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Question-161322

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Question Number 161322 by kapoorshah last updated on 16/Dec/21 Commented by cortano last updated on 16/Dec/21 $$\mathrm{sin}\:\left(\mathrm{30}°+\mathrm{10}°+\alpha\right)={b} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\left(\mathrm{10}°+\alpha\right)+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\left(\mathrm{10}°+\alpha\right)={b} \\ $$$$\mathrm{cos}\:\left(\mathrm{10}°+\alpha\right)+\sqrt{\mathrm{3}}\:\mathrm{sin}\:\left(\mathrm{10}°+\alpha\right)=\mathrm{2}{b} \\ $$$$\sqrt{\mathrm{3}}\:\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {t}}\:=\:\mathrm{2}{b}−\mathrm{cos}\:{t}\:;\:{t}=\mathrm{10}°+\alpha \\…

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Three-quarters-of-a-number-added-to-two-and-a-half-of-that-number-gives-13-find-the-number-

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Question Number 161316 by otchereabdullai@gmail.com last updated on 16/Dec/21 $$\mathrm{Three}\:\mathrm{quarters}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\:\mathrm{added}\:\mathrm{to} \\ $$$$\mathrm{two}\:\mathrm{and}\:\mathrm{a}\:\mathrm{half}\:\mathrm{of}\:\mathrm{that}\:\mathrm{number}\:\mathrm{gives}\: \\ $$$$\mathrm{13}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number} \\ $$$$ \\ $$ Answered by FelipeLz last updated on 16/Dec/21…

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1-2-3-2-5-2-7-2-17-2-19-2-

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Question Number 30245 by .none. last updated on 19/Feb/18 $$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\bullet\bullet\bullet+\mathrm{17}^{\mathrm{2}} −\mathrm{19}^{\mathrm{2}} \\ $$ Commented by Penguin last updated on 19/Feb/18 $$=\underset{{n}=\mathrm{1}}…

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the-app-doesn-t-work-properly-for-me-any-more-I-open-it-and-most-of-the-time-the-home-screen-doesn-t-show-the-forum-refreshing-or-trying-to-switch-to-the-forum-ends-up-in-an-endless-turning-loop-

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Question Number 95770 by MJS last updated on 27/May/20 $$\mathrm{the}\:\mathrm{app}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{work}\:\mathrm{properly}\:\mathrm{for}\:\mathrm{me}\:\mathrm{any} \\ $$$$\mathrm{more}.\:\mathrm{I}\:\mathrm{open}\:\mathrm{it}\:\mathrm{and}\:\mathrm{most}\:\mathrm{of}\:\mathrm{the}\:\mathrm{time}\:\mathrm{the} \\ $$$$\mathrm{home}\:\mathrm{screen}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{show}\:\mathrm{the}\:\mathrm{forum}. \\ $$$$\mathrm{refreshing}\:\mathrm{or}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{switch}\:\mathrm{to}\:\mathrm{the}\:\mathrm{forum} \\ $$$$\mathrm{ends}\:\mathrm{up}\:\mathrm{in}\:\mathrm{an}\:\mathrm{endless}\:\mathrm{turning}\:\mathrm{loop}… \\ $$ Commented by PRITHWISH SEN 2…

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2-2-x-3-cos-x-2-1-2-4-x-2-dx-

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Question Number 161294 by floor(10²Eta[1]) last updated on 15/Dec/21 $$\int_{−\mathrm{2}} ^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{3}} \mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by puissant last updated on 20/Dec/21 $${f}\left({x}\right)={x}^{\mathrm{3}} {cos}\left(\frac{{x}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}}…

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1-1-1-1-1-1-1-1-x-x-3-1-2-

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Question Number 30206 by .none. last updated on 18/Feb/18 $$\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}}}} \\ $$$${x}=\frac{\sqrt{\mathrm{3}}−\mathrm{1}}{\mathrm{2}} \\ $$ Commented by abdo imad last updated on 18/Feb/18 $${let}\:{put}\:{a}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−{x}}}\:\Rightarrow{N}=\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{{a}}}=\frac{\mathrm{1}}{\frac{{a}−\mathrm{1}}{{a}}}\:=\frac{{a}}{{a}−\mathrm{1}}\:{but} \\ $$$${a}=\mathrm{1}−\frac{\mathrm{1}}{\frac{{x}}{{x}−\mathrm{1}}}=\mathrm{1}−\frac{{x}−\mathrm{1}}{{x}}=\frac{\mathrm{1}}{{x}}\Rightarrow{N}=\:\frac{\frac{\mathrm{1}}{{x}}}{\frac{\mathrm{1}}{{x}}−\mathrm{1}}=\:\frac{\mathrm{1}}{{x}\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{1}−{x}}…

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