Question Number 213054 by 281981 last updated on 29/Oct/24 Commented by Ghisom last updated on 30/Oct/24 $$\mathrm{in}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{and}\:\mathrm{its}\:\mathrm{circumcircle} \\ $$$$\mathrm{is} \\ $$$$\mathrm{1}:\frac{\mathrm{4}\pi\sqrt{\mathrm{3}}}{\:\mathrm{9}}\:\approx\:\mathrm{1}:\mathrm{2}.\mathrm{4} \\ $$$$\mathrm{here}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{is}…
Question Number 213055 by MrGaster last updated on 29/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{{x}} \mid\mathrm{sin}\:{t}\mid{dx}}{{x}} \\ $$$$ \\ $$ Answered by Ghisom last updated on…
Question Number 213045 by MrGaster last updated on 29/Oct/24 $$\overset{\rightharpoonup} {{a}},\overset{\rightharpoonup} {{b}ls}\:{the}\:{unit}\:{vector},\mid\overset{\rightharpoonup} {{a}}+\overset{\rightharpoonup} {{b}}\mid=\mathrm{1} \\ $$$${ask}\:\mid\overset{\rightharpoonup} {{a}}−\overset{\rightharpoonup} {{b}}\mid? \\ $$ Answered by mr W last…
Question Number 213047 by hardmath last updated on 29/Oct/24 $$\boldsymbol{\mathrm{n}}\:=\:\mathrm{15} \\ $$$$\mathrm{find}:\:\:\:\:\:\frac{\mathrm{4n}^{\mathrm{2}} \:\:+\:\:\mathrm{4n}\:\:+\:\:\mathrm{120}}{\:\sqrt{\mathrm{n}^{\mathrm{4}} \:\:+\:\:\mathrm{2n}^{\mathrm{3}} \:\:+\:\:\mathrm{n}^{\mathrm{2}} }}\:\:=\:\:? \\ $$ Answered by mehdee7396 last updated on 29/Oct/24…
Question Number 213073 by ajfour last updated on 29/Oct/24 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }}−\mathrm{1}\right)\right\} \\ $$ Answered by universe last updated on 29/Oct/24 $${L}\:=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 213074 by Spillover last updated on 29/Oct/24 Answered by MrGaster last updated on 29/Oct/24 $$=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \left[−\frac{\mathrm{cos}\left({x}+{y}^{\mathrm{2}} +{z}^{\mathrm{3}} \right)}{\mathrm{3}{z}^{\mathrm{2}} }\right]_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{3}}}…
Question Number 213043 by ajfour last updated on 29/Oct/24 Commented by ajfour last updated on 29/Oct/24 $${Find}\:\beta\:{such}\:{that}\:{it}\:{remains}\:{constant} \\ $$$${while}\:{the}\:{motion}\:{of}\:{frame}\:{down}\:{the} \\ $$$${slope}\:{of}\:{inclination}\:\alpha. \\ $$ Commented by…
Question Number 213034 by MrGaster last updated on 29/Oct/24 Commented by MrGaster last updated on 29/Oct/24 English: The diagram shows that if $AB > AC$, and $BD = CE$, $\angle BCD = \angle CBE$, find the measure of $\angle CFE$. Japanese: グラフによると、$AB>AC$で、$BD = CE$，$\angle BCD = \angle CBE$の場合、$\angle CFE$の測定値を求めます。 Commented by mr W last updated on 29/Oct/24…
Question Number 213060 by a.lgnaoui last updated on 29/Oct/24 $$\mathrm{determiner}\:\mathrm{les}\:\mathrm{coordonnes}\:\mathrm{de}\:\:\mathrm{X}\:\mathrm{et}\:\:\mathrm{Y} \\ $$$$\boldsymbol{\mathrm{r}}=\mathrm{1} \\ $$ Commented by a.lgnaoui last updated on 29/Oct/24 Commented by Frix last…
Question Number 213063 by a.lgnaoui last updated on 29/Oct/24 $$\mathrm{Area}\:\mathrm{of}\:\left[\mathrm{ACBD}\right]\:\:? \\ $$$$\left\{\mathrm{A}\:,\mathrm{B}\:\right\}\in\:\mathrm{elipse}\:\mathrm{verticale}\:\: \\ $$$$\left[\mathrm{AB}\right]\bot\mathrm{MC} \\ $$$$\mathrm{M}\in\:\mathrm{elipse}\:\mathrm{horizontale}\:\: \\ $$$$\mathrm{A}\:\in\left[\mathrm{elipse}\:\mathrm{horizontale}\:\cap\mathrm{elipse}\:\mathrm{veeticale}\right]. \\ $$ Commented by a.lgnaoui last updated…