Question Number 186996 by Mingma last updated on 12/Feb/23 Answered by aba last updated on 12/Feb/23 $$\mathrm{0}<\mathrm{ln}\left(\mathrm{3}/\mathrm{2}\right)<\mathrm{6}/\mathrm{13} \\ $$ Commented by MJS_new last updated on…
Question Number 186926 by cortano12 last updated on 12/Feb/23 Commented by cortano12 last updated on 12/Feb/23 Q2 A 6ft tall man is moving at a speed of 2ft/s towards a building with a window whose base is 10ft above the ground and the height of the window is 4ft. If the angle between the lines of the man’s gaze is up and down the window, find the rate of change of the angle when the man is 16ft away from the base of the building Answered by manxsol last updated on 12/Feb/23 $$\frac{{dx}}{{dt}}=−\mathrm{2}\frac{{ft}}{{s}}\:\:\:\:\:\:\:…
Question Number 121303 by talminator2856791 last updated on 06/Nov/20 $$\: \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:{x}\:−\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:=\:\mathrm{2}\:\mathrm{cos}\:\mathrm{2}{x} \\ $$$$\: \\ $$$$\: \\ $$ Commented…
Question Number 186830 by ajfour last updated on 11/Feb/23 Commented by ajfour last updated on 11/Feb/23 $${Find}\:{x}. \\ $$ Answered by ajfour last updated on…
Question Number 55704 by gunawan last updated on 03/Mar/19 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{2}\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}\theta\mathrm{cos}\:\frac{\mathrm{3}}{\mathrm{2}}\theta+\mathrm{2sin}\:\frac{\mathrm{5}}{\mathrm{2}}\theta\: \\ $$$$+\mathrm{2}\:\mathrm{sin}\:\frac{\mathrm{3}}{\mathrm{2}}\theta+\mathrm{2sin}\:\frac{\mathrm{3}}{\mathrm{2}}\theta\mathrm{cos}\:\frac{\mathrm{7}}{\mathrm{2}}\theta \\ $$$$=\mathrm{sin}\:\mathrm{4}\theta+\mathrm{sin}\:\mathrm{5}\theta \\ $$ Answered by Kunal12588 last updated on 03/Mar/19…
Question Number 186741 by cortano12 last updated on 09/Feb/23 $$\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{18}}\right).\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{18}}\right).\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{18}}\right).\mathrm{cos}\:\left(\frac{\mathrm{7}\pi}{\mathrm{18}}\right)=? \\ $$ Answered by pablo1234523 last updated on 09/Feb/23 $$\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{18}}+\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{18}}\right]\centerdot\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{18}}+\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{18}}\right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{cos}^{\mathrm{2}} \:\frac{\mathrm{4}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}\mathrm{cos}\:\frac{\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{9}}\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{9}}\mathrm{cos}\:\frac{\pi}{\mathrm{9}}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{1}+\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{7}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}+\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}\right)…
Question Number 186737 by Rupesh123 last updated on 09/Feb/23 Commented by Frix last updated on 09/Feb/23 $$\mathrm{No}. \\ $$$$\mathrm{There}'\mathrm{s}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{area}\:\frac{\mathrm{1}}{\mathrm{17425}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}. \\ $$ Answered by mr W…
Question Number 121052 by mathocean1 last updated on 05/Nov/20 $$\mathrm{show}\:\mathrm{that} \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{x}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 121051 by mathocean1 last updated on 05/Nov/20 $$\mathrm{show}\:\mathrm{that} \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tanx}}{\mathrm{x}}=\mathrm{1} \\ $$$$ \\ $$$$ \\ $$ Answered by 675480065 last updated on…
Question Number 121050 by mathocean1 last updated on 05/Nov/20 $$\mathrm{show}\:\mathrm{that}\: \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}\:} {\mathrm{lim}}\:\frac{\mathrm{sinx}}{\mathrm{x}}=\mathrm{1} \\ $$ Answered by 675480065 last updated on 05/Nov/20 $$\mathrm{as}\:\mathrm{x}\rightarrow\mathrm{0},\:\mathrm{sinx}\rightarrow\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}!}+\mathrm{0}\left(\mathrm{x}^{\mathrm{3}} \right)\right)…