Question Number 127152 by mnjuly1970 last updated on 27/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{differential}\:\:{equation}…\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:{if}\:\:\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:=\:{y}\left({x}\right)\:\:\&\:{y}\left(\mathrm{0}\right)=−{y}'\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\:\:{then}\:\:\:{evaluate}\:\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {y}\left({x}\right).{y}^{−\mathrm{1}} \left(−{x}\right){dx}=? \\ $$$$ \\ $$…
Question Number 127119 by liberty last updated on 27/Dec/20 $${The}\:{barometric}\:{pressure}\:{p}\:{at}\:{an}\:{altitude} \\ $$$${of}\:{h}\:{miles}\:{above}\:{sea}\:{level}\:{satisfies}\:{the} \\ $$$${differential}\:{equation}\:\frac{{dp}}{{dh}}\:=\:−\mathrm{0}.\mathrm{2}{p}\:. \\ $$$${If}\:{the}\:{pressure}\:{at}\:{sea}\:{level}\:{is}\:\mathrm{29}.\mathrm{92}\:{inches} \\ $$$${of}\:{mercury},\:{find}\:{the}\:{barometric}\: \\ $$$${preassure}\:{at}\:\mathrm{17},\mathrm{000}\:{ft}\: \\ $$$$\left({A}\right)\:\mathrm{56}.\mathrm{97}\:{in}\:\:\:\:\:\:\left({B}\right)\:\mathrm{15}.\mathrm{71}\:{in} \\ $$$$\left({C}\right)\:\mathrm{7}.\mathrm{86}\:{in}\:\:\:\:\:\:\:\:\:\:\left({D}\right)\:\mathrm{1}\:{in} \\…
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Question Number 192545 by peter frank last updated on 20/May/23 Answered by BaliramKumar last updated on 20/May/23 $$\mathrm{plnx}+\mathrm{qlny}=\:\left(\mathrm{p}+\mathrm{q}\right)\mathrm{ln}\left(\mathrm{x}+\mathrm{y}\right) \\ $$$$\frac{\mathrm{p}}{\mathrm{x}}−\frac{\mathrm{p}+\mathrm{q}}{\mathrm{x}+\mathrm{y}}=\:\left\{\frac{\mathrm{p}+\mathrm{q}}{\mathrm{x}+\mathrm{y}}−\frac{\mathrm{q}}{\mathrm{y}}\right\}\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\frac{\mathrm{py}}{\mathrm{x}}\frac{−\mathrm{qx}}{}=\:\left\{\frac{\mathrm{py}−}{}\frac{\mathrm{qx}}{\mathrm{y}}\right\}\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}}{\mathrm{x}} \\…
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Question Number 126994 by bramlexs22 last updated on 26/Dec/20 $$\:\int\:\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:=? \\ $$ Answered by liberty last updated on 26/Dec/20 $$\Omega=\int\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:=\:\int\frac{{dx}}{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}}…
Question Number 126987 by sdfg last updated on 25/Dec/20 Answered by mr W last updated on 26/Dec/20 $${Q}\mathrm{4} \\ $$$$\boldsymbol{{C}}=\alpha\boldsymbol{{A}}+\beta\boldsymbol{{B}} \\ $$$$\mid\boldsymbol{{C}}\mid=\sqrt{\alpha^{\mathrm{2}} \mid\boldsymbol{{A}}\mid^{\mathrm{2}} +\beta^{\mathrm{2}} \mid\boldsymbol{{B}}\mid^{\mathrm{2}}…
Question Number 126971 by mnjuly1970 last updated on 25/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{evaluate}\:': \\ $$$$\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({arctan}\left({x}\right)\right)^{\mathrm{2}} {dx}=? \\ $$$$\:\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 126969 by mnjuly1970 last updated on 25/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{calculus} \\ $$$$\:\:\:\:\:\:{please}\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\phi\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \lfloor{ln}\left({x}\right)\rfloor{dx}=? \\ $$$$ \\ $$ Answered by mindispower last updated…
Question Number 192466 by Engr_Jidda last updated on 18/May/23 Commented by Frix last updated on 19/May/23 $$\left(\mathrm{sin}^{\mathrm{4}} \:\theta\:−\mathrm{cos}^{\mathrm{4}} \:\theta\right)\mathrm{csc}^{\mathrm{2}} \:\theta\:=\mathrm{2} \\ $$$$\frac{\mathrm{2sin}^{\mathrm{2}} \:\theta\:−\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \:\theta}=\mathrm{2} \\…