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Category: Mensuration

Question-28399

Question Number 28399 by ajfour last updated on 25/Jan/18 Answered by ajfour last updated on 25/Jan/18 $${eq}.\:{of}\:{circle}: \\ $$$${x}={r}+{r}\mathrm{cos}\:\theta\:\:,\:{y}={r}+{r}\mathrm{sin}\:\theta \\ $$$${eq}.\:{of}\:{line}: \\ $$$$\frac{{x}}{{a}}+\frac{{y}}{{b}}=\mathrm{1} \\ $$$$\:{intersection}\:{points}:\:\:\theta_{\mathrm{1}}…

Question-27771

Question Number 27771 by ajfour last updated on 14/Jan/18 Commented by ajfour last updated on 14/Jan/18 $${If}\:{an}\:{equilateral}\:{triangle}\:{of} \\ $$$${edge}\:{length}\:{a}\:{is}\:{rotated}\:{about} \\ $$$${about}\:{its}\:{vertex}\:{A}\:{by}\:{an}\:{angle}\:\theta \\ $$$${find}\:{the}\:{area}\:{common}\:{in}\:{its} \\ $$$${new}\:{and}\:{previous}\:{positions}.…

Q-158528-P-n-1-n-1-3-1-n-1-3-1-P-n-1-n-1-3-1-3-n-1-3-1-3-P-n-1-n-1-1-n-2-2n-1-n-1-1-n-1-1-n-2-2n-1-n-1-1-P-n-1-

Question Number 158751 by puissant last updated on 08/Nov/21 $${Q}\:\mathrm{158528} \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathbb{P}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\left({n}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{1}}{\left({n}+\mathrm{1}\right)^{\mathrm{3}} +\mathrm{1}}\right) \\ $$$$\Rightarrow\:\mathbb{P}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\left({n}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{1}^{\mathrm{3}} }{\left({n}+\mathrm{1}\right)^{\mathrm{3}} +\mathrm{1}^{\mathrm{3}}…

Question-93166

Question Number 93166 by john santu last updated on 11/May/20 Answered by john santu last updated on 11/May/20 $$\mathrm{let}\:\mathrm{put}\:\mathrm{the}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{B}\left(\mathrm{0},\mathrm{0}\right)\:,\:\mathrm{A}\left(\mathrm{0},\mathrm{3}\right) \\ $$$$\mathrm{C}\left(\mathrm{4},\mathrm{0}\right)\:.\:\mathrm{for}\:\mathrm{a}\:\mathrm{general}\:\mathrm{right}\:\mathrm{triangle} \\ $$$$\mathrm{A}\left(\mathrm{0},\mathrm{a}\right),\:\mathrm{B}\left(\mathrm{0},\mathrm{0}\right),\mathrm{C}\left(\mathrm{c},\mathrm{0}\right) \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{X}\left({x},\mathrm{y}\right)\:\Rightarrow\mathrm{T}\left({x},\mathrm{y}\right)=\:…