Question Number 19554 by Nayon last updated on 12/Aug/17 $${proof}\:\left(\overset{−} {{a}}+\overset{−} {{b}}\right).\overset{−} {{c}}=\overset{−} {{a}}.\overset{−} {{c}}+\overset{−} {{b}}.\overset{−} {{c}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150627 by puissant last updated on 14/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(−\mathrm{1}\right)^{{E}\left(\frac{\mathrm{1}}{{x}}\right)} {dx}}{{x}} \\ $$ Answered by puissant last updated on 14/Aug/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(−\mathrm{1}\right)^{{E}\left(\frac{\mathrm{1}}{{x}}\right)}…
Question Number 85088 by pew_247 last updated on 18/Mar/20 Commented by pew_247 last updated on 18/Mar/20 $${help}\:{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 150626 by puissant last updated on 14/Aug/21 $${S}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right){x}^{{n}} \\ $$$${S}\left(−\mathrm{1}\right)=\:?.. \\ $$$${please}\:{help}.. \\ $$ Answered by puissant last updated on 14/Aug/21…
Question Number 19547 by dioph last updated on 12/Aug/17 $$\mathrm{A}\:\mathrm{matrix}\:\mathrm{has}\:{N}\:\mathrm{rows}\:\mathrm{and}\:\mathrm{2}{k}−\mathrm{1}\: \\ $$$$\mathrm{columns}.\:\mathrm{Each}\:\mathrm{column}\:\mathrm{is}\:\mathrm{filled}\:\mathrm{with} \\ $$$${M}\:\mathrm{ones}\:\mathrm{and}\:{N}−{M}\:\mathrm{zeros}. \\ $$$$\mathrm{A}\:\mathrm{given}\:\mathrm{row}\:{j}\:\mathrm{is}\:“{cool}''\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{k}−\mathrm{1}} {\sum}}{a}_{{ji}} \:\geqslant\:{k}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{number}\:\mathrm{of}\:\mathrm{cool}\:\mathrm{rows} \\ $$$$\mathrm{for}\:\mathrm{given}\:{N},\:{k}\:\mathrm{and}\:{M}.…
Question Number 85083 by mathocean1 last updated on 18/Mar/20 $${a}^{\mathrm{3}} −{b}^{\mathrm{3}} =…? \\ $$ Commented by pew_247 last updated on 18/Mar/20 $$\left({x}−{y}\right)\left({x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \right) \\…
Question Number 150609 by ajfour last updated on 13/Aug/21 $${I}\:{thought}\:{this}\:{as}\:{more}\:{basic}: \\ $$$$\frac{{sinA}}{{a}}=\frac{\mathrm{1}}{\mathrm{2}{R}} \\ $$$$\frac{{cosA}}{{a}}=\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{abc}} \\ $$$$\Rightarrow\:\:\boldsymbol{{tanA}}=\frac{\boldsymbol{{abc}}}{\boldsymbol{{R}}\left(\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} −\boldsymbol{{a}}^{\mathrm{2}} \right)} \\ $$ Terms…
Question Number 85074 by ajfour last updated on 18/Mar/20 Commented by ajfour last updated on 19/Mar/20 $${If}\:{a}\:{cylindrical}\:{cavity}\:{be}\:{drilled} \\ $$$${out}\:{of}\:{a}\:{hemisphere}\:{of}\:{radius}\:{R}, \\ $$$${in}\:{the}\:{place}\:{shown};\:{with}\:{a}\:{driller} \\ $$$$\:{of}\:{radius}\:{r},\:{find}\:{fraction}\:{of} \\ $$$${hemisphere}\:{material}\:{drilled}\:{out}.…
Question Number 85073 by Roland Mbunwe last updated on 18/Mar/20 $${Prove}\:{by}\:{mathematical}\:{induction}\:{that} \\ $$$$\mathrm{2002}^{{n}+\mathrm{2}} +\mathrm{2003}^{\mathrm{2}{n}+\mathrm{1}} \:\:\:\:{is}\:{divisible}\:{by}\:\mathrm{4005} \\ $$ Commented by MJS last updated on 18/Mar/20 $$\mathrm{it}'\mathrm{s}\:\mathrm{true}\:\mathrm{for}\:{n}=\mathrm{1}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{wrong}\:\mathrm{for}\:{n}=\mathrm{2},\:\mathrm{3},\:\mathrm{4}…
Question Number 85068 by pew_247 last updated on 18/Mar/20 Commented by pew_247 last updated on 18/Mar/20 $${help}\:{please} \\ $$ Commented by MJS last updated on…