Question Number 200309 by sonukgindia last updated on 17/Nov/23 Answered by Mathspace last updated on 17/Nov/23 $${J}=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{{a}^{\mathrm{2}} −\mathrm{2}{asinx}\:+\mathrm{1}} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\frac{{e}^{{ix}}…
Question Number 200356 by sonukgindia last updated on 17/Nov/23 Commented by mr W last updated on 17/Nov/23 $${i}\:{guess}\:{you}\:{meant}\:{that}\:{the}\:{plane}\: \\ $$$${x}+\mathrm{8}{y}−\mathrm{4}{z}+{k}=\mathrm{0}\:{should}\:{touch}\:{the} \\ $$$${sphere}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +\mathrm{2}{y}−\mathrm{3}=\mathrm{0}.…
Question Number 200275 by sonukgindia last updated on 16/Nov/23 Answered by Mathspace last updated on 16/Nov/23 $${I}=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{{a}^{\mathrm{2}} −\mathrm{2}{acosx}+\mathrm{1}}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{{dx}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\frac{{e}^{{ix}}…
Question Number 200262 by sonukgindia last updated on 16/Nov/23 Answered by Frix last updated on 17/Nov/23 $$\mathrm{I}\:\mathrm{get}\:\frac{{a}}{{b}}=−\mathrm{1}+\sqrt{\mathrm{2}+\mathrm{2}\sqrt{\mathrm{2}}}\approx\mathrm{1}.\mathrm{19737} \\ $$ Answered by AST last updated on…
Question Number 200187 by sonukgindia last updated on 15/Nov/23 Answered by Mathspace last updated on 15/Nov/23 $${I}={Re}\left(\int_{−\infty} ^{+\infty} \frac{{e}^{{iax}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\right) \\ $$$${and}\:\int_{−\infty} ^{+\infty} \frac{{e}^{{iax}}…
Question Number 200175 by mokys last updated on 15/Nov/23 $${find}\:{all}\:{values}\:{of}\:{x}\:{if}\:{x}^{\mathrm{2}} \equiv\mathrm{4}{mod}\left(\mathrm{5}\right)\:{and}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{11}\:? \\ $$ Commented by AST last updated on 15/Nov/23 $$\mathrm{2},\mathrm{3},\mathrm{7},\mathrm{8} \\ $$ Commented by…
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Question Number 200109 by sonukgindia last updated on 14/Nov/23 Answered by mr W last updated on 14/Nov/23 $$\mathrm{2}^{{x}} =\mathrm{5}−{x} \\ $$$$\mathrm{2}^{{x}−\mathrm{5}} =\frac{\mathrm{5}−{x}}{\mathrm{32}} \\ $$$${e}^{\left({x}−\mathrm{5}\right)\mathrm{ln}\:\mathrm{2}} =\frac{\mathrm{5}−{x}}{\mathrm{32}}…
Question Number 200110 by sonukgindia last updated on 14/Nov/23 Answered by mr W last updated on 14/Nov/23 $${x}^{{x}^{{x}} } ={x}^{\mathrm{3}} \\ $$$$\Rightarrow{x}=\pm\mathrm{1} \\ $$$$\Rightarrow{x}^{{x}} =\mathrm{3}\Rightarrow{e}^{\mathrm{ln}\:{x}}…
Question Number 200133 by sonukgindia last updated on 14/Nov/23 Answered by Frix last updated on 14/Nov/23 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$${x}\approx\mathrm{1}.\mathrm{68421311} \\ $$ Terms of Service Privacy…