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Question-174871

Question Number 174871 by Ml last updated on 13/Aug/22 Answered by Rasheed.Sindhi last updated on 13/Aug/22 $${a}_{\mathrm{15}} =\mathrm{32},\:\:\:{S}_{\mathrm{9}} +{S}_{\mathrm{29}} =\mathrm{100},\:\:{a}_{\mathrm{23}} =? \\ $$$$\underline{{Assuming}\:{a}_{{n}} \:{an}\:{AP}} \\…

x-cos-where-3pi-2-lt-lt-2pi-and-that-2cos-sin-2-show-that-1-x-2-2-1-x-Hence-or-otherwise-find-x-and-deduce-that-tan2-24-7-

Question Number 109337 by ZiYangLee last updated on 22/Aug/20 $${x}=\mathrm{cos}\theta,\:\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\theta<\mathrm{2}\pi,\:\mathrm{and}\:\mathrm{that}\:\mathrm{2cos}\theta−\mathrm{sin}\theta=\mathrm{2}, \\ $$$$\mathrm{show}\:\mathrm{that}\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }=\mathrm{2}\left(\mathrm{1}−{x}\right). \\ $$$$\mathrm{Hence}\:\mathrm{or}\:\mathrm{otherwise},\:\mathrm{find}\:{x}\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{tan2}\theta=\frac{\mathrm{24}}{\mathrm{7}} \\ $$ Answered by Aziztisffola last updated on 22/Aug/20 $$\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…

Question-43748

Question Number 43748 by naka3546 last updated on 15/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 15/Sep/18 $${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{3}} +{x}−\mathrm{1} \\ $$$${f}\left(\mathrm{0}\right)=−{ve} \\ $$$${f}\left(\mathrm{1}\right)=+{ve} \\ $$$${f}\left(\mathrm{0}.\mathrm{5}\right)=−{ve} \\…

Question-43749

Question Number 43749 by naka3546 last updated on 15/Sep/18 Answered by MrW3 last updated on 16/Sep/18 $$\mathrm{2}\left({n}^{\mathrm{2}} +\mathrm{3}{n}−\mathrm{1993}\right)={k}^{\mathrm{2}} \\ $$$${k}\:{must}\:{be}\:{even}\:\Rightarrow{k}=\mathrm{2}{m} \\ $$$${n}^{\mathrm{2}} +\mathrm{3}{n}−\mathrm{1993}=\mathrm{2}{m}^{\mathrm{2}} \\ $$$${n}\left({n}+\mathrm{3}\right)=\mathrm{2}{m}^{\mathrm{2}}…