Question Number 12403 by sin (x) last updated on 21/Apr/17 $${f}\left({x}\right)=\lfloor{x}−\frac{\mathrm{3}}{{e}}\rfloor+\lfloor{x}+\frac{\mathrm{3}}{{e}}\rfloor\Rightarrow{f}\left(\mathrm{1}\right)=? \\ $$ Answered by FilupS last updated on 21/Apr/17 $$\lfloor{x}\rfloor\:=\:\mathrm{floor}\left({x}\right) \\ $$$${f}\left(\mathrm{1}\right)=\lfloor\mathrm{1}−\frac{\mathrm{3}}{{e}}\rfloor+\lfloor\mathrm{1}+\frac{\mathrm{3}}{{e}}\rfloor \\ $$$$\mathrm{2}{e}>\mathrm{3}>{e}\:\:\Rightarrow\:\:\:\mathrm{2}>\frac{\mathrm{3}}{{e}}>\mathrm{1}…
Question Number 12401 by sin (x) last updated on 21/Apr/17 $$\int_{\mathrm{0}} ^{\mathrm{2}\pi} {sgn}\left({cosx}\right){dx}=? \\ $$ Commented by FilupS last updated on 21/Apr/17 $${n}\in\mathbb{Z} \\ $$$$\mathrm{for}\:\mathrm{cos}\left({x}\right)>\mathrm{0},\:\:\:\frac{\pi}{\mathrm{2}}\left(\mathrm{4}{n}−\mathrm{1}\right)<{x}<\frac{\pi}{\mathrm{2}}\left(\mathrm{4}{n}+\mathrm{1}\right)…
Question Number 12402 by sin (x) last updated on 21/Apr/17 $$\mathrm{12}{sgn}\left({x}^{\mathrm{2}} −{x}−\mathrm{20}\right)+\mathrm{3}\geqslant\mathrm{0}\Rightarrow \\ $$$$\left({ss}\right)=? \\ $$ Commented by FilupS last updated on 21/Apr/17 $$\mathrm{sgn}\left({x}\right)=\begin{cases}{\mathrm{1}\:\:\:\mathrm{if}\:\:{x}>\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\mathrm{if}\:\:{x}=\mathrm{0}}\\{−\mathrm{1}\:\:\:\mathrm{if}\:\:{x}<\mathrm{0}}\end{cases} \\…
Question Number 77902 by TawaTawa last updated on 12/Jan/20 Commented by mr W last updated on 12/Jan/20 $${try}\:{to}\:{solve}\:{by}\:{yourself}.\:{i}\:{think}\:{you} \\ $$$${can}\:{solve}. \\ $$$${but}\:{the}\:{question}\:{is}\:{not}\:{a}\:{good}\:{one}.\:{it}\:{says} \\ $$$${only}\:\alpha,\beta,\gamma>\mathrm{0}.\:{but}\:\alpha+\beta−\gamma\:{could}\:{be}\:>\mathrm{0}, \\…
Question Number 12368 by sin (x) last updated on 20/Apr/17 Answered by mrW1 last updated on 22/Apr/17 $${EF}×\mathrm{cot}\:\mathrm{55}+{EF}×\mathrm{cot}\:\mathrm{35}+\mathrm{4}=\mathrm{10} \\ $$$${EF}×\mathrm{tan}\:\:\mathrm{35}+{EF}×\mathrm{tan}\:\:\mathrm{55}=\mathrm{6} \\ $$$${EF}=\frac{\mathrm{6}}{\mathrm{tan}\:\mathrm{35}+\mathrm{tan}\:\mathrm{55}}=\mathrm{2}.\mathrm{819}\approx\mathrm{3} \\ $$$$\Rightarrow{Answer}\:\boldsymbol{{A}} \\…
Question Number 143436 by mathdanisur last updated on 14/Jun/21 $${Find}\:{matrix}\:{rank}=? \\ $$$$\begin{pmatrix}{\mathrm{47}}&{−\mathrm{67}}&{\mathrm{35}}&{\mathrm{201}}&{\mathrm{155}}\\{\mathrm{26}}&{\mathrm{98}}&{\mathrm{23}}&{−\mathrm{294}}&{\mathrm{86}}\\{\mathrm{16}}&{−\mathrm{428}}&{\mathrm{1}}&{\mathrm{1284}}&{\mathrm{53}}\end{pmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12361 by Joel576 last updated on 20/Apr/17 $$\left(\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{3}}\:+\mathrm{2}\:+\:\sqrt{\mathrm{5}}\right)\left(−\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}\:+\:\mathrm{2}\:−\:\sqrt{\mathrm{5}}\right)\left(\sqrt{\mathrm{10}}\:+\:\mathrm{2}\sqrt{\mathrm{3}}\right) \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{without}\:\mathrm{solving}\:\mathrm{them}\:\mathrm{manually}? \\ $$ Answered by ajfour last updated on 20/Apr/17 $$\left({a}+{b}+{c}+{d}\right)\left({b}+{c}−{a}−{d}\right)\left({ad}+{bc}\right) \\…
Question Number 12359 by sin (x) last updated on 20/Apr/17 Answered by ajfour last updated on 20/Apr/17 $${for}\:{given}\:{range}\:{of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}, \\ $$$$\left(\boldsymbol{{a}}^{\mathrm{4}} +\boldsymbol{{b}}^{\mathrm{3}} \right)_{\boldsymbol{{max}}} \:=\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{8}}=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$$$\left(\boldsymbol{{a}}^{\mathrm{4}}…
Question Number 143431 by enter last updated on 14/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143427 by bramlexs22 last updated on 14/Jun/21 $${if}\:{f}\left({x}\right)\:{is}\:{polynomial}\:{satisfying} \\ $$$${f}\left({x}\right){f}\left(\frac{\mathrm{1}}{{x}}\right)−\mathrm{2}{f}\left({x}\right)+\mathrm{2}{f}\left(\frac{\mathrm{1}}{{x}}\right)=\mathrm{5} \\ $$$${and}\:{f}\left(\mathrm{2}\right)=\mathrm{14}\:{then}\:{f}\left(\mathrm{3}\right)=? \\ $$ Answered by qaz last updated on 14/Jun/21 $$\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{2f}\left(\mathrm{x}\right)+\mathrm{2f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\mathrm{5}…….\left(\mathrm{1}\right)}\\{\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{f}\left(\mathrm{x}\right)−\mathrm{2f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{2f}\left(\mathrm{x}\right)=\mathrm{5}…….\left(\mathrm{2}\right)}\end{cases} \\…