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Question-91465

Question Number 91465 by Zainal Arifin last updated on 30/Apr/20 Commented by Prithwish Sen 1 last updated on 01/May/20 $$\mathrm{8}.\frac{\mathrm{2}.\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}.\mathrm{cos}\frac{\mathrm{2}\pi}{\mathrm{15}}}{\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}}\:.\mathrm{cos}\frac{\mathrm{4}\pi}{\mathrm{15}}\mathrm{cos}\frac{\mathrm{8}\pi}{\mathrm{15}}\mathrm{cos}\frac{\mathrm{14}\pi}{\mathrm{15}} \\ $$$$=\mathrm{2}.\frac{\mathrm{sin}\frac{\mathrm{16}\pi}{\mathrm{15}}}{\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}}.\mathrm{cos}\frac{\mathrm{14}\pi}{\mathrm{15}}=\mathrm{2}.\frac{\mathrm{sin}\left(\pi+\frac{\pi}{\mathrm{15}}\right)}{\mathrm{sin}\frac{\mathrm{2}\pi}{\mathrm{15}}}.\mathrm{cos}\left(\pi−\frac{\pi}{\mathrm{15}}\right) \\ $$$$=\mathrm{2}.\frac{\mathrm{sin}\frac{\pi}{\mathrm{15}}}{\mathrm{2}.\mathrm{sin}\frac{\pi}{\mathrm{15}}.\mathrm{cos}\frac{\pi}{\mathrm{15}}}\:.\:\mathrm{cos}\frac{\pi}{\mathrm{15}}\:=\:\mathrm{1}\: \\…

x-3-4-5-

Question Number 25924 by vipinrana4542@gmail.com last updated on 16/Dec/17 $${x}+\mathrm{3}+\mathrm{4}=\mathrm{5} \\ $$ Answered by Rasheed.Sindhi last updated on 16/Dec/17 $$\mathrm{x}+\mathrm{7}=\mathrm{5} \\ $$$$\mathrm{x}=\mathrm{5}−\mathrm{7} \\ $$$$\mathrm{x}=−\mathrm{2} \\…

Question-156933

Question Number 156933 by CAIMAN last updated on 17/Oct/21 Answered by mindispower last updated on 17/Oct/21 $$\frac{\mathrm{1}}{{t}}={x} \\ $$$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{3}}} \frac{{ln}\left({x}\right)}{{x}\left(\mathrm{1}+{x}\right)}{dx}=\int\frac{{ln}\left({x}\right)}{{x}}−\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$=\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}}−{ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right)+\int\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx} \\…

k-2-k-3-1-k-3-1-

Question Number 156924 by cortano last updated on 17/Oct/21 $$\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\prod}}\:\left(\frac{{k}^{\mathrm{3}} −\mathrm{1}}{{k}^{\mathrm{3}} +\mathrm{1}}\right)\:=? \\ $$ Answered by puissant last updated on 17/Oct/21 $${P}=\underset{{k}=\mathrm{2}} {\overset{\infty}…

How-many-eleven-digits-palindrome-numbers-can-be-formed-by-0-2-3-4-and-8-Zero-in-the-middle-of-order-always-

Question Number 91336 by naka3546 last updated on 30/Apr/20 $${How}\:\:{many}\:\:{eleven}\:\:{digits}\:\:{palindrome}\:\:{numbers}\:\:{can}\:\:{be} \\ $$$${formed}\:\:{by}\:\:\mathrm{0},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\:{and}\:\:\mathrm{8}\:? \\ $$$${Zero}\:\:{in}\:\:{the}\:{middle}\:\:{of}\:\:{order}\:\:{always}\:. \\ $$ Commented by jagoll last updated on 30/Apr/20 $$\mathrm{4}!\:=\:\mathrm{24}\: \\…

Find-the-sum-9-1-2-10-2-2-3-10-3-3-4-10-99-99-100-x-the-greatest-integer-function-

Question Number 91328 by Maclaurin Stickker last updated on 30/Apr/20 $${Find}\:{the}\:{sum} \\ $$$$\frac{\mathrm{9}}{\mathrm{1}+\sqrt{\mathrm{2}}}+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{2}}\rfloor}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{3}}\rfloor}{\:\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+…+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{99}}\rfloor}{\:\sqrt{\mathrm{99}}+\sqrt{\mathrm{100}}} \\ $$$$\lfloor{x}\rfloor={the}\:{greatest}\:{integer}\:{function} \\ $$ Commented by Prithwish Sen 1 last updated on…