Question Number 39650 by KMA last updated on 09/Jul/18 $${If}\:{f}\:{be}\:{a}\:{linear}\:{function}\:{f}\:\left(\mathrm{6}\right)−{f}\left(\mathrm{12}\right) \\ $$$$=\mathrm{2}\:{What}\:{is}\:{f}\left(\mathrm{12}\right)−{f}\left(\mathrm{2}\right). \\ $$$$ \\ $$ Answered by MrW3 last updated on 09/Jul/18 $${assume}\:{f}\left({x}\right)={ax}+{b} \\…
Question Number 39640 by Rio Mike last updated on 09/Jul/18 $${John}'{s}\:{age}\:{is}\:\mathrm{3}{x}\:{years}\:\mathrm{3}\:{years} \\ $$$${after}\:{he}\:{was}\:\mathrm{27}\:{years}\:{old} \\ $$$${what}\:{was}\:{his}\:{age}\:\mathrm{3}\:{years}\:{before} \\ $$$${hence}\:{find}\:{the}\:{sum}\:{of}\:{the} \\ $$$${family}\:{ages}\:\underset{{x}=\mathrm{1}} {\overset{\mathrm{60}} {\sum}}\left(\mathrm{3}{x}\right)^{\mathrm{3}{x}−\mathrm{1}} \\ $$ Answered by…
Question Number 39611 by tanmay.chaudhury50@gmail.com last updated on 08/Jul/18 $${write}\:{the}\:{expression}\:{of}\:{electrostatic}\:{force} \\ $$$${between}\:{two}\:{charges}\:{Q}_{\mathrm{1}\:} {and}\:{Q}_{\mathrm{2}} \:{separated}\:{by} \\ $$$${distance}\:{r}.\:{for}\:{the}\:{following}\:{condition} \\ $$$$\left.\mathrm{1}\right){in}\:{air} \\ $$$$\left.\mathrm{2}\right){when}\:{die}\:{electric}\:{present}\:{between}\:{them} \\ $$$$\left.\mathrm{3}\right){when}\:{die}\:{electric}\:{partially}\:{fill}\:{space}\:{betweenp} \\ $$$${them} \\…
Question Number 39607 by Rio Mike last updated on 08/Jul/18 $${find}\:{the}\: \\ $$$${minimum}\:{and}\:{maximum}\:{value} \\ $$$${of}\:{the}\:{quadratic}\:{functions} \\ $$$$\left.{a}\right)\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\:\mathrm{1} \\ $$$$\left.{b}\right)\:{x}\:+\:\frac{\mathrm{2}}{{x}}\:=\:\mathrm{3} \\ $$$$\left.{c}\right)\:{x}^{\mathrm{2}} \:−\:\frac{{x}}{\mathrm{4}}\:+\:\mathrm{6} \\ $$$${hence}\:{draw}\:{each}\:{draw}…
Question Number 170673 by solomonwells last updated on 28/May/22 Commented by cortano1 last updated on 29/May/22 $$\:\Rightarrow\mathrm{2}\left(\mathrm{2}{x}+\sqrt{{x}}\:\right)=\:\mathrm{3}\sqrt{{x}}\:+\mathrm{2}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −{x}}\:;\:{x}>\mathrm{0} \\ $$$$\Rightarrow\mathrm{4}{x}−\sqrt{{x}}\:=\:\mathrm{2}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −{x}} \\ $$$$\Rightarrow\mathrm{4}\left(\sqrt{{x}}\:\right)^{\mathrm{2}} −\sqrt{{x}}\:=\:\mathrm{2}\sqrt{{x}}\:\sqrt{\mathrm{4}{x}−\mathrm{1}} \\…
Question Number 105130 by 175mohamed last updated on 26/Jul/20 $${To}\:{now}\:{the}\:{real}\:{sequence}\:{in}\:{the} \\ $$$${follwing}\:{image}\:: \\ $$$${a}_{\mathrm{1}} =\mathrm{1}\:\:\:,{a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{{nk}\:+\mathrm{1}} \:=\:\frac{{a}_{\mathrm{2}{k}−\mathrm{1}} \:+{a}_{\mathrm{2}{k}} }{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\forall\:{k}\:\in\:{Z}^{+} \\ $$$${a}_{\mathrm{2}{k}+\mathrm{2}} \:=\:\sqrt{{a}_{\mathrm{2}{k}} \:{a}_{\mathrm{2}{k}+\mathrm{1}}…
Question Number 39591 by Rio Mike last updated on 08/Jul/18 $${Given}\:{the}\:{lines}\: \\ $$$${l}_{\mathrm{1}} :−\mathrm{3}{mx}\:+\:\mathrm{3}{y}\:=\:\mathrm{9}\: \\ $$$${and}\:{l}_{\mathrm{2}\:} :\:{y}\:=\:{mx}\:+\:{c} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{m}\:{and}\:{c}\:{if} \\ $$$${the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right)\:{lie}\:{on}\:{both}\:{lines}. \\ $$$${hence}\:{the}\:{tangent}\:{of}\:{the} \\ $$$${curve}\:{y}\:=\:\left({mx}\:+\:{c}\right)^{\mathrm{2}}…
Question Number 39588 by Rio Mike last updated on 08/Jul/18 $${if}\:{cos}\:{A}=\:\frac{\mathrm{3}}{\mathrm{5}}\:{and}\:{tan}\:{B}\:=\:\frac{\mathrm{12}}{\mathrm{5}} \\ $$$${where}\:{A}\:{and}\:{B}\:{are}\:{reflex}\:{angles} \\ $$$${find}\:{without}\:{using}\:{tables},{the} \\ $$$${value}\:{of} \\ $$$$\left.{a}\left.\right)\:{sin}\:\left({A}\:−\:{B}\right)\:{b}\right)\:{tan}\left({A}−{B}\right) \\ $$$$\left.{c}\right)\:{cos}\:\left({A}\:+\:{B}\right). \\ $$ Answered by…
Question Number 39586 by Rio Mike last updated on 08/Jul/18 $${show}\:{that}\: \\ $$$$\left.{a}\right)\:\frac{\mathrm{1}\:+\:\mathrm{2}{sin}\mathrm{2}\theta\:−\:{cos}\mathrm{2}\theta}{\mathrm{1}+{sin}\mathrm{2}\theta\:+\:{cos}\:\mathrm{2}\theta}\:=\:{tan}\:\theta \\ $$$$\left.{b}\right)\:{tan}^{\mathrm{2}} {A}\:−\:{tan}^{\mathrm{2}} {B}\:=\:\frac{{sin}^{\mathrm{2}} {A}−{sin}^{\mathrm{2}} {B}}{{cos}^{\mathrm{2}} {A}\:{cos}^{\mathrm{2}} {B}} \\ $$$$ \\ $$$$…
Solve-for-x-in-the-range-0-x-2pi-the-equations-a-cos-x-pi-3-0-b-sin-x-cos-x-c-sin-2x-2sin-x-1-cos-x-
Question Number 39587 by Rio Mike last updated on 08/Jul/18 $${Solve}\:{for}\:{x}\:{in}\:{the}\:{range}\:\mathrm{0}\:\leqslant\:{x}\:\leqslant\mathrm{2}\pi \\ $$$${the}\:{equations} \\ $$$$\left.{a}\right)\:{cos}\left({x}\:+\:\frac{\pi}{\mathrm{3}}\right)\:=\:\mathrm{0}\: \\ $$$$\left.{b}\right)\:{sin}\:{x}\:=\:{cos}\:{x}. \\ $$$$\left.{c}\right)\:{sin}\:\mathrm{2}{x}\:+\:\mathrm{2}{sin}\:{x}\:=\:\mathrm{1}\:+\:{cos}\:{x} \\ $$$$ \\ $$ Answered by…