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Author: Tinku Tara

Given-x-4-16-y-2-2y-2-0-Show-that-is-a-reunion-of-and-Ellipsis-and-an-hyperbole-then-give-their-equations-

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…

Q-An-AP-has-even-number-of-terms-the-sum-of-odd-terms-is-24-and-of-even-terms-is-30-the-last-term-exceeds-the-first-term-by-10-1-2-find-AP-and-number-of-terms-

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…

x-5-x-5-tan-find-the-value-of-

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}.…

sin-101x-sin-90-x-dx-

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) \\…