Question Number 75302 by vishalbhardwaj last updated on 09/Dec/19 $$\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{eleminated}\:\mathrm{from}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}\:=\: \\ $$$${a}\:{cos}\left(\theta−\alpha\right)\:\mathrm{and}\:{y}\:=\:{b}\:{cos}\left(\theta−\beta\right)\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:−\:\frac{\mathrm{2}{xy}}{{ab}}\:{cos}\left(\alpha−\beta\right)\:=\:{sin}^{\mathrm{2}} \left(\alpha−\beta\right)\:? \\ $$ Commented by vishalbhardwaj last…
Question Number 75300 by vishalbhardwaj last updated on 09/Dec/19 $$\mathrm{A}\:\mathrm{line}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{segment}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{lines}\:\mathrm{5x}−\mathrm{y}+\mathrm{4}\:=\:\mathrm{0}\:\mathrm{and}\:\mathrm{3x}+\mathrm{4y}−\mathrm{4}\:=\:\mathrm{0} \\ $$$$\mathrm{is}\:\mathrm{bisected}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{5}\right).\:\mathrm{Obtain}\:\mathrm{its} \\ $$$$\mathrm{equation}\:? \\ $$ Answered by mr W last updated on…
Question Number 75303 by vishalbhardwaj last updated on 09/Dec/19 $$\mathrm{If}\:{cos}\theta\:=\:\frac{{cos}\alpha−\mathrm{cos}\beta}{\mathrm{1}−{cos}\alpha\:{cos}\beta}\:,\:\mathrm{prove}\:\mathrm{that}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\frac{\theta}{\mathrm{2}}\:\mathrm{is}\:{tan}\frac{\alpha}{\mathrm{2}}\:.\:{tan}\frac{\beta}{\mathrm{2}}\:?? \\ $$ Answered by mind is power last updated on 09/Dec/19 $$\frac{\mathrm{1}−\mathrm{cos}\left(\theta\right)}{\mathrm{1}+\mathrm{cos}\left(\theta\right)}=\mathrm{tg}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right)…
Question Number 75301 by vishalbhardwaj last updated on 09/Dec/19 $$\mathrm{Find}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{S}_{\infty} \:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\::\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{3}.\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:.\:.\:. \\ $$ Commented by vishalbhardwaj last updated on 09/Dec/19 $$\mathrm{please}\:\mathrm{solve}\:\mathrm{this} \\ $$ Commented…
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Question Number 75280 by otchereabdullai@gmail.com last updated on 09/Dec/19 $$\mathrm{A}\:\mathrm{car}\:\mathrm{travels}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{speed}\:\mathrm{and}\: \\ $$$$\mathrm{covers}\:\mathrm{240km}\:\mathrm{in}\:\mathrm{8hours}\:.\:\mathrm{How}\:\mathrm{far}\:\mathrm{does} \\ $$$$\mathrm{it}\:\mathrm{travel}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{speed}\:\mathrm{in}\:\mathrm{5hours} \\ $$$$ \\ $$ Answered by mr W last updated on…
Question Number 75276 by vishalbhardwaj last updated on 09/Dec/19 $$\mathrm{Write}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{if}\:\mathrm{coordinates} \\ $$$$\mathrm{of}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{given}\:? \\ $$ Commented by mr W last updated on 09/Dec/19 $$\left({x}−\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} }{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 75277 by otchereabdullai@gmail.com last updated on 09/Dec/19 $$\mathrm{The}\:\mathrm{scale}\:\mathrm{of}\:\mathrm{a}\:\mathrm{map}\:\mathrm{is}\:\mathrm{1}:\mathrm{40},\mathrm{000}\:.\:\mathrm{Calculate} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{in}\:\mathrm{square}\:\mathrm{centimeters}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{map}\:\mathrm{of}\:\mathrm{forest}\:\mathrm{reserved}\:\mathrm{which}\:\mathrm{covers}\: \\ $$$$\mathrm{170km}^{\mathrm{2}} . \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{question} \\ $$ Answered by mr W…
Question Number 9734 by geovane10math last updated on 29/Dec/16 $${What}\:{is}\:{the}\:{group}\:\:\:\:\mathbb{Z}/\boldsymbol{{n}}\mathbb{Z}\:?? \\ $$ Commented by FilupSmith last updated on 29/Dec/16 $$\mathbb{Z}\:\mathrm{is}\:\mathrm{all}\:\mathrm{whole}\:\mathrm{numbers}. \\ $$$$\mathrm{e}.\mathrm{g}.\:\forall{x}\in\mathbb{R}\Rightarrow\lfloor{x}\rfloor\in\mathbb{Z} \\ $$$$\: \\…
Question Number 9727 by geovane10math last updated on 29/Dec/16 $$\mathrm{Find}\:\mathrm{a}\:\boldsymbol{{x}}\:{integer}: \\ $$$$\left[\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{kx}\pi\right)}{{k}}\right]\:+\:\left[\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{2}\Pi{kxe}\right)}{{k}}\right]\:=\:\mathrm{0}\: \\ $$$$ \\ $$$$\boldsymbol{\mathrm{Where}}: \\ $$$$\boldsymbol{\Pi}\:\mathrm{represents}\:\mathrm{180}°\:; \\ $$$$\boldsymbol{\pi}\:\mathrm{represents}\:\mathrm{3},\mathrm{14159265358}…\:. \\…