Question Number 146465 by mathdanisur last updated on 13/Jul/21 $${arccos}\left({cos}\:\mathrm{9}\right)\:=\:? \\ $$ Answered by gsk2684 last updated on 13/Jul/21 $$\mathrm{5}\frac{\Pi}{\mathrm{2}}<\mathrm{9}<\:\mathrm{3}\Pi \\ $$$$\left(\mathrm{5}\frac{\Pi}{\mathrm{2}}−\mathrm{2}\Pi\right)<\left(\mathrm{9}−\mathrm{2}\Pi\right)<\left(\mathrm{3}\Pi−\mathrm{2}\Pi\right) \\ $$$$\frac{\Pi}{\mathrm{2}}<\left(\mathrm{9}−\mathrm{2}\Pi\right)<\Pi \\…
Question Number 146467 by mathdanisur last updated on 13/Jul/21 $${if}\:\:\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\boldsymbol{{i}}\:\:\:\:{find}\:\:\:\boldsymbol{{z}}^{\mathrm{11}} \:=\:? \\ $$ Answered by gsk2684 last updated on 13/Jul/21 $${z}^{\mathrm{11}} \:=\:\left({cis}\:\frac{\Pi}{\mathrm{6}}\right)^{\mathrm{11}} =\:{cis}\left(\frac{\mathrm{11}\Pi}{\mathrm{6}}\right) \\ $$$$={cis}\left(\mathrm{2}\Pi−\frac{\Pi}{\mathrm{6}}\right)…
Question Number 80927 by peter frank last updated on 08/Feb/20 Commented by john santu last updated on 08/Feb/20 $${f}\left({x}\right)={ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+\mathrm{4} \\ $$$${tangent}\:{line}\:{parallel}\:{to}\:{x}−{axis}\: \\…
Question Number 146457 by mathdanisur last updated on 13/Jul/21 Commented by mathdanisur last updated on 13/Jul/21 $${find}\:\:{x}=? \\ $$ Answered by gsk2684 last updated on…
Question Number 146459 by mathdanisur last updated on 13/Jul/21 $${if}\:\:\:{x}^{\mathrm{2}} ={y}^{\mathrm{3}} \:\:\:{find}\:\:\:\:{log}_{\boldsymbol{{x}}} {x}\sqrt{{y}}\:=\:?\:\:\: \\ $$ Answered by MJS_new last updated on 13/Jul/21 $$\mathrm{log}_{{x}} \:{x}\sqrt{{y}}\:=\frac{\mathrm{ln}\:{x}\sqrt{{y}}}{\mathrm{ln}\:{x}}=\frac{\mathrm{ln}\:{x}\:+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:{y}}{\mathrm{ln}\:{x}}=\mathrm{1}+\frac{\mathrm{ln}\:{y}}{\mathrm{2ln}\:{x}}= \\…
Question Number 80912 by TawaTawa last updated on 07/Feb/20 Commented by john santu last updated on 08/Feb/20 $$\frac{{x}^{\mathrm{4}} }{{q}^{\mathrm{3}} }\:+\:\frac{{y}^{\mathrm{4}} }{{p}^{\mathrm{3}} }\:=\:\mathrm{1}\: \\ $$$$\Rightarrow\left\{\left(\frac{{x}^{\mathrm{4}} }{{q}^{\mathrm{3}}…
Question Number 146440 by KONE last updated on 13/Jul/21 Answered by Olaf_Thorendsen last updated on 13/Jul/21 $$\mathrm{Soit}\:\varphi\::\:\mathrm{H}\rightarrow{a}\mathrm{H}\:\mathrm{definie}\:\mathrm{par}\:\varphi\left({h}\right)\:=\:{ah}.\: \\ $$$$\mathrm{Il}\:\mathrm{sagit}\:\mathrm{clairement}\:\mathrm{d}'\mathrm{une}\:\mathrm{surjection}\:\mathrm{de} \\ $$$$\mathrm{H}\:\mathrm{sur}\:{a}\mathrm{H}.\:\mathrm{De}\:\mathrm{plus},\:\mathrm{si}\:{ah}_{\mathrm{1}} \:\:=\:{ah}_{\mathrm{2}} \:\mathrm{alors} \\ $$$${h}_{\mathrm{1}}…
Question Number 80907 by peter frank last updated on 07/Feb/20 $$\left.{a}\right)\int{e}^{{x}} \mathrm{tan}\:{xdx} \\ $$$$\left.{b}\right)\int{x}\mathrm{tan}\:{xdx} \\ $$ Answered by M±th+et£s last updated on 07/Feb/20 Commented by…
Question Number 146436 by mathdanisur last updated on 13/Jul/21 $$\frac{{sin}^{\mathrm{2}} \:\mathrm{25}\:-\:{sin}^{\mathrm{2}} \:\mathrm{5}}{{sin}\:\mathrm{20}}\:=\:? \\ $$ Answered by gsk2684 last updated on 13/Jul/21 $$\frac{\mathrm{sin}\:\left(\mathrm{25}^{\mathrm{0}} +\mathrm{5}^{\mathrm{0}} \right)\:\mathrm{sin}\:\left(\mathrm{25}^{\mathrm{0}} −\mathrm{5}^{\mathrm{0}}…
Question Number 146425 by mathdanisur last updated on 13/Jul/21 $$\mathrm{4}\:{people}\:{took}\:{the}\:{elevator}\:{to}\:{the}\:{first} \\ $$$${floor}\:{of}\:{the}\:\mathrm{6}\:-\:{storey}\:{building}.\:{Find} \\ $$$${the}\:{probability}\:{that}\:{they}\:{fall}\:{on} \\ $$$${different}\:{floors}. \\ $$ Commented by ajfour last updated on 13/Jul/21…