Question Number 7399 by Tawakalitu. last updated on 27/Aug/16 $${In}\:{an}\:{AP}\:,\:{if}\:{the}\:{m}^{{th}} \:{term}\:{is}\:{n}\:{and}\:{the}\:{n}^{{th}} \:{term} \\ $$$${is}\:{m}.\:{where}\:{m}\:{is}\:{not}\:{equal}\:{to}\:{n}.\:{find} \\ $$$$\left(\mathrm{1}\right)\:{The}\:{value}\:{of}\:\left({m}\:+\:{n}\right)^{{th}} \:{term} \\ $$$$\left(\mathrm{2}\right)\:{The}\:{p}^{{th}} \:{term}. \\ $$ Answered by Yozzia…
Question Number 7397 by Tawakalitu. last updated on 26/Aug/16 Answered by sandy_suhendra last updated on 27/Aug/16 $${sin}\:{x}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \:{x}^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!} \\ $$$$\frac{\mathrm{1}}{{x}}\:{sin}\:{x}\:=\:\frac{\mathrm{1}}{{x}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}}…
Question Number 138470 by mathocean1 last updated on 13/Apr/21 $${Given}\:\left(\Gamma\right):\:{x}^{\mathrm{4}} −\mathrm{16}\left({y}^{\mathrm{2}} −\mathrm{2}{y}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${Show}\:{that}\:\left(\Gamma\right)\:{is}\:{a}\:{reunion}\:{of}\:\:{and}\: \\ $$$${Ellipsis}\:{and}\:{an}\:{hyperbole}\:{then}\:{give} \\ $$$${their}\:{equations}. \\ $$ Answered by MJS_new last…
Question Number 72930 by TawaTawa last updated on 05/Nov/19 Answered by ajfour last updated on 05/Nov/19 Commented by ajfour last updated on 05/Nov/19 $${R}\mathrm{sin}\:\alpha={R}−\mathrm{2}{r} \\…
Question Number 7395 by 2402@gmail.com last updated on 26/Aug/16 $${Q}.\:{An}\:{AP}\:{has}\:{even}\:{number}\:{of}\:{terms} \\ $$$$\:\:\:\:\:\:\:{the}\:{sum}\:{of}\:{odd}\:{terms}\:{is}\:\mathrm{24}\:{and}\: \\ $$$$\:\:\:\:\:\:{of}\:{even}\:{terms}\:{is}\:\mathrm{30}.\:{the}\:{last}\:{term} \\ $$$$\:\:\:\:\:{exceeds}\:{the}\:{first}\:{term}\:{by}\:\mathrm{10}\frac{\mathrm{1}}{\mathrm{2}}\:. \\ $$$$\:\:\:\:\:{find}\:{AP}\:{and}\:{number}\:{of}\:{terms}. \\ $$ Commented by Yozzia last updated…
Question Number 72931 by Maclaurin Stickker last updated on 05/Nov/19 $${Find}\:{the}\:{numeric}\:{value}\:{of} \\ $$$$\frac{\mathrm{2}−\mathrm{sin}\:^{\mathrm{2}} \left(\alpha\right)}{\mathrm{cos}\:^{\mathrm{2}} \left(\alpha\right)−\mathrm{tan}\:^{\mathrm{2}} \left(\alpha\right)} \\ $$ Answered by ajfour last updated on 05/Nov/19…
Question Number 7392 by Tawakalitu. last updated on 26/Aug/16 $$\sqrt{{x}}\:+\:\mathrm{5}\:+\:\sqrt{{x}}\:+\:\mathrm{5}\:=\:{tan}\Theta \\ $$$$ \\ $$$${find}\:{the}\:{value}\:{of}\:\Theta \\ $$ Commented by Yozzia last updated on 26/Aug/16 $${general}\:{solution},\:\Theta={n}\pi+{tan}^{−\mathrm{1}} \left(\mathrm{2}\sqrt{{x}}+\mathrm{10}\right),\:{n}\in\mathbb{Z}.…
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Question Number 138456 by I want to learn more last updated on 13/Apr/21 Commented by mr W last updated on 13/Apr/21 $${sum}\:{of}\:{shaded}\:{areas}\:{is}\:{the}\:{red}\:{triangle} \\ $$$${which}\:{is}\:\mathrm{1}/\mathrm{4}\:{of}\:{the}\:{square}. \\…
Question Number 7385 by Tawakalitu. last updated on 25/Aug/16 $$\int{sin}\left(\mathrm{101}{x}\right)\:.\:{sin}^{\mathrm{90}} \left({x}\right)\:{dx} \\ $$ Commented by Yozzia last updated on 26/Aug/16 $${Let}\:{I}\left({n}\right)=\int{e}^{\mathrm{101}{ix}} {sin}^{{n}} {xdx}\:\:\:\left({n}\in\mathbb{Z}^{\geqslant} \:{i}=\sqrt{−\mathrm{1}}\right) \\…