Question Number 17830 by Tinkutara last updated on 11/Jul/17 $$\mathrm{Two}\:\mathrm{candles}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{height}\:\mathrm{are} \\ $$$$\mathrm{lighted}\:\mathrm{together}.\:\mathrm{First}\:\mathrm{one}\:\mathrm{gets}\:\mathrm{burnt}\:\mathrm{up} \\ $$$$\mathrm{completely}\:\mathrm{in}\:\mathrm{3}\:\mathrm{hours}\:\mathrm{while}\:\mathrm{the}\:\mathrm{second} \\ $$$$\mathrm{in}\:\mathrm{4}\:\mathrm{hours}.\:\mathrm{At}\:\mathrm{what}\:\mathrm{point}\:\mathrm{of}\:\mathrm{time},\:\mathrm{the} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{second}\:\mathrm{candle}\:\mathrm{will}\:\mathrm{be}\:\mathrm{double} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{candle}? \\ $$ Answered by mrW1…
Question Number 17828 by Abbas-Nahi last updated on 11/Jul/17 Answered by Tinkutara last updated on 11/Jul/17 $$\mathrm{sin}\:\left(\alpha\:+\:\beta\right)\:=\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta\:+\:\mathrm{cos}\:\alpha\:\mathrm{sin}\:\beta \\ $$$$\mathrm{sin}\:\left(\alpha\:−\:\beta\right)\:=\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta\:−\:\mathrm{cos}\:\alpha\:\mathrm{sin}\:\beta \\ $$$$\mathrm{sin}\:\left(\alpha\:+\:\beta\right)\:+\:\mathrm{sin}\:\left(\alpha\:−\:\beta\right)\:=\:\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\beta \\ $$$$\mathrm{Let}\:\alpha\:+\:\beta\:=\:{x}\:\mathrm{and}\:\alpha\:−\:\beta\:=\:{y} \\ $$$$\mathrm{so}\:\mathrm{that}\:\alpha\:=\:\frac{{x}\:+\:{y}}{\mathrm{2}}\:\mathrm{and}\:\beta\:=\:\frac{{x}\:−\:{y}}{\mathrm{2}}.…
Question Number 83361 by john santu last updated on 01/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}\right)}{\:\sqrt{\mathrm{x}}}\:=\: \\ $$ Commented by john santu last updated on 01/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 148895 by Integrals last updated on 01/Aug/21 Commented by Canebulok last updated on 01/Aug/21 nice bro Commented by Canebulok last updated on 01/Aug/21 i'm Kevin Pilipiña, your friend facebook…
Question Number 148894 by Integrals last updated on 01/Aug/21 Commented by Tinku Tara last updated on 01/Aug/21 $$\mathrm{If}\:\mathrm{you}\:\mathrm{update}\:\mathrm{to}\:\mathrm{latest}\:\mathrm{verion}.\:\mathrm{There} \\ $$$$\mathrm{will}\:\mathrm{not}\:\mathrm{be}\:\mathrm{any}\:\mathrm{watermark}\:\mathrm{as}\:\mathrm{app}\:\mathrm{is} \\ $$$$\mathrm{now}\:\mathrm{free}. \\ $$ Terms…
Question Number 83354 by TawaTawa1 last updated on 01/Mar/20 Commented by jagoll last updated on 01/Mar/20 $$\mathrm{NC}\:=\:\mathrm{MC}\:=\:\mathrm{x} \\ $$$$\mathrm{2x}^{\mathrm{2}} \:=\:\mathrm{25}\:\Rightarrow\mathrm{x}^{\mathrm{2}} \:=\:\frac{\mathrm{25}}{\mathrm{2}} \\ $$$$\mathrm{area}\:\mathrm{triangle}\:=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} \:=\:\frac{\mathrm{25}}{\mathrm{4}}\: \\…
Question Number 83352 by jagoll last updated on 01/Mar/20 $$\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\left(\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}\right)\right)}\:=\:−\mathrm{sin}\:\left(−\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\ $$ Commented by jagoll last updated on 01/Mar/20 $$\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}\:=\:\mathrm{sin}\:\left(\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\ $$$$\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} \:}=\:\mathrm{sin}\:\left(\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\…
Question Number 148890 by mathdanisur last updated on 01/Aug/21 $${if}\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\sqrt{\mathrm{3}} \\ $$$${find}\:\:\:{x}^{\mathrm{18}} \:+\:{x}^{\mathrm{12}} \:+\:{x}^{\mathrm{6}} \:+\:\mathrm{1}\:=\:? \\ $$ Answered by nimnim last updated on 01/Aug/21 $$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\sqrt{\mathrm{3}}\Rightarrow\mathrm{x}^{\mathrm{2}}…
Question Number 17816 by Tinkutara last updated on 11/Jul/17 $$\mathrm{A}\:\mathrm{man}\:\mathrm{is}\:\mathrm{standing}\:\mathrm{on}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{building} \\ $$$$\mathrm{100}\:\mathrm{m}\:\mathrm{high}.\:\mathrm{He}\:\mathrm{throws}\:\mathrm{two}\:\mathrm{balls} \\ $$$$\mathrm{vertically},\:\mathrm{one}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\:\mathrm{and}\:\mathrm{other}\:\mathrm{after} \\ $$$$\mathrm{a}\:\mathrm{time}\:\mathrm{interval}\:\left(\mathrm{less}\:\mathrm{than}\:\mathrm{2}\:\mathrm{seconds}\right). \\ $$$$\mathrm{The}\:\mathrm{later}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{at}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of} \\ $$$$\mathrm{half}\:\mathrm{the}\:\mathrm{first}.\:\mathrm{The}\:\mathrm{vertical}\:\mathrm{gap}\:\mathrm{between} \\ $$$$\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{ball}\:\mathrm{is}\:+\mathrm{15}\:\mathrm{m}\:\mathrm{at}\:{t}\:=\:\mathrm{2}\:\mathrm{s}. \\ $$$$\mathrm{The}\:\mathrm{gap}\:\mathrm{is}\:\mathrm{found}\:\mathrm{to}\:\mathrm{remain}\:\mathrm{constant}. \\…
Question Number 17815 by Tinkutara last updated on 11/Jul/17 $$\mathrm{For}\:{x}\:\in\:\left(\mathrm{0},\:\pi\right),\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}\:−\:\mathrm{sin}\:\mathrm{3}{x}\:=\:\mathrm{3}\:\mathrm{has} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Infinitely}\:\mathrm{many}\:\mathrm{solutions} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Three}\:\mathrm{solutions} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{One}\:\mathrm{solution} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{No}\:\mathrm{solution} \\ $$ Commented by alex041103…