Question Number 10872 by Saham last updated on 28/Feb/17 $$\mathrm{In}\:\mathrm{a}\:\mathrm{cultural}\:\mathrm{gathering}\:\mathrm{of}\:\mathrm{400}\:\mathrm{people},\:\mathrm{there}\:\mathrm{are}\:\mathrm{270}\:\mathrm{men}\:\mathrm{and}\:\mathrm{200} \\ $$$$\mathrm{musicians}.\:\mathrm{Of}\:\mathrm{the}\:\mathrm{latter},\:\mathrm{80}\:\mathrm{are}\:\mathrm{singers}.\:\mathrm{60}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are}\:\mathrm{not}\:\:\mathrm{musicians} \\ $$$$\mathrm{and}\:\mathrm{220}\:\mathrm{of}\:\mathrm{the}\:\mathrm{men}\:\mathrm{are}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are} \\ $$$$\mathrm{musicians}\:\mathrm{but}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{150}\:\mathrm{singers}\:\mathrm{altogether}\:\mathrm{and}\: \\ $$$$\mathrm{40}\:\mathrm{men}\:\mathrm{are}\:\mathrm{both}\:\mathrm{musicians}\:\mathrm{and}\:\mathrm{singers}. \\ $$ Answered by Abdulhalim Ghadady last…
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Question Number 141943 by cesarL last updated on 25/May/21 $$\int\frac{{dx}}{{x}\sqrt{\mathrm{16}−\mathrm{4}{x}^{\mathrm{2}} }} \\ $$ Answered by MJS_new last updated on 25/May/21 $$\int\frac{{dx}}{{x}\sqrt{\mathrm{16}−\mathrm{4}{x}^{\mathrm{2}} }}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{2}+\sqrt{\mathrm{4}−{x}^{\mathrm{2}}…
Question Number 76404 by mind is power last updated on 27/Dec/19 $$\mathrm{Hello}\:\mathrm{have}\:\mathrm{nice}\:\mathrm{end}\:\mathrm{of}\:\mathrm{year}\:\mathrm{good}\:\mathrm{bless}\:\mathrm{you} \\ $$$$\mathrm{all}\:\mathrm{i}\:\mathrm{respond}\:\mathrm{note}\:\mathrm{in}\:\mathrm{y}\:\mathrm{re}\:\mathrm{message}\:\mathrm{becsuse}\:\mathrm{i}\:\mathrm{have}\:\mathrm{so}\:\mathrm{many}\:\mathrm{problemes} \\ $$$$\mathrm{that}\:\mathrm{mack}\:\mathrm{me}\:\mathrm{feel}\:\mathrm{no}\:\mathrm{pleasur}\:\mathrm{any}\:\mathrm{more}\:\mathrm{to}\:\mathrm{do}\:\mathrm{somthing} \\ $$$$\mathrm{i}\:\mathrm{think}\:\mathrm{its}\:\mathrm{importante}\:\mathrm{to}\:\mathrm{say}\:\mathrm{it}\:\mathrm{i}\:\mathrm{will}\:\mathrm{back}\:\mathrm{Soon}\:\mathrm{i}\:\mathrm{hop}\:\mathrm{so}\:\:\mathrm{Sorry}\:\mathrm{for} \\ $$$$\mathrm{my}\:\mathrm{English} \\ $$ Commented by mr…
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Question Number 141937 by cesarL last updated on 24/May/21 $${Write}\:{and}\:{graph}\:{the}\:{equation}\:{of}\:{the}\:{graph}\:{of}\:{y}={sin}\left(\pi{x}\right) \\ $$$${It}\:{is}\:{stretched}\:{up}\:{by}\:{a}\:{factor}\:{of}\:\mathrm{5}\:{and}\:{shifted}\:\frac{\mathrm{1}}{\mathrm{2}}\:{unit}\:{to}\:{the}\:{right} \\ $$$${Help}\:{me}\:{please} \\ $$$$ \\ $$ Commented by MJS_new last updated on 25/May/21…
Question Number 10867 by Saham last updated on 28/Feb/17 $$\left(\mathrm{1}\right) \\ $$$$\mathrm{Show}\:\mathrm{that}\:: \\ $$$$\frac{\mathrm{x}^{\mathrm{2n}\:+\:\mathrm{1}} \:−\:\mathrm{y}^{\mathrm{2n}\:+\:\mathrm{1}} }{\mathrm{x}\:−\:\mathrm{y}}\:=\:\mathrm{x}^{\mathrm{2n}\:} +\:\mathrm{x}^{\mathrm{2n}\:−\:\mathrm{1}} \mathrm{y}\:+\:…\:+\:\mathrm{xy}^{\mathrm{2n}\:−\:\mathrm{1}} \:+\:\mathrm{y}^{\mathrm{2n}} \\ $$$$\left(\mathrm{2}\right) \\ $$$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2n}}…
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Question Number 10864 by chux last updated on 28/Feb/17 Answered by ridwan balatif last updated on 28/Feb/17 $$\mathrm{first}\:\mathrm{step} \\ $$$$\left(\frac{\mathrm{sinx}}{\mathrm{cosx}}\right)^{\mathrm{2}} =\left(\mathrm{tanx}\right)^{\mathrm{2}} \\ $$$$\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}=\mathrm{tan}^{\mathrm{2}}…
Question Number 141933 by mathmax by abdo last updated on 24/May/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{t}^{\mathrm{2}} }\mathrm{dx}\:\:\:\left(\mathrm{t}>\mathrm{0}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{t}\right)\:\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$ Commented…