Question Number 132230 by pticantor last updated on 12/Feb/21 $$ \\ $$$$ \\ $$$$\boldsymbol{{S}}=\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{+\infty} {\sum}}\left(\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} −\mathrm{1}}}−\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{k}}^{\mathrm{2}} +\mathrm{1}}}\right) \\ $$$$\boldsymbol{{S}}\:={l}\:{or}\:\boldsymbol{{S}}=\infty\:\:??? \\ $$ Answered by JDamian…
Question Number 66693 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 1156 by 112358 last updated on 06/Jul/15 $${Determine}\:{the}\:{general}\:{solution} \\ $$$${of}\:{the}\:{following}\:\:{linear}\:{diophantine} \\ $$$${equation}\:{for}\:\forall{N}\in\mathbb{Z}^{+} ,{m}\in\mathbb{Z}^{+} : \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{8}{N}=\mathrm{81}{m}+\mathrm{65}\:. \\ $$ Commented by prakash…
Question Number 132225 by bemath last updated on 12/Feb/21 $$ \\ $$$$\rightarrow\mathrm{A}\:\mathrm{lighthouse}\:\mathrm{L}\:\mathrm{is}\:\mathrm{located}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{small}\:\mathrm{island}\:\mathrm{2}\:\mathrm{km}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{nearest}\:\mathrm{point}\:\mathrm{A}\:\mathrm{on}\:\mathrm{a}\:\mathrm{long}\:\mathrm{the} \\ $$$$\mathrm{straigh}\:\mathrm{shoreline}\:.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{lighthouse}\:\mathrm{lamp}\:\mathrm{rotates}\:\mathrm{at}\:\mathrm{3} \\ $$$$\mathrm{revolutions}\:\mathrm{per}\:\mathrm{minute}.\:\mathrm{how}\:\mathrm{fast}\: \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{illuminated}\:\mathrm{spot}\:\mathrm{P}\:\mathrm{on}\:\mathrm{the} \\…
Question Number 1155 by 123456 last updated on 05/Jul/15 $$\mathrm{what}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{60}{x}+\mathrm{120}{y}+\mathrm{1250}{z} \\ $$$$\mathrm{if} \\ $$$${x}+{y}+\mathrm{5}{z}=\mathrm{150} \\ $$$${x}\in\left\{\mathrm{0},…,\mathrm{150}\right\} \\ $$$${y}\in\left\{\mathrm{0},…,\mathrm{150}\right\} \\ $$$${z}\in\left\{\mathrm{0},…,\mathrm{30}\right\} \\ $$ Answered…
Question Number 132226 by kaivan.ahmadi last updated on 12/Feb/21 $${li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\:\:{xln}\left({sinx}\right) \\ $$ Answered by Olaf last updated on 12/Feb/21 $$\mathrm{sin}{x}\:\underset{\mathrm{0}} {\sim}\:{x} \\ $$$$\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 1151 by 123456 last updated on 05/Jul/15 $$\mathrm{what}\:\mathrm{the}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{60}{x}+\mathrm{120}{y} \\ $$$$\mathrm{where} \\ $$$${x}+{y}=\mathrm{150} \\ $$$${x}\in\left\{\mathrm{0},\mathrm{1},…,\mathrm{150}\right\} \\ $$$${y}\in\left\{\mathrm{0},\mathrm{1},…,\mathrm{150}\right\} \\ $$ Answered by prakash…
Question Number 132220 by aurpeyz last updated on 12/Feb/21 Answered by Olaf last updated on 12/Feb/21 $$\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6}\left(\mathrm{cos60}°\overset{\rightarrow} {{i}}+\mathrm{sin60}°\overset{\rightarrow} {{j}}\right) \\ $$$$\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6}\left(\frac{\mathrm{1}}{\mathrm{2}}\overset{\rightarrow} {{i}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\overset{\rightarrow} {{j}}\right)…
Question Number 66684 by Tinkutara@ last updated on 18/Aug/19 Answered by MJS last updated on 18/Aug/19 $$\mathrm{this}\:\mathrm{is}\:\mathrm{old}… \\ $$$$\mathrm{you}\:\mathrm{always}\:\mathrm{say}\:\mathrm{in}\:\mathrm{words}\:\mathrm{what}\:\mathrm{you}\:\mathrm{read}\:\mathrm{and} \\ $$$$\mathrm{write}\:\mathrm{down}\:\mathrm{in}\:\mathrm{numbers} \\ $$$$\mathrm{1} \\ $$$$\mathrm{one}\:“\mathrm{1}''\:=\:\mathrm{1}\:\mathrm{1}…
Question Number 1147 by prakash jain last updated on 04/Jul/15 $${f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$$${f}\left(\mathrm{0}\right)=? \\ $$ Commented by prakash jain last updated on 04/Jul/15 $${f}\left({f}\left(\mathrm{0}\right)\right)=\mathrm{1}…