Question Number 136466 by aurpeyz last updated on 22/Mar/21 $$\int\frac{\mathrm{4}{dx}}{\mathrm{3}−\mathrm{5}{sin}\:{x}} \\ $$ Answered by mathmax by abdo last updated on 22/Mar/21 $$\Phi=\int\:\:\frac{\mathrm{4dx}}{\mathrm{3}−\mathrm{5sinx}}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{tan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)=\mathrm{t}\:\Rightarrow \\ $$$$\Phi=\int\:\:\frac{\mathrm{4}}{\left(\mathrm{3}−\mathrm{5}\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}\frac{\mathrm{2dt}}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
Question Number 136463 by Plutonic last updated on 22/Mar/21 $${Evaluate}\:\mathrm{4}\sqrt{\mathrm{3}\:}\left(\frac{\mathrm{3}}{\:\sqrt{\mathrm{3}}}+\sqrt{\mathrm{3}}\right) \\ $$ Answered by aurpeyz last updated on 22/Mar/21 $${multiply}\:{through}\:{by}\:\mathrm{4}\sqrt{\mathrm{3}} \\ $$$$\mathrm{12}+\mathrm{12}=\mathrm{24} \\ $$ Terms…
Question Number 136457 by byaw last updated on 22/Mar/21 Commented by mr W last updated on 22/Mar/21 $${A},{B},{C}\:{are}\:{true}. \\ $$$${question}\:{D}\:{is}\:{not}\:{clear}.\:{one}\:{angle} \\ $$$${alone}\:{can}\:{not}\:{be}\:{complementary}. \\ $$$${if}\:{question}\:{D}\:{means}\:{that}\:{the}\:{angle} \\…
Question Number 5386 by sanusihammed last updated on 12/May/16 $${Solve}\:{simultaneously} \\ $$$$ \\ $$$${x}^{{x}} \:+\:\:{y}^{{y}\:} \:=\:\:\mathrm{31} \\ $$$${x}\:\:+\:\:{y}\:\:=\:\:\mathrm{5} \\ $$$$ \\ $$$${Please}\:{i}\:{did}\:{workings}\:… \\ $$$$ \\…
Question Number 70920 by TawaTawa last updated on 09/Oct/19 $$\mathrm{i}\:!\:\:=\:\:? \\ $$ Commented by prakash jain last updated on 10/Oct/19 $${i}!=\Gamma\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{where}\:{i}=\sqrt{−\mathrm{1}} \\ $$…
Question Number 5385 by sanusihammed last updated on 12/May/16 $${Find}\:{the}\:{value}\:{of}\:{x}\:{if}\: \\ $$$$ \\ $$$$\sqrt{{x}^{{x}^{\mathrm{6}} } }\:=\:\:\mathrm{729} \\ $$ Answered by prakash jain last updated on…
Question Number 136458 by aurpeyz last updated on 22/Mar/21 $$\int\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mathmax by abdo last updated on 22/Mar/21 $$\mathrm{I}=\int\sqrt{\mathrm{1}−\mathrm{4x}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{chamgement}\:\mathrm{2x}=\mathrm{sin}\theta\:\Rightarrow \\…
Question Number 5381 by Rasheed Soomro last updated on 12/May/16 Commented by Rasheed Soomro last updated on 15/May/16 $$\bigtriangleup\mathrm{ABC}\sim\bigtriangleup\mathrm{EFD} \\ $$ Terms of Service Privacy…
Question Number 70917 by Kunal12588 last updated on 09/Oct/19 $$\int\sqrt{{tan}^{\mathrm{2}} {x}+\mathrm{3}}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 09/Oct/19 $$\left.\sqrt{\mathrm{3}}{t}={tanx}\:\Rightarrow{x}={arctan}\left({t}\sqrt{\mathrm{3}}\right)\right)\:\Rightarrow \\ $$$$\int\sqrt{\mathrm{3}+{tan}^{\mathrm{2}}…
Question Number 5380 by 314159 last updated on 12/May/16 $${Suppose}\:{that}\:{a},{b},{c}>\mathrm{0}.{Prove}\:{that}\: \\ $$$$\frac{\mathrm{1}}{{a}\left(\mathrm{1}+{b}\right)}+\frac{\mathrm{1}}{{b}\left(\mathrm{1}+{c}\right)}+\frac{\mathrm{1}}{{c}\left(\mathrm{1}+{a}\right)}\:\geqslant\frac{\mathrm{3}}{\mathrm{1}+{abc}}. \\ $$ Commented by Rasheed Soomro last updated on 14/May/16 $$\mathrm{LHS}=\frac{{bc}\left(\mathrm{1}+{c}\right)\left(\mathrm{1}+{a}\right)+{ac}\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{a}\right)+{ab}\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)}{{a}\mathrm{bc}\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+\mathrm{c}\right)} \\ $$$$=\frac{{ab}\left(\mathrm{1}+{c}+{b}+{bc}\right)+{bc}\left(\mathrm{1}+{a}+{c}+{ca}\right)+{ca}\left(\mathrm{1}+{a}+{b}+{ab}\right)}{{a}\mathrm{bc}\left(\mathrm{1}+\mathrm{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+\mathrm{c}\right)}…