Question Number 147778 by mnjuly1970 last updated on 23/Jul/21 Answered by liberty last updated on 23/Jul/21 $$\left(\bullet\right)\angle{ABC}=\angle{CBD}=\theta \\ $$$$\Rightarrow\mathrm{sin}\:\theta=\frac{\mathrm{3}}{{AB}}\: \\ $$$$\left(\bullet\right)\mathrm{cos}\:\mathrm{2}\theta=\frac{\mathrm{7}}{{AB}}=\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \theta \\ $$$$\Rightarrow\frac{\mathrm{7}}{{AB}}=\mathrm{1}−\mathrm{2}\left(\frac{\mathrm{9}}{{AB}^{\mathrm{2}} }\right)\:\Rightarrow{AB}={x}…
Question Number 16703 by Tinkutara last updated on 25/Jun/17 $$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{dx}}{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 26/Jun/17 $${x}={tg}\varphi\Rightarrow{dx}=\left(\mathrm{1}+{tg}^{\mathrm{2}} \varphi\right){d}\varphi…
Question Number 16701 by Tinkutara last updated on 25/Jun/17 $$\mathrm{Find}\:\mathrm{distinct}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1} \\ $$$$\mathrm{to}\:\mathrm{9}\:\mathrm{such}\:\mathrm{that}\:\mathrm{these}\:\mathrm{six}\:\mathrm{equations}\:\mathrm{are} \\ $$$$\mathrm{satisfied}\:\mathrm{simultaneously}: \\ $$$$\left(\mathrm{1}\right)\:{a}\:+\:{bc}\:=\:\mathrm{20} \\ $$$$\left(\mathrm{2}\right)\:{d}\:+\:{e}\:+\:{f}\:=\:\mathrm{20} \\ $$$$\left(\mathrm{3}\right)\:{g}\:−\:{hi}\:=\:−\mathrm{20} \\ $$$$\left(\mathrm{4}\right)\:{adg}\:=\:\mathrm{20} \\ $$$$\left(\mathrm{5}\right)\:{b}\:+\:{eh}\:=\:\mathrm{20} \\…
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Question Number 16699 by mrW1 last updated on 25/Jun/17 $$\mathrm{Related}\:\mathrm{to}\:\mathrm{Q16675}: \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{points} \\ $$$$\mathrm{of}\:\mathrm{graph}\:\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{x}}{\mathrm{10}}. \\ $$$$ \\ $$$$\mathrm{Let}'\mathrm{s}\:\mathrm{see}\:\mathrm{sin}\:\mathrm{x}\:=\:\frac{\mathrm{x}}{\mathrm{n}}\:\mathrm{with}\:\mathrm{n}>\mathrm{1}. \\ $$$$\mathrm{For}\:\mathrm{n}\leqslant\mathrm{1}\:\mathrm{there}\:\mathrm{is}\:\mathrm{one}\:\mathrm{intersection}\:\mathrm{point}. \\ $$$$ \\…
Question Number 147768 by aliibrahim1 last updated on 23/Jul/21 Answered by liberty last updated on 23/Jul/21 $${Let}\:{BC}\:=\:{x}\:\Rightarrow\mathrm{tan}\:\mathrm{44}°=\frac{{CD}}{{x}} \\ $$$$\Rightarrow{CD}={x}\:\mathrm{tan}\:\mathrm{44}° \\ $$$$\mathrm{L}{et}\:{AC}\:={y}\Rightarrow\mathrm{tan}\:\mathrm{48}°=\frac{{CD}}{{y}} \\ $$$$\Rightarrow{CD}={y}\:\mathrm{tan}\:\mathrm{48}° \\ $$$${where}\:{y}=\sqrt{\mathrm{30}^{\mathrm{2}}…
Question Number 82232 by mhmd last updated on 19/Feb/20 Commented by JDamian last updated on 19/Feb/20 $$\mathrm{I}\:\mathrm{guess}\:\mathrm{eventually}\:\mathrm{we}\:\mathrm{will}\:\mathrm{have}\:\mathrm{to}\:\mathrm{bear}\:\mathrm{ads} \\ $$ Answered by mind is power last…
Question Number 147764 by puissant last updated on 23/Jul/21 Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$\mathrm{Le}\:\mathrm{plan}\:\pi\:\mathrm{a}\:\mathrm{pour}\:\mathrm{equation}\:: \\ $$$${x}−{y}+{z}\:=\:\mathrm{2} \\ $$$$\mathrm{Le}\:\mathrm{vecteur}\:\overset{\rightarrow} {\mathrm{N}}\begin{pmatrix}{+\mathrm{1}}\\{−\mathrm{1}}\\{+\mathrm{1}}\end{pmatrix}\:\:\mathrm{est}\:\mathrm{un}\:\mathrm{vecteur} \\ $$$$\mathrm{normal}\:\mathrm{a}\:\pi. \\…
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Question Number 16691 by Tinkutara last updated on 25/Jun/17 $$\mathrm{The}\:\mathrm{horizontal}\:\mathrm{range}\:\mathrm{of}\:\mathrm{a}\:\mathrm{projectile} \\ $$$$\mathrm{is}\:{R}\:\mathrm{and}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{height}\:\mathrm{attained} \\ $$$$\mathrm{by}\:\mathrm{it}\:\mathrm{is}\:{H}.\:\mathrm{A}\:\mathrm{strong}\:\mathrm{wind}\:\mathrm{now}\:\mathrm{begins}\:\mathrm{to} \\ $$$$\mathrm{blow}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{horizontal} \\ $$$$\mathrm{motion}\:\mathrm{of}\:\mathrm{projectile},\:\mathrm{giving}\:\mathrm{it}\:\mathrm{a}\:\mathrm{constant} \\ $$$$\mathrm{horizontal}\:\mathrm{acceleration}\:\mathrm{equal}\:\mathrm{to}\:{g}. \\ $$$$\mathrm{Under}\:\mathrm{the}\:\mathrm{same}\:\mathrm{conditions}\:\mathrm{of}\:\mathrm{projection}, \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{range}\:\mathrm{will}\:\mathrm{be} \\…