Question Number 73542 by Rio Michael last updated on 13/Nov/19 $${Given}\:{that}\:{the}\:{function}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} \:{is}\:{differentiable} \\ $$$${in}\:{the}\:{interval}\:\left(−\mathrm{2},\mathrm{2}\right),\:{Use}\:{the}\:{mean}\:{value}\:{theorem} \\ $$$${to}\:{find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$${is}\:{parallel}\:{to}\:{the}\:{chord}\:{through}\:{the}\:{point}\:\left(−\mathrm{2},\mathrm{8}\right)\:{and}\:\left(\mathrm{2},\mathrm{8}\right) \\ $$ Terms of Service Privacy Policy…
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 138758 by EnterUsername last updated on 17/Apr/21 Answered by mr W last updated on 18/Apr/21 Commented by mr W last updated on 18/Apr/21…
Question Number 138548 by I want to learn more last updated on 14/Apr/21 Answered by nimnim last updated on 14/Apr/21 $${Let}\:{the}\:{centre}\:{of}\:{the}\:{circle}\:{be}\:{C}\left({h},{k}\right) \\ $$$${Since},\:{it}\:{touches}\:{the}\:{x}−{axis}\:{at}\:{P}\left(−\mathrm{3},\mathrm{0}\right), \\ $$$$\:{CP}\bot\:{x}−{axis}\:{and}\:{h}=−\mathrm{3}…
Question Number 72863 by ajfour last updated on 04/Nov/19 Commented by ajfour last updated on 04/Nov/19 $${Find}\:{equations}\:{of}\:{AB}\:{dividing} \\ $$$${the}\:{composite}\:{area}\:{in}\:{two}\:{equal} \\ $$$${parts},\:{when}\:\:{segment}\:{AB}\:{has} \\ $$$${least}\:{length}\:{and}\:{maximum}\:{length}. \\ $$…
Question Number 7258 by Tawakalitu. last updated on 19/Aug/16 Commented by Yozzia last updated on 19/Aug/16 $${y}'=\frac{{x}}{\:\sqrt{\mathrm{5}−{x}^{\mathrm{2}} }}\Rightarrow{y}=\int\frac{{x}}{\:\sqrt{\mathrm{5}−{x}^{\mathrm{2}} }}{dx}. \\ $$$${Let}\:{u}=\mathrm{5}−{x}^{\mathrm{2}} \Rightarrow{du}=−\mathrm{2}{xdx}\Rightarrow{xdx}=\frac{−\mathrm{1}}{\mathrm{2}}{du}. \\ $$$${y}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−{du}}{\:\sqrt{{u}}}=\frac{−\mathrm{1}}{\mathrm{2}}\int{u}^{−\mathrm{1}/\mathrm{2}} {du}=\frac{−\mathrm{1}}{\mathrm{2}}×\mathrm{2}{u}^{\mathrm{1}/\mathrm{2}}…
Question Number 72721 by mr W last updated on 01/Nov/19 Commented by mr W last updated on 01/Nov/19 $${find}\:{the}\:{correlation}\:{of}\:{A}\:{and}\:{B}\:{such} \\ $$$${that}\:{the}\:{circle}\:{is}\:{inscribed}\:{between}\:{the} \\ $$$${parabola}\:{and}\:{the}\:{x}−{axis}\:{as}\:{shown}. \\ $$…
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…
Question Number 6716 by Tawakalitu. last updated on 15/Jul/16 $${Prove}\:{that}\:{the}\:{locus}\:{of}\:{a}\:{point}\:{which}\:{moves}\:{its}\:{distance}\:{from}\: \\ $$$${the}\:{point}\:\left(−{b},\:\mathrm{0}\right)\:{is}\:{p}\:{times}\:{its}\:{distance}\:{from}\:{the}\:{point}\:\left({b},\:\mathrm{0}\right)\:{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right)\:−\:\mathrm{2}{b}\left({p}^{\mathrm{2}} \:+\:\mathrm{1}\right){x}\:=\:\mathrm{0} \\ $$$${Show}\:{that}\:{this}\:{locus}\:{is}\:{a}\:{circle}\:{and}\:{find}\:{its}\:{radius}. \\ $$ Answered by…
Question Number 137768 by mr W last updated on 06/Apr/21 Commented by mr W last updated on 06/Apr/21 $${find}\:{the}\:{maximal}\:{area}\:{of}\:{the}\:{shadow} \\ $$$${in}\:{terms}\:{of}\:{r},\:{h},\:{H}\:{and}\:{d}. \\ $$ Answered by…