Question Number 3519 by Rasheed Soomro last updated on 14/Dec/15 $${n}\:{is}\:{a}\:{number}\:{such}\:{that}\:{regular}\:\:{n}−{gon}\:{is} \\ $$$${possible}\:{with}\:{straightedge}\:{and}\:\:{compass}\:{only}. \\ $$$$\ast{Write}\:{first}\:{thirty}\:{values}\:{of}\:{n}. \\ $$$$\ast{What}\:{are}\:{other}\:{properties}\:{of}\:{such}\:{numbers}\:? \\ $$$$\ast{If}\:{values}\:{of}\:{n}\:{are}\:{arranged}\:{in}\:{order},\:{what}\:{is} \\ $$$${the}\:{formula}\:{for}\:{generating}\:{Nth}\:{number}? \\ $$ Commented by…
Question Number 134591 by bobhans last updated on 05/Mar/21 $$\mathrm{Precalculus} \\ $$What is the volume of the solid obtained by rotating the region bounded by…
Question Number 3517 by Tinku Tara last updated on 14/Dec/15 $$\mathrm{App}\:\mathrm{has}\:\mathrm{been}\:\mathrm{updated}\:\mathrm{today}\:\mathrm{to}\:\mathrm{fix} \\ $$$$\mathrm{intermittent}\:\mathrm{scrolling}\:\mathrm{problem}\:\mathrm{while} \\ $$$$\mathrm{answering}\:\mathrm{or}\:\mathrm{commenting}. \\ $$$$\mathrm{Filup},\:\mathrm{please}\:\mathrm{let}\:\mathrm{us}\:\mathrm{know}\:\mathrm{if}\:\mathrm{this}\:\mathrm{addresses} \\ $$$$\mathrm{your}\:\mathrm{concerns}. \\ $$ Commented by Filup last…
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Question Number 134587 by bobhans last updated on 05/Mar/21 $$\mathrm{Precalculus}\: \\ $$How do I find the volume of a solid obtained by rotating the region…
Question Number 134581 by EDWIN88 last updated on 05/Mar/21 $$\mathrm{Given}\:\begin{cases}{\mathrm{sin}\:\mathrm{A}+\mathrm{sin}\:\mathrm{B}=\mathrm{0}.\mathrm{7}}\\{\mathrm{cos}\:\mathrm{A}+\mathrm{cos}\:\mathrm{B}=\mathrm{0}.\mathrm{8}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$ Answered by liberty last updated on 05/Mar/21 $$\Leftrightarrow\:\mathrm{2}+\mathrm{2cos}\:\left(\mathrm{A}−\mathrm{B}\right)=\:\frac{\mathrm{49}+\mathrm{64}}{\mathrm{100}} \\ $$$$\Leftrightarrow\mathrm{2cos}\:\left(\mathrm{A}−\mathrm{B}\right)\:=\:−\frac{\mathrm{87}}{\mathrm{100}} \\…
Question Number 69046 by Rio Michael last updated on 18/Sep/19 Commented by mathmax by abdo last updated on 18/Sep/19 $$\left.\mathrm{4}\right){we}\:{have}\:\:{y}={xarctanx}\:\Rightarrow{y}^{'} ={arctanx}\:+\frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\Rightarrow \\ $$$$\left({x}+{x}^{\mathrm{3}} \right){y}^{'}…
Question Number 134580 by metamorfose last updated on 05/Mar/21 $$\int\sqrt{{tan}\left({x}\right)}{dx}=…? \\ $$ Answered by Olaf last updated on 05/Mar/21 $$\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{arccos}\left(\mathrm{cos}{x}−\mathrm{sin}{x}\right) \\ $$$$+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\mathrm{cos}{x}+\mathrm{sin}{x}+\sqrt{\mathrm{sin2}{x}}\right)+\mathrm{C} \\ $$ Answered…
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Question Number 69044 by mathmax by abdo last updated on 18/Sep/19 $$\left.\mathrm{1}\right)\:{let}\:{f}\left({a}\right)\:=\int\sqrt{{a}+{tanx}}{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({a}\right)\:=\int\:\:\frac{{dx}}{\:\sqrt{{a}+{tanx}}} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int\sqrt{\mathrm{2}+{tanx}}{dx}\:{and}\:\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{2}+{tanx}}} \\ $$ Answered by mind is power…