Question Number 196780 by Tawa11 last updated on 31/Aug/23 A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity…
Question Number 196738 by Tawa11 last updated on 30/Aug/23 Commented by Tawa11 last updated on 30/Aug/23 $$\mathrm{Please}\:\mathrm{is}\:\mathrm{this}\:\mathrm{solution}\:\mathrm{correct}???. \\ $$$$ \\ $$$$\mathrm{My}\:\mathrm{thinking}. \\ $$$$\mathrm{I}\:\mathrm{thought}\:\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{force} \\ $$$$\mathrm{that}\:\mathrm{should}\:\mathrm{accelerate}\:\mathrm{the}\:\mathrm{body},\:\mathrm{not}\:\mathrm{resultant}\:\mathrm{force}.…
Question Number 196657 by Tawa11 last updated on 28/Aug/23 $$\mathrm{A}\:\mathrm{pilot}\:\mathrm{flies}\:\mathrm{his}\:\mathrm{plane}\:\mathrm{directly}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{A}\:\mathrm{to}\:\mathrm{a}\:\mathrm{point}\:\mathrm{B}, \\ $$$$\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{450Km}.\:\mathrm{The}\:\mathrm{bearing}\:\mathrm{of}\:\mathrm{B}\:\mathrm{from}\:\mathrm{A}\:\mathrm{is}\:\mathrm{030}°.\:\mathrm{A} \\ $$$$\mathrm{wind}\:\mathrm{of}\:\mathrm{80Km}/\mathrm{hr}\:\mathrm{is}\:\mathrm{blowing}\:\mathrm{from}\:\mathrm{the}\:\mathrm{east}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{plane}\:\mathrm{can}\:\mathrm{travel}\:\mathrm{at}\:\mathrm{320Km}/\mathrm{hr}\:\mathrm{in}\:\mathrm{still}\:\mathrm{air}.\:\mathrm{Find}\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{bearing}\:\mathrm{on}\:\mathrm{which}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{must}\:\mathrm{be}\:\mathrm{steered}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{to}\:\mathrm{fly}\:\mathrm{from}\:\mathrm{A}\:\mathrm{to}\:\mathrm{B}. \\ $$ Terms of Service…
Question Number 196567 by pete last updated on 27/Aug/23 $$\mathrm{Show}\:\mathrm{that}\:\left(\frac{\mathrm{1}+\:\mathrm{itan}\theta}{\mathrm{1}−\:\mathrm{itan}\theta}\right)^{\mathrm{n}} =\frac{\mathrm{1}+\:\mathrm{itan}\left(\mathrm{n}\theta\right)}{\mathrm{1}−\:\mathrm{tan}\left(\mathrm{n}\theta\right)} \\ $$ Commented by mokys last updated on 27/Aug/23 $$\left(\frac{\mathrm{1}+{itan}\theta}{\mathrm{1}−{itan}\theta}\right)^{{n}} =\left(\frac{\frac{{cos}\theta+{isin}\theta}{{cos}\theta}}{\frac{{cos}\theta−{isin}\theta}{{cos}\theta}}\right)^{{n}} =\left(\frac{{cos}\left({n}\theta\right)+{isin}\left({n}\theta\right)}{{cos}\left({n}\theta\right)−{isin}\left({n}\theta\right)}\right) \\ $$$$…
Question Number 196560 by peter frank last updated on 27/Aug/23 Commented by Spillover last updated on 27/Aug/23 Check your solution https://m.facebook.com/story.php?story_fbid=pfbid0QHNhoZjesQzGqy7jHAgbvRSRUx25yXHezsGoh2qHLCapd9KB4z5PFi88czsFYxZ6l&id=100084816875916&mibextid=Nif5oz Answered by MM42 last updated on 27/Aug/23…
Question Number 196525 by Mastermind last updated on 26/Aug/23 Answered by mr W last updated on 27/Aug/23 $$\sqrt{{m}^{\mathrm{2}} +\mathrm{1}}>\sqrt{{m}^{\mathrm{2}} }={m} \\ $$$$\sqrt{{m}^{\mathrm{2}} +\mathrm{1}}<\sqrt{{m}^{\mathrm{2}} +\mathrm{2}{m}+\mathrm{1}}=\sqrt{\left({m}+\mathrm{1}\right)^{\mathrm{2}} }={m}+\mathrm{1}…
Question Number 196444 by Mastermind last updated on 24/Aug/23 Commented by AST last updated on 25/Aug/23 $$=\left(\frac{\mathrm{6}+\mathrm{16}+\mathrm{6}+\mathrm{24}+\mathrm{20}+\mathrm{21}+\mathrm{144}}{\:\mathrm{24}}\right)×\frac{\mathrm{1}}{\mathrm{7}}=\frac{\mathrm{79}}{\mathrm{56}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 196242 by pete last updated on 20/Aug/23 $$\mathrm{Simplify}\:\left(\frac{\mathrm{1}+\mathrm{cos2}\theta\:+\mathrm{isin2}\theta}{\mathrm{1}+\mathrm{cos2}\theta\:−\mathrm{isin2}\theta}\right)^{\mathrm{30}} \\ $$ Answered by MM42 last updated on 20/Aug/23 $$\left(\frac{\mathrm{2}{cos}^{\mathrm{2}} \theta+\mathrm{2}{isin}\theta{cos}\theta}{\mathrm{2}{cos}^{\mathrm{2}} \theta−\mathrm{2}{isin}\theta{cos}\theta}\right)^{\mathrm{30}} =\left(\frac{{cos}\theta+{isin}\theta}{{cos}\theta−{isin}\theta}\right)^{\mathrm{30}} \\ $$$$={cos}\left(\mathrm{60}\theta\right)+{isin}\left(\mathrm{60}\theta\right)\:\checkmark…
Question Number 196211 by pete last updated on 20/Aug/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{cos}\left(\frac{\pi}{\mathrm{3}}+\mathrm{i}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{e}+\frac{\mathrm{1}}{\mathrm{e}}\right)\:−\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}\left(\mathrm{e}−\frac{\mathrm{1}}{\mathrm{e}}\right)\mathrm{i} \\ $$ Answered by Frix last updated on 20/Aug/23 $$\mathrm{cos}\:{x}\:=\frac{\mathrm{e}^{\mathrm{2i}{x}} +\mathrm{1}}{\mathrm{2e}^{\mathrm{i}{x}} } \\ $$$$\mathrm{cos}\:\left({a}+{b}\mathrm{i}\right)\:=\mathrm{cos}\:{a}\:\mathrm{cosh}\:{b}\:−\mathrm{i}\:\mathrm{sin}\:{a}\:\mathrm{sinh}\:{b} \\…
Question Number 196205 by Mastermind last updated on 19/Aug/23 $$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:!\mathrm{7}\:? \\ $$ Answered by AST last updated on 19/Aug/23 $$!\mathrm{7}=\mathrm{7}!\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}+\frac{\mathrm{1}}{\mathrm{6}!}−\frac{\mathrm{1}}{\mathrm{7}!}\right)=\mathrm{1854} \\ $$ Commented by AST…