Category: Coordinate Geometry

Question Number 139106 by mr W last updated on 23/Apr/21 Commented by mr W last updated on 25/Apr/21 $${an}\:{uniform}\:{dense}\:{rope}\:{with}\:{length}\:\boldsymbol{{L}}\: \\ $$$${and}\:{mass}\:\boldsymbol{{m}}\:{is}\:{pulled}\:{by}\:{a}\:{truck}\:{with} \\ $$$${constant}\:{speed}.\:{on}\:{the}\:{end}\:{of}\:{rope}\:{a} \\ $$$${mass}\:\boldsymbol{{M}}\:{is}\:{connected}.\:{if}\:{the}\:{friction}…

Question Number 138774 by Bekzod Jumayev last updated on 18/Apr/21 Commented by Bekzod Jumayev last updated on 18/Apr/21 $$\:\:\:\:\:\:\boldsymbol{{x}}=?? \\ $$$$\boldsymbol{{Please}}\:\boldsymbol{{help}} \\ $$ Answered by…

Question Number 138548 by I want to learn more last updated on 14/Apr/21 Answered by nimnim last updated on 14/Apr/21 $${Let}\:{the}\:{centre}\:{of}\:{the}\:{circle}\:{be}\:{C}\left({h},{k}\right) \\ $$$${Since},\:{it}\:{touches}\:{the}\:{x}−{axis}\:{at}\:{P}\left(−\mathrm{3},\mathrm{0}\right), \\ $$$$\:{CP}\bot\:{x}−{axis}\:{and}\:{h}=−\mathrm{3}…

Question Number 7258 by Tawakalitu. last updated on 19/Aug/16 Commented by Yozzia last updated on 19/Aug/16 $${y}'=\frac{{x}}{\:\sqrt{\mathrm{5}−{x}^{\mathrm{2}} }}\Rightarrow{y}=\int\frac{{x}}{\:\sqrt{\mathrm{5}−{x}^{\mathrm{2}} }}{dx}. \\ $$$${Let}\:{u}=\mathrm{5}−{x}^{\mathrm{2}} \Rightarrow{du}=−\mathrm{2}{xdx}\Rightarrow{xdx}=\frac{−\mathrm{1}}{\mathrm{2}}{du}. \\ $$$${y}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−{du}}{\:\sqrt{{u}}}=\frac{−\mathrm{1}}{\mathrm{2}}\int{u}^{−\mathrm{1}/\mathrm{2}} {du}=\frac{−\mathrm{1}}{\mathrm{2}}×\mathrm{2}{u}^{\mathrm{1}/\mathrm{2}}…

Question Number 138203 by liberty last updated on 11/Apr/21 $${Three}\:{circles}\:{each}\:{radius}\:\mathrm{1},\:{touch}\:{one} \\ $$$${another}\:{externally}\:{and}\:{they}\:{lie} \\ $$$${between}\:{two}\:{parallel}\:{line}.\:{The}\: \\ $$$${minimum}\:{possible}\:{distance}\:{between}\: \\ $$$${the}\:{lines}\:{is}\:\_\: \\ $$ Answered by bobhans last updated…