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Category: Mensuration

3cos-2-x-1-sin-5-x-dx-

Question Number 148137 by Willson last updated on 25/Jul/21 $$\int\:\:\frac{\mathrm{3}{cos}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}{{sin}^{\mathrm{5}} \left({x}\right)}{dx}\:=\:??? \\ $$ Answered by puissant last updated on 25/Jul/21 $$=\int\frac{\mathrm{4cos}^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{sin}^{\mathrm{5}} \left(\mathrm{x}\right)}\mathrm{dx}=\int\frac{\mathrm{4}+\mathrm{tan}^{\mathrm{2}}…

Question-147905

Question Number 147905 by puissant last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:=\:\mathrm{13} \\ $$$$\mathrm{2}{xdx}+\mathrm{2}{ydy}\:=\:\mathrm{0} \\ $$$${x}+{y}\frac{{dy}}{{dx}}\:=\:\mathrm{0} \\ $$$$\bullet\:\mathrm{En}\:\left(\mathrm{2},−\mathrm{3}\right)\::…

Question-147904

Question Number 147904 by puissant last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{Il}\:\mathrm{y}\:\mathrm{a}\:\mathrm{6}\:\mathrm{valeurs}\:\mathrm{de}\:{x}\:\left({x}_{\mathrm{0}} \:\mathrm{a}\:{x}_{\mathrm{5}} \right),\:\mathrm{ce}\:\mathrm{qui} \\ $$$$\mathrm{definit}\:\mathrm{5}\:\mathrm{intervalles}\:\mathrm{qui}\:\mathrm{correspondent} \\ $$$$\mathrm{a}\:\mathrm{5}\:\mathrm{trapezes}. \\ $$$$\mathrm{Chaque}\:\mathrm{trapeze}\:{k}\:\mathrm{a}\:\mathrm{une}\:\mathrm{surface}\:\mathrm{egale}…

p-0-n-ch-2-a-pb-

Question Number 147819 by puissant last updated on 23/Jul/21 $$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{ch}^{\mathrm{2}} \left(\mathrm{a}+\mathrm{pb}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$\mathrm{S}\:=\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}\mathrm{ch}^{\mathrm{2}}…

Question-147602

Question Number 147602 by puissant last updated on 22/Jul/21 Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\mathrm{Soit}\:\mathrm{E}\:\mathrm{le}\:\mathrm{nombre}\:\mathrm{d}'\mathrm{eleves}. \\ $$$$\mathrm{Soit}\:\mathrm{T}\:\mathrm{le}\:\mathrm{nombre}\:\mathrm{de}\:\mathrm{tables}. \\ $$$$\begin{cases}{\mathrm{E}\:=\:\mathrm{2T}+\mathrm{11}\:\:\:\left(\mathrm{1}\right)}\\{\mathrm{T}\:=\:\frac{\mathrm{E}}{\mathrm{3}}+\mathrm{7}\:\:\:\:\:\:\left(\mathrm{2}\right)}\end{cases} \\ $$$$ \\ $$$$\mathrm{En}\:\mathrm{injectant}\:\left(\mathrm{2}\right)\:\mathrm{dans}\:\left(\mathrm{1}\right)\::…

Question-147603

Question Number 147603 by puissant last updated on 22/Jul/21 Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\mathrm{Soit}\:\mathrm{G}\:\mathrm{le}\:\mathrm{nombre}\:\mathrm{de}\:\mathrm{garcons}. \\ $$$$\mathrm{Soit}\:\mathrm{F}\:\mathrm{le}\:\mathrm{nombre}\:\mathrm{de}\:\mathrm{filles}. \\ $$$$\mathrm{G}+\mathrm{F}\:=\:\mathrm{10}\:\:\:\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{Chaque}\:\mathrm{garcon}\:\mathrm{a}\:\mathrm{G}−\mathrm{1}\:\mathrm{freres}\:\mathrm{F}\:\mathrm{soeurs}…