbol{{of}}\:\boldsymbol{{centers}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{two}}\:\boldsymbol{{sphere}}. \\ $$$$\boldsymbol{{The}}\:\boldsymbol{{coefficient}}\:\boldsymbol{{of}}\:\boldsymbol{{restitution}}\:\boldsymbol{{between}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{spheres}}\:\boldsymbol{{is}}\:\frac{\mathrm{1}}{\mathrm{2}}.\:\boldsymbol{{Find}}\:\boldsymbol{{the}}\:\boldsymbol{{magnitude}}\:\boldsymbol{{and}}\: \\ $$$$\boldsymbol{{directions}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{velovities}}\:\boldsymbol{{of}}\:\boldsymbol{{A}}\:\boldsymbol{{and}}\:\boldsymbol{{B}}…
Question Number 200739 by mr W last updated on 22/Nov/23 $${solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−\mathrm{2}}+\mathrm{2}=\mathrm{0} \\ $$ Commented by Frix last updated on 23/Nov/23 $${x}^{\mathrm{3}} −{px}+{q}=\mathrm{0}…