Category: Differentiation

Question Number 185453 by cortano1 last updated on 22/Jan/23 $$Findthelargestpossiblearea$$$$oftrapezoidthatcanbedrawn$$$$underthex-axissothatone$$$$ofitsbasesisonthex-axis$$$$andtheothertwoverticesare$$$$onthecurvey=x^2-9$$ Commented by…

Question Number 119692 by bemath last updated on 26/Oct/20 $$Ifxisrealnumbersatisfying$$$$3x+\frac{1}{2x}=4,findthevalueof$$$$27x^3+\frac{1}{8x^3}.$$ Commented by bemath last updated on 26/Oct/20…

Question Number 54137 by ajfour last updated on 29/Jan/19 Commented by ajfour last updated on 29/Jan/19 $$CentresoftwospheresofradiiR$$$$rare2adistanceapart.Finda$$$$pointonthecircumferenceofthe$$$$circlewithABasdiameterfrom$$$${which}\:{maximum}\:{surface}\:{area}\:{is}…

Question Number 53965 by maxmathsup by imad last updated on 28/May/19 $$solve(x+1)y^{{}^{″}}+(2-3x^2)y^{{}^{\prime }}=xsin\left(x\right)$$$$let{y}^{{}^{\prime }}=zso\left(e\right)\iff (x+1)z^{{}^{\prime }}+(2-3x^2)z=xsinx\left(e\right)letfirstfindz$$$$\left({he}\right)\:\rightarrow\left({x}+\mathrm{1}\right){z}^{'} \:+\left(\mathrm{2}−\mathrm{3}{x}^{\mathrm{2}} \right){z}\:=\mathrm{0}\:\Rightarrow\left({x}+\mathrm{1}\right){z}^{'} \:=\left(\mathrm{3}{x}^{\mathrm{2}}…

Question Number 185000 by cortano1 last updated on 15/Jan/23 $$Amanwalksalongstraightpath$$$$ataspeed4ft/s.Aspotlightis$$$$locatedontheground20ftfrom$$$$thepathandiskeptfocusedontheman.$$$$Atwhatrateisspotlightrotating$$$$whenthemanis15ftfromthe$$$$pointonthepathclosesttothelight?$$$$\: \…