Question Number 10374 by ridwan balatif last updated on 06/Feb/17 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{\left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)\mathrm{sin}\left(\mathrm{3x}−\mathrm{3}\frac{\pi}{\mathrm{4}}\right)}{\mathrm{2}\left(\mathrm{1}−\mathrm{sin2x}\right)}=…? \\ $$ Answered by mrW1 last updated on 06/Feb/17 $${let}\:{u}={x}−\frac{\pi}{\mathrm{4}} \\ $$$${with}\:{x}\rightarrow\frac{\pi}{\mathrm{4}},\:{u}\rightarrow\mathrm{0} \\…
Question Number 141446 by ZiYangLee last updated on 19/May/21 $$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right),{a}\left({t}−\frac{\mathrm{1}}{{t}}\right)\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{P},\:\mathrm{as}\:{t}\:\mathrm{varies}. \\ $$ Answered by 1549442205PVT last updated on 19/May/21 $$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}}…
Question Number 10369 by Tawakalitu ayo mi last updated on 05/Feb/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{2}\:+\:\mathrm{5}\:+\:\mathrm{8}\:+\:\mathrm{12}\:…\:\mathrm{n}\: \\ $$ Commented by mrW1 last updated on 06/Feb/17 $${the}\:{n}−{th}\:{term}\:{of}\:{the}\:{series}\:{is}\:{not} \\…
Question Number 75905 by Master last updated on 20/Dec/19 Commented by Master last updated on 21/Dec/19 $$\mathrm{sir}\:\mathrm{mind}\:\mathrm{is}\:\mathrm{power}\:\mathrm{plz} \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 75902 by Mr. K last updated on 20/Dec/19 Commented by Mr. K last updated on 20/Dec/19 $${find}\:{the}\:{area}\:{of}\:{the}\:{square} \\ $$ Answered by mr W…
Question Number 75901 by Master last updated on 20/Dec/19 Answered by MJS last updated on 20/Dec/19 $$\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \:{x}}=\mathrm{4tan}\:\mathrm{2}{x} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}}=\mathrm{2tan}\:\mathrm{2}{x} \\ $$$${x}=\mathrm{arctan}\:{t} \\ $$$$\frac{{t}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{4}{t}}{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 10364 by Joel575 last updated on 05/Feb/17 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}\:=\:{x}^{{y}} \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y}\:\mathrm{is}\:… \\ $$ Answered by mrW1 last updated on 05/Feb/17 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}=\frac{\mathrm{11}×\mathrm{12}}{\mathrm{2}}=\mathrm{66} \\ $$$${x}^{{y}} =\mathrm{66}…
Question Number 10363 by Joel575 last updated on 05/Feb/17 $$\Delta{ABC}\:\mathrm{with}\:{AB}\:=\:\mathrm{5},\:{BC}\:=\:\mathrm{7},\:{CA}\:=\:\mathrm{8} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left(\mathrm{sin}\:{A}\:+\:\mathrm{sin}\:{B}\:+\:\mathrm{sin}\:{C}\right)\:.\:\left(\mathrm{cot}\:\frac{{A}}{\mathrm{2}}\:+\:\mathrm{cot}\:\frac{{B}}{\mathrm{2}}\:+\:\mathrm{cot}\:\frac{{C}}{\mathrm{2}}\right) \\ $$ Answered by mrW1 last updated on 06/Feb/17 $${a}={BC}=\mathrm{7} \\…
Question Number 10362 by Tawakalitu ayo mi last updated on 05/Feb/17 $$\mathrm{An}\:\mathrm{helium}\:\mathrm{atom}\:\mathrm{has}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{6}.\mathrm{64}\:×\:\mathrm{10}^{−\mathrm{27}} \mathrm{kg}\:\mathrm{and}\:\mathrm{a}\:\mathrm{charge} \\ $$$$\mathrm{Q}\:\mathrm{is}\:+\mathrm{2}\:\mathrm{electon}.\:\mathrm{Compare}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{electric}\: \\ $$$$\mathrm{repulsion}\:\mathrm{to}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gravitational}\:\mathrm{attraction}\:\mathrm{between}\:\mathrm{them}. \\ $$ Terms of Service Privacy Policy Contact:…