Question Number 142656 by qaz last updated on 03/Jun/21 $$\int_{−\pi} ^{\pi} \frac{\mathrm{xsin}\:\mathrm{x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=? \\ $$ Answered by Ar Brandon last updated on 03/Jun/21 $$\xi\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\pi}…
Question Number 77123 by mathocean1 last updated on 03/Jan/20 $$\mathrm{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{non}−\mathrm{right}\:\mathrm{triangle}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Demonstrate}\:\mathrm{that} \\ $$$$\mathrm{tan}\left(\hat {\mathrm{A}}+\hat {\mathrm{B}}\right)=−\mathrm{tan}\hat {\mathrm{C}}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{By}\:\mathrm{using}\:\mathrm{tan}\left(\hat {\mathrm{A}}+\hat {\mathrm{B}}\right)=\frac{\mathrm{tan}\hat {\mathrm{A}}+\mathrm{tan}\hat {\mathrm{B}}}{\mathrm{1}−\mathrm{tan}\hat {\mathrm{A}tan}\hat {\mathrm{B}}}…
Question Number 142653 by Gbenga last updated on 03/Jun/21 $${x}^{\mathrm{3}} .{e}^{{x}} =\mathrm{216} \\ $$ Answered by MJS_new last updated on 03/Jun/21 $$\mathrm{you}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$${x}\approx\mathrm{2}.\mathrm{55781651} \\…
Question Number 77119 by necxxx last updated on 03/Jan/20 $${suppose}\:{the}\:{equations}\:{x}^{\mathrm{2}} +{px}+\mathrm{4}=\mathrm{0} \\ $$$${and}\:{x}^{\mathrm{2}} +{qx}+\mathrm{3}=\mathrm{0}\:\:{have}\:{a}\:{common}\:{root}, \\ $$$${write}\:{this}\:{root}\:{in}\:{terms}\:{of}\:{the}\:{other}\:{root}. \\ $$ Answered by jagoll last updated on 03/Jan/20…
Question Number 142655 by mnjuly1970 last updated on 03/Jun/21 $$\:\:{evaluate}….. \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{{n}.{cos}\left({n}\pi\right)}{\Gamma\:\left(\mathrm{2}{n}+\mathrm{2}\right)}\right)=?\:….. \\ $$$$\:\:\:……. \\ $$ Answered by qaz last updated on 03/Jun/21…
Question Number 11581 by Nayon last updated on 28/Mar/17 $${cAn}\:{you}\:{prove}\:{the}\:{chAin}\:{role}?? \\ $$ Answered by linkelly0615 last updated on 28/Mar/17 $${yes}\sim \\ $$ Commented by linkelly0615…
Question Number 77117 by necxxx last updated on 03/Jan/20 $${Interview}\:{indicates}\:{that}\:{all}\:{the}\:\mathrm{4}\:{maths} \\ $$$${students},\mathrm{5}\:{physics}\:{and}\:\mathrm{7}\:{chemistry} \\ $$$${students}\:{who}\:{applied}\:{for}\:{a}\:{scholarship} \\ $$$${in}\:{their}\:{respective}\:{disciplines}\:{qualified} \\ $$$${for}\:{an}\:{award}.\:{In}\:{how}\:{many}\:{ways}\:{the}\:{aeard} \\ $$$${can}\:{be}\:{made}\:{if}; \\ $$$$\left({i}\right){only}\:{one}\:{scholarship}\:{is}\:{available}\:{in} \\ $$$${each}\:{of}\:{the}\:{disciplines} \\…
Question Number 11580 by Nayon last updated on 28/Mar/17 $${why}\:\frac{{dy}}{{dx}}=\frac{{dy}}{{du}}.\frac{{du}}{{dx}} \\ $$ Answered by mrW1 last updated on 28/Mar/17 $${the}\:{chain}\:{rule}\:{is}\:{one}\:{of}\:{the}\:{elementary} \\ $$$${rules}.\:{you}\:{should}\:{know}\:{them},\:{but}\:\: \\ $$$${you}\:{don}'{t}\:{need}\:{to}\:{prove}\:{them}.\:{if} \\…
Question Number 142647 by iloveisrael last updated on 03/Jun/21 $$\:\frac{\mathrm{1}}{\mathrm{2018}}−\frac{\mathrm{2}}{\mathrm{2018}}+\frac{\mathrm{3}}{\mathrm{2018}}−\frac{\mathrm{4}}{\mathrm{2018}}+…−\frac{\mathrm{2016}}{\mathrm{2018}}+\frac{\mathrm{2017}}{\mathrm{2018}}=? \\ $$ Answered by MJS_new last updated on 03/Jun/21 $$\underset{{j}=\mathrm{1}} {\overset{{n}+\mathrm{1}} {\sum}}\left(\mathrm{2}{j}+\mathrm{1}\right)−\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{2}{j}\right)={n}+\mathrm{1} \\…
Question Number 142646 by naka3546 last updated on 03/Jun/21 $${Prove}\:\:{that} \\ $$$$\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{3}} }\right)\:\ldots\:<\:\mathrm{3} \\ $$ Answered by 1549442205PVT last updated on 04/Jun/21 $$\mathrm{l}.\mathrm{h}.\mathrm{s}=\frac{\mathrm{3}\left(\mathrm{2}^{\mathrm{2}}…