Question Number 161866 by Tawa11 last updated on 23/Dec/21 Commented by mr W last updated on 23/Dec/21 $$\frac{{BC}}{\mathrm{10}}=\frac{\mathrm{6}}{\mathrm{6}+\mathrm{9}}\:\Rightarrow{BC}=\mathrm{4} \\ $$$$\frac{{AC}}{\mathrm{6}}=\frac{\mathrm{7}.\mathrm{5}}{\mathrm{9}}\:\Rightarrow{AC}=\mathrm{5} \\ $$$$\frac{{AX}}{\mathrm{6}}=\frac{\mathrm{5}−{AX}}{\mathrm{4}}\:\Rightarrow{AX}=\mathrm{3}\:\Rightarrow{XC}=\mathrm{5}−\mathrm{3}=\mathrm{2} \\ $$ Commented…
Question Number 161861 by Rasheed.Sindhi last updated on 23/Dec/21 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\frac{\mathrm{1}^{\mathrm{2}} \centerdot\mathrm{2}!+\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}!+\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{4}!+\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)!−\mathrm{2}}{\left({n}+\mathrm{1}\right)!} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={n}^{\mathrm{2}} +{n}−\mathrm{2} \\ $$ Commented by mr W…
Question Number 96329 by M±th+et+s last updated on 31/May/20 $${x}\lfloor{x}\lfloor{x}\lfloor{x}\rfloor\rfloor\rfloor=\mathrm{88} \\ $$$${x}>\mathrm{0} \\ $$ Commented by prakash jain last updated on 31/May/20 $$\mathrm{88}=\mathrm{2}^{\mathrm{3}} ×\mathrm{11} \\…
Question Number 96321 by Mathudent last updated on 31/May/20 $${It}\:{is}\:{given}\:{that}\:{x}^{\mathrm{2}} =\mathrm{2}^{{x}} .\:{Find}\:{x}. \\ $$ Commented by bemath last updated on 31/May/20 $$\mathrm{look}\:\mathrm{qn}\:\mathrm{96241} \\ $$ Answered…
Question Number 161854 by mnjuly1970 last updated on 23/Dec/21 Commented by cortano last updated on 23/Dec/21 $$\:{yx}^{\mathrm{2}} −{yx}−\mathrm{6}{y}={x}^{\mathrm{2}} −{ax}+{a} \\ $$$$\:\left({y}−\mathrm{1}\right){x}^{\mathrm{2}} +\left({a}−{y}\right){x}−\left(\mathrm{6}{y}+{a}\right)=\mathrm{0} \\ $$$$\:\Delta\geqslant\mathrm{0} \\…
Question Number 161848 by mnjuly1970 last updated on 23/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f}\:\:\:\:{tan}\:\left(\alpha\:\right)=\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{K}=\frac{\:\:\mathrm{1}+{sin}\left(\:\mathrm{8}\:\alpha\right)−{cos}\:\left(\mathrm{8}\alpha\:\right)}{\mathrm{1}+{sin}\left(\:\mathrm{8}\alpha\:\right)\:+\:{cos}\:\left(\mathrm{8}\:\alpha\:\right)}\:=? \\ $$$$ \\ $$$$ \\ $$ Commented…
Question Number 96311 by bemath last updated on 31/May/20 $$\left(\mathrm{4}+\sqrt{\mathrm{15}}\right)^{{x}} \:+\:\left(\mathrm{4}−\sqrt{\mathrm{15}}\right)^{{x}} \:=\:\mathrm{62}\: \\ $$$${x}=? \\ $$ Answered by bobhans last updated on 31/May/20 $$\mathrm{4}−\sqrt{\mathrm{15}}\:×\:\frac{\mathrm{4}+\sqrt{\mathrm{15}}}{\mathrm{4}+\sqrt{\mathrm{15}}}\:=\:\frac{\mathrm{1}}{\mathrm{4}+\sqrt{\mathrm{15}}} \\…
Question Number 96296 by Enyz last updated on 31/May/20 Answered by Enyz last updated on 01/Jun/20 Commented by Enyz last updated on 01/Jun/20 Is this correct? Terms…
Question Number 96289 by rb222 last updated on 31/May/20 $$\mathrm{1010}^{{x}} +\mathrm{2020}^{{x}} =\mathrm{4040}^{{x}} \\ $$$${x}=? \\ $$ Commented by bobhans last updated on 31/May/20 $$\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{{x}} +\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{x}}…
Question Number 161820 by HongKing last updated on 22/Dec/21 $$\mathrm{Solve}\:\mathrm{this}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$${a}\:\frac{\partial{L}\left(\alpha\right)}{\partial{a}}\:+\:{b}\:\frac{\partial{L}\left(\alpha\right)}{\partial{b}}\:=\:{L}\left(\alpha\right) \\ $$$$\mathrm{where}:\:{L}\left(\alpha\right)\:=\:\underset{\:\mathrm{0}} {\overset{\:\boldsymbol{{a}}} {\int}}\sqrt{{a}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({t}\right)\:+\:{b}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({t}\right)}\:{dt} \\ $$ Answered by aleks041103…