Question Number 207395 by hardmath last updated on 13/May/24 $$\mathrm{Geometric}\:\mathrm{series}: \\ $$$$\frac{\mathrm{b}_{\mathrm{4}} \:\centerdot\:\mathrm{b}_{\mathrm{7}} \:\centerdot\:\mathrm{b}_{\mathrm{10}} }{\mathrm{b}_{\mathrm{1}} \:\centerdot\:\mathrm{b}_{\mathrm{3}} \:\centerdot\:\mathrm{b}_{\mathrm{5}} }\:\:=\:\:\mathrm{2}^{\mathrm{12}} \:\:\:\:\:\mathrm{find}:\:\:\:\frac{\mathrm{b}_{\mathrm{5}} }{\mathrm{b}_{\mathrm{2}} }\:\:=\:\:? \\ $$ Answered by…
Question Number 207372 by sniper237 last updated on 12/May/24 $$\mathrm{2}\:{students}\:{are}\:{passing}\: \\ $$$${a}\:{test}\:{of}\:\:{n}\:{questions}\:{with} \\ $$$${the}\:{same}\:{chance}\:{to}\:{find}\:{each}\:{one} \\ $$$${Show}\:\:{the}\:{chance}\:{that}\:{they}\:{both} \\ $$$$\:{don}'{t}\:{find}\:{a}\:{same}\:{question}\:{is}\:\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$ Commented by A5T last updated…
Question Number 207341 by mr W last updated on 12/May/24 Answered by som(math1967) last updated on 12/May/24 Commented by som(math1967) last updated on 12/May/24 $${ar}\:{of}\:\bigtriangleup{BOC}…
Question Number 207359 by Shrodinger last updated on 12/May/24 $$\int\frac{{ln}\left({x}^{\mathrm{2}} +{sin}\left({sin}\left({e}^{{x}} \right)\right)\right)}{\:\sqrt{{x}+{tan}\left({ln}\left({x}\right)\right)}}{dx} \\ $$ Answered by Berbere last updated on 12/May/24 $${it}\:{semms}\:{non}\:{close}\:{forme}\: \\ $$ Commented…
Question Number 207352 by NasaSara last updated on 12/May/24 $${calculate}: \\ $$$$\:\int_{\frac{\Pi}{\mathrm{4}}} ^{\frac{\Pi}{\mathrm{2}}} \lfloor{cot}\left({x}\right)\rfloor\:{dx} \\ $$ Commented by NasaSara last updated on 12/May/24 $${thank}\:{you} \\…
Question Number 207354 by NasaSara last updated on 12/May/24 Commented by mr W last updated on 12/May/24 $${there}\:{are}\:{integrals}\:{like}\:{following} \\ $$$$\int\int…\int\int{f}\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,…,{x}_{{n}} \right){dx}_{\mathrm{1}} {dx}_{\mathrm{2}} …{dx}_{{n}}…
Question Number 207339 by Ghisom last updated on 12/May/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({x}+{a}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }{\left({x}+{b}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }\:=? \\ $$ Answered by sniper237 last updated on 12/May/24 $$\:\frac{{a}}{{b}}\:\:\:{cause}\:\:\overset{{X}=\mathrm{1}/{x}}…
Question Number 207332 by mustafazaheen last updated on 12/May/24 $$\left(\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}\right)×\left(\overset{\rightarrow} {\mathrm{a}}\right)=? \\ $$$$\mathrm{how}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution} \\ $$ Commented by Ghisom last updated on 12/May/24 $$\left(\begin{pmatrix}{{a}_{\mathrm{1}}…
Question Number 207361 by hardmath last updated on 12/May/24 $$\mathrm{y}\:=\:\frac{\mathrm{tg}\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{ctg}\boldsymbol{\mathrm{x}}}{\mathrm{8}}\:\:\:\:\:,\:\:\:\:\:\left(\mathrm{0}\:;\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{y}\right)\:=\:? \\ $$ Answered by Berbere last updated on 12/May/24 $${ctg}\left({x}\right)=\frac{\mathrm{1}}{{y}};{y}={tan}\left({x}\right) \\ $$$$\Leftrightarrow{Min}\left(\frac{\mathrm{1}}{\mathrm{8}}\left({y}+\frac{\mathrm{1}}{{y}}\right);{y}\in\right]\mathrm{0},\infty\left[\right) \\…
Question Number 207362 by mr W last updated on 12/May/24 Answered by A5T last updated on 12/May/24 $${Ptolemy}'{s}\:{theorem}:\:{AC}×{BP}={AP}×{BC}+{AB}×{PC} \\ $$$${AB}={AC}={BC}\Rightarrow{PB}={PA}+{PC} \\ $$ Answered by sniper237…