Question Number 138763 by mathsuji last updated on 17/Apr/21 $${Make}\:{arbitrary}\:{movements}\:{between} \\ $$$${the}\:\mathrm{7}\:{people}\:{sitting}\:{around}\:{the}\:{table} \\ $$$${so}\:{that}\:{at}\:{least}\:{one}\:{of}\:{the}\:{people}\:{sitting} \\ $$$${next}\:{to}\:{you}\:{is}\:{not}\:{a}\:{Mathematician}.. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73224 by mr W last updated on 09/Nov/19 $${find}\:{the}\:{coefficient}\:{a}_{{k}} \:{of}\:{term}\:{x}^{{k}} \:{in} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+{x}^{{r}} \right)\:{with}\:\mathrm{0}\leqslant{k}\leqslant\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$$$ \\ $$$${example}:\:{n}=\mathrm{100},\:{k}=\mathrm{50} \\ $$ Answered…
Question Number 73225 by mathmax by abdo last updated on 08/Nov/19 $${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} −\mathrm{2}{xcos}\theta\:+\mathrm{1}\right){d}\theta\:\:{with}\:{x}\:{real}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73222 by Tanmay chaudhury last updated on 08/Nov/19 Answered by Tanmay chaudhury last updated on 08/Nov/19 $$\left[\overset{\rightarrow} {{a}}\overset{\rightarrow} {{b}}\overset{\rightarrow} {{c}}\right]=\mathrm{2}=\left(\overset{\rightarrow} {{a}}×\overset{\rightarrow} {{b}}\right).\overset{\rightarrow} {{c}}…
Question Number 138756 by 676597498 last updated on 17/Apr/21 $${show}\:{that} \\ $$$$\mathrm{0}\:\leqslant\:\left(\int_{\mathrm{0}} ^{\:\mathrm{2}} \left(\frac{\left(\mathrm{2}−{x}\right)^{{n}} {e}^{{x}} }{{n}!}{dx}\right)\right)\:\leqslant\:\frac{\mathrm{2}^{{n}} \left({e}^{\mathrm{2}} −\mathrm{1}\right)}{{n}!} \\ $$ Answered by mr W last…
Question Number 73223 by malwaan last updated on 08/Nov/19 $$\boldsymbol{{lim}}\:\frac{\mathrm{0}}{\infty}\:\overset{?} {=}\:\mathrm{0}\:? \\ $$$$\boldsymbol{{lim}}\:\frac{\infty}{\mathrm{0}}\:\overset{?} {=}\:\infty\:? \\ $$ Commented by MJS last updated on 08/Nov/19 $$\mathrm{these}\:\mathrm{are}\:\mathrm{not}\:\mathrm{of}\:\mathrm{correct}\:\mathrm{syntax}\:\Rightarrow\:\mathrm{we}\:\mathrm{cannot} \\…
Question Number 7686 by Alimudin last updated on 09/Sep/16 $${f}\:×=\left(\mathrm{81}\right)\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{2}\left(\mathrm{9}\right)\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{4} \\ $$$$\left(\mathrm{2}+\frac{\mathrm{1}}{×}\right)^{\mathrm{3}} =… \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on 09/Sep/16…
Question Number 138758 by EnterUsername last updated on 17/Apr/21 Answered by mr W last updated on 18/Apr/21 Commented by mr W last updated on 18/Apr/21…
Question Number 73221 by aliesam last updated on 08/Nov/19 Answered by MJS last updated on 08/Nov/19 $${A}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix}\:\:{B}=\begin{pmatrix}{{a}}\\{\mathrm{0}}\end{pmatrix}\:\:{C}=\begin{pmatrix}{{a}}\\{{a}}\end{pmatrix}\:\:{D}=\begin{pmatrix}{\mathrm{0}}\\{{a}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{E}=\begin{pmatrix}{{b}}\\{\mathrm{0}}\end{pmatrix}\:\:{F}=\begin{pmatrix}{{b}}\\{{b}}\end{pmatrix}\:\:{G}=\begin{pmatrix}{\mathrm{0}}\\{{b}}\end{pmatrix} \\ $$$${T}=\begin{pmatrix}{\frac{{a}+{b}}{\mathrm{2}}}\\{\mathrm{0}}\end{pmatrix}\:\:{I}=\begin{pmatrix}{\frac{{a}+{b}}{\mathrm{2}}}\\{\frac{{a}−{b}}{\mathrm{2}}}\end{pmatrix} \\ $$$${M}=\begin{pmatrix}{{b}}\\{\frac{{a}−{b}}{\mathrm{2}}}\end{pmatrix}\:\:{N}=\begin{pmatrix}{\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\left({a}+{b}\right)+{b}}\\{\frac{\mathrm{3}{a}−{b}}{\mathrm{4}}}\end{pmatrix}\:\:{L}=\begin{pmatrix}{{b}}\\{{a}}\end{pmatrix} \\ $$$$\mathrm{radius}\:\mathrm{of}\:\mathrm{incircle}\:\mathrm{of}\:{ETIM}=\frac{{r}}{\mathrm{2}}=\frac{{a}−{b}}{\mathrm{4}}…
Question Number 7683 by new phone last updated on 08/Sep/16 $$\mathrm{If}\:\mathrm{sin}\:\theta+\mathrm{2cos}\:\theta=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2sin}\:\theta−\mathrm{cos}\:\theta=\mathrm{2} \\ $$ Commented by sandy_suhendra last updated on 08/Sep/16 $${sin}\theta+^{} \mathrm{2}{cos}\theta=\mathrm{1} \\…