Menu Close

Author: Tinku Tara

if-two-finite-sets-have-m-and-n-term-if-the-no-of-subset-of-first-set-is-112-more-then-the-no-of-subset-of-second-set-find-m-and-n-

Question Number 69175 by Aditya789 last updated on 21/Sep/19 $${if}\:{two}\:{finite}\:{sets}\:{have}\:{m}\:{and}\:{n}\:{term}.{if}\:{the}\:{no}\:{of}\:{subset}\:{of}\:{first}\:{set}\:{is}\:\mathrm{112}\:{more}\:{then}\:{the}\:{no}\:{of}\:{subset}\:{of}\:{second}\:{set}.{find}\:{m}\:{and}\:{n}? \\ $$ Answered by Rasheed.Sindhi last updated on 21/Sep/19 $$\mid\mathrm{A}\mid={m}\:,\:\mid\mathrm{B}\mid={n} \\ $$$$\mathrm{P}\left(\mathrm{A}\right)=\mathrm{2}^{{m}} \:,\:\mathrm{P}\left(\mathrm{B}\right)=\mathrm{2}^{{n}} \\ $$$$\mathrm{P}\left(\mathrm{A}\right)−\mathrm{P}\left(\mathrm{B}\right)=\mathrm{2}^{{m}}…

Find-the-solution-2-3-cos-2x-sin-2x-1-

Question Number 134705 by bramlexs22 last updated on 06/Mar/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\:\:\:\:\:\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)\:\mathrm{cos}\:\mathrm{2x}\:+\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{1} \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\:{We}\:{can}\:{setting}\:\rightarrow\begin{cases}{{X}=\mathrm{cos}\:\mathrm{2}{x}}\\{{Y}=\mathrm{sin}\:\mathrm{2}{x}}\end{cases} \\ $$$${so}\:{the}\:{equation}\:{becomes}\:\begin{cases}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right){X}+{Y}\:=\:\mathrm{1}}\\{{X}^{\mathrm{2}} +{Y}^{\:\mathrm{2}}…

Question-69167

Question Number 69167 by rajesh4661kumar@gmail.com last updated on 21/Sep/19 Answered by petrochengula last updated on 21/Sep/19 $${from}\:{tan}^{−\mathrm{1}} \left(\frac{{x}+{y}}{\mathrm{1}−{xy}}\right)={tan}^{−\mathrm{1}} {x}+{tan}^{−\mathrm{1}} {y} \\ $$$${tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right)={tan}^{−\mathrm{1}} \left(\frac{{x}+{x}−\mathrm{1}}{\mathrm{1}−{x}\left({x}−\mathrm{1}\right)}\right)={tan}^{−\mathrm{1}}…

Prove-that-sum-of-all-prime-numbers-p-such-that-n-p-2-k-n-is-2-k-n-n-p-2-k-n-p-2-k-n-p-prime-

Question Number 3630 by prakash jain last updated on 16/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{numbers}\:{p} \\ $$$$\mathrm{such}\:\mathrm{that}\:{n}\leqslant{p}\leqslant\mathrm{2}^{{k}} {n}\:\mathrm{is}\:\geqslant\mathrm{2}^{{k}} {n}. \\ $$$$\underset{{n}\leqslant{p}\leqslant\mathrm{2}^{{k}} {n}} {\sum}{p}\:\:\geqslant\:\mathrm{2}^{{k}} {n}\:\:\:\:\:\left({p}−{prime}\right) \\ $$ Terms of Service…

if-the-fibonacci-sequence-is-1-1-2-3-5-8-13-21-34-where-it-is-1-1-2-2-3-5-3-5-8-how-can-we-represent-this-sequence-in-summitation-notation-or-product-notation-

Question Number 3628 by madscientist last updated on 16/Dec/15 $${if}\:{the}\:{fibonacci}\:{sequence}\:{is}\: \\ $$$$\mathrm{1},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{8},\mathrm{13},\mathrm{21},\mathrm{34}… \\ $$$${where}\:{it}\:{is}\:\mathrm{1}+\mathrm{1}=\mathrm{2},\:\mathrm{2}+\mathrm{3}=\mathrm{5},\:\mathrm{3}+\mathrm{5}=\mathrm{8},… \\ $$$${how}\:{can}\:{we}\:{represent}\:{this}\:{sequence}\: \\ $$$${in}\:{summitation}\:{notation}\:\Sigma \\ $$$${or}\:{product}\:{notation}\:\Pi? \\ $$ Commented by 123456…