Question Number 9211 by tawakalitu last updated on 23/Nov/16 $$\mathrm{If} \\ $$$$\mathrm{sinA}\:+\:\mathrm{sinB}\:=\:\mathrm{a} \\ $$$$\mathrm{tanA}\:+\:\mathrm{tanB}\:=\:\mathrm{b} \\ $$$$\mathrm{secA}\:+\:\mathrm{secB}\:=\:\mathrm{c} \\ $$$$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\mathrm{8bc}\:=\:\mathrm{a}\left[\mathrm{4b}^{\mathrm{2}} \:+\:\left(\mathrm{b}^{\mathrm{2}} \:−\:\mathrm{c}^{\mathrm{2}} \right)\right]^{\mathrm{2}} \\ $$…
Question Number 74747 by mr W last updated on 30/Nov/19 Answered by mind is power last updated on 30/Nov/19 $$\mathrm{let}\:\mathrm{p},\mathrm{q},\mathrm{r}\:\mathrm{side}\:\mathrm{of}\:\mathrm{red}\:\mathrm{squar},\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{blue} \\ $$$$\alpha,\beta,\varsigma\:\:\mathrm{angle}\:\mathrm{thetriangl}\:\mathrm{inside}\:\mathrm{red}\:\mathrm{squar} \\ $$$$\mathrm{a}^{\mathrm{2}} =\mathrm{p}^{\mathrm{2}}…
Question Number 9209 by tawakalitu last updated on 23/Nov/16 Commented by tawakalitu last updated on 23/Nov/16 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140282 by qaz last updated on 06/May/21 $$\underset{{k}=\mathrm{0}} {\overset{{p}−\mathrm{1}} {\sum}}\begin{pmatrix}{{p}}\\{{k}}\end{pmatrix}\mathrm{sin}\:\left[\mathrm{2}\left({p}−{k}\right){x}\right]=? \\ $$$$\begin{pmatrix}{{p}}\\{\mathrm{0}}\end{pmatrix}\mathrm{sin}\:\left(\mathrm{2}{px}\right)+\begin{pmatrix}{{p}}\\{\mathrm{1}}\end{pmatrix}\mathrm{sin}\:\left[\left(\mathrm{2}{p}−\mathrm{2}\right){x}\right]+\begin{pmatrix}{{p}}\\{\mathrm{2}}\end{pmatrix}\mathrm{sin}\:\left[\left(\mathrm{2}{p}−\mathrm{4}\right){x}\right]+…+\begin{pmatrix}{\:\:\:{p}}\\{{p}−\mathrm{1}}\end{pmatrix}\mathrm{sin}\:\left(\mathrm{2}{x}\right)=\mathrm{2}^{{p}} \centerdot\mathrm{cos}\:^{{p}} \left({x}\right)\centerdot\mathrm{sin}\:\left({px}\right)\:\:\:\:\:??? \\ $$$${or}\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{cos}\:^{{p}} \left({x}\right)\centerdot\mathrm{sin}\:\left({px}\right)}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\mathrm{2}^{−{p}} \right)\:\:\:\:\:{why}\:??? \\ $$ Terms…
Question Number 74742 by TawaTawa last updated on 30/Nov/19 $$\mathrm{If}\:\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1}\:\:\:=\:\:\mathrm{0},\:\: \\ $$$$\mathrm{Find}\:\:\:\:\:\:\:\:\:\alpha^{\mathrm{23}} \:+\:\beta^{\mathrm{23}} \:\:\:\:\:\mathrm{without}\:\mathrm{demoivre}'\mathrm{s}\:\mathrm{theorem}. \\ $$ Commented by abdomathmax last updated on 02/Dec/19 $${x}^{\mathrm{2}}…
Question Number 140276 by cherokeesay last updated on 06/May/21 Answered by mr W last updated on 06/May/21 Commented by mr W last updated on 06/May/21…
Question Number 140278 by MarhAH last updated on 06/May/21 $$\int\sqrt{{x}\:\frac{}{}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9204 by tawakalitu last updated on 23/Nov/16 Answered by mrW last updated on 23/Nov/16 $$\mathrm{300}×\mathrm{9}.\mathrm{81}×\mathrm{20}/\mathrm{60}=\mathrm{981}\:\mathrm{Nm}/\mathrm{s} \\ $$$$\mathrm{The}\:\mathrm{power}\:\mathrm{rating}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pump}: \\ $$$$\mathrm{981}/\mathrm{0}.\mathrm{80}=\mathrm{1226}\:\mathrm{Watt} \\ $$$$\mathrm{The}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{loss}\:\mathrm{of}\:\mathrm{energy}\:\mathrm{is}\:\mathrm{20\%}. \\ $$…
Question Number 140273 by liberty last updated on 06/May/21 $$\mathrm{2}\sqrt{\mathrm{x}−\mathrm{1}}\:+\mathrm{5x}\:=\:\sqrt{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4}\right)\left(\mathrm{x}+\mathrm{24}\right)} \\ $$ Answered by MJS_new last updated on 06/May/21 $${x}=\mathrm{5} \\ $$$$\mathrm{I}\:\mathrm{saw}\:\mathrm{that}\:\left(\mathrm{5}^{\mathrm{2}} +\mathrm{4}\right)\left(\mathrm{5}+\mathrm{24}\right)=\mathrm{29}^{\mathrm{2}} \\…
Question Number 9203 by tawakalitu last updated on 23/Nov/16 $$\mathrm{The}\:\mathrm{position}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{A}\:\mathrm{is}\:\left(\mathrm{41}°\mathrm{N},\:\mathrm{18}°\mathrm{E}\right) \\ $$$$\mathrm{point}\:\mathrm{B}\:\mathrm{is}\:\mathrm{8000}\:\mathrm{km}\:\mathrm{due}\:\mathrm{west}\:\mathrm{of}\:\mathrm{A}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{longitude}\:\mathrm{of}\:\mathrm{B}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{degree}. \\ $$ Answered by mrW last updated on 23/Nov/16 $$\mathrm{The}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Earth}\:\mathrm{is}\:\mathrm{roughly} \\…