Question Number 158035 by HongKing last updated on 30/Oct/21 Answered by mr W last updated on 30/Oct/21 $${say}\:{BC}=\mathrm{1} \\ $$$$\frac{{BD}}{\mathrm{sin}\:\mathrm{9}}=\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{3}+\mathrm{9}\right)}\: \\ $$$$\Rightarrow{BD}=\frac{\mathrm{sin}\:\mathrm{9}}{\mathrm{sin}\:\mathrm{12}} \\ $$$$\frac{{BA}}{\mathrm{sin}\:\left(\mathrm{9}+\mathrm{45}\right)}=\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{27}+\mathrm{3}+\mathrm{9}+\mathrm{45}\right)} \\…
Question Number 158039 by HongKing last updated on 30/Oct/21 $$\mathrm{f}\:\left(\frac{\mathrm{x}\:+\:\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{x}\:+\:\mathrm{2}\:\:\Rightarrow\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$ Answered by puissant last updated on 30/Oct/21 $${y}=\frac{{x}+\mathrm{1}}{\mathrm{2}}\:\rightarrow\:{x}=\mathrm{2}{y}−\mathrm{1} \\ $$$$\Rightarrow\:{f}\left({x}\right)\:=\:\left(\mathrm{2}{x}−\mathrm{1}\right)+\mathrm{2}\:=\:\mathrm{2}{x}+\mathrm{1} \\ $$ Answered…
Question Number 92488 by hmamarques1994@gmail.com last updated on 07/May/20 $$\:\left(\mathrm{3x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{3}} \:=\:\left(\mathrm{5x}\right)^{\mathrm{log}_{\mathrm{b}} \:\mathrm{5}} \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$ Commented by jagoll last updated on…
Question Number 158030 by VIDDD last updated on 30/Oct/21 $$\:\:\:\:{solve}\:{equation}\: \\ $$$$\:\:\:\mathrm{5}#+\left(\sqrt{\frac{\mathrm{5}!+\mathrm{5}}{\mathrm{5}!!+\mathrm{5}!!!}+!\mathrm{5}}−\mathrm{5}\right)\$=\mathrm{2}^{{x}} \\ $$ Commented by mkam last updated on 31/Oct/21 $${x}\:=\:\mathrm{5} \\ $$ Answered…
Question Number 92489 by ajfour last updated on 07/May/20 $$\left(\mathrm{3}+\frac{{cq}}{\mathrm{12}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{6}{c}}{{b}}{s}+\left(\frac{\mathrm{8}{c}^{\mathrm{2}} }{\mathrm{3}{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$$\left(\mathrm{1}+\frac{{cq}}{\mathrm{4}{b}}\right){s}^{\mathrm{2}} +\frac{\mathrm{3}{c}}{{b}}\left(\mathrm{1}−\frac{{cq}}{\mathrm{12}{b}}\right){s}+\left(\frac{\mathrm{12}{c}^{\mathrm{2}} }{{b}^{\mathrm{2}} }−{b}\right)=\mathrm{0} \\ $$$${solve}\:{simultaneously}\:{for}\:\boldsymbol{{q}}\:{and}\:\boldsymbol{{s}} \\ $$$${in}\:{terms}\:{of}\:{b}\:{and}\:{c}. \\ $$ Terms…
Question Number 26942 by Mr eaay last updated on 31/Dec/17 Answered by mrW1 last updated on 31/Dec/17 $$\alpha^{\mathrm{3}} −\mathrm{2}\alpha+\mathrm{2}=\mathrm{0} \\ $$$$\beta^{\mathrm{3}} −\mathrm{2}\beta+\mathrm{2}=\mathrm{0} \\ $$$$\gamma^{\mathrm{3}} −\mathrm{2}\gamma+\mathrm{2}=\mathrm{0}…
Question Number 157989 by mnjuly1970 last updated on 30/Oct/21 $$\: \\ $$$${find}\:{the}\:{value}\:{of}\:: \\ $$$$\: \\ $$$$\:\:\mathrm{Max}_{\:{x}\in\:\mathbb{R}} \:\left(\:\left(\mathrm{sin}\left({x}\right)+\sqrt{\mathrm{3}}\:{cos}\left({x}\right)+\mathrm{1}\right)^{\:\mathrm{2}} =?\right. \\ $$$$ \\ $$ Commented by cortano…
Question Number 92448 by jagoll last updated on 07/May/20 $$\begin{cases}{\mathrm{5}^{\mathrm{x}} .\mathrm{6}^{\mathrm{y}} \:=\:\mathrm{150}}\\{\mathrm{5}^{\mathrm{y}} .\mathrm{6}^{\mathrm{x}} \:=\:\mathrm{180}\:}\end{cases} \\ $$ Commented by john santu last updated on 07/May/20 ����������…
Question Number 157967 by HongKing last updated on 30/Oct/21 $$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{7}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\:\mathrm{divide}\:\:\mathrm{3}^{\mathrm{7}^{\boldsymbol{\mathrm{n}}} } \:+\:\mathrm{5}^{\mathrm{7}^{\boldsymbol{\mathrm{n}}} } \:-\:\mathrm{1} \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{positive}\:\mathrm{integers}\:\:\boldsymbol{\mathrm{n}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 157964 by HongKing last updated on 30/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{4tan}\left(\mathrm{x}\right)\:+\:\frac{\mathrm{sin}\left(\mathrm{5x}\right)}{\mathrm{cos}^{\mathrm{5}} \left(\mathrm{x}\right)}\:=\:\mathrm{0} \\ $$$$ \\ $$ Commented by tounghoungko last updated on 30/Oct/21 $$\mathrm{sin}\:\left(\mathrm{5}{x}\right)=\mathrm{5sin}\:{x}\:\mathrm{cos}\:^{\mathrm{4}}…