Question Number 85557 by naka3546 last updated on 23/Mar/20 $${x}\:\:=\:\:\sqrt{\mathrm{1}+\:\sqrt{\mathrm{5}+\:\sqrt{\mathrm{11}+\:\sqrt{\mathrm{19}+…}}}} \\ $$$${x}\:\:=\:\:\:? \\ $$ Commented by MJS last updated on 23/Mar/20 $$\mathrm{2}? \\ $$ Commented…
Question Number 85554 by luxlavanish last updated on 22/Mar/20 $$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$ Commented by naka3546 last updated on 23/Mar/20 $${what}'{s}\:\:{the}\:\:{question}\:? \\ $$ Terms of…
Question Number 20019 by Tinkutara last updated on 20/Aug/17 $$\mathrm{In}\:\mathrm{any}\:\mathrm{triangle}\:{ABC},\:\mathrm{prove}\:\mathrm{that} \\ $$$${a}\:\left(\mathrm{cos}\:{C}\:−\:\mathrm{cos}\:{B}\right)\:=\:\mathrm{2}\:\left({b}\:−\:{c}\right)\:\mathrm{cos}^{\mathrm{2}} \:\frac{{A}}{\mathrm{2}} \\ $$ Answered by ajfour last updated on 20/Aug/17 $${l}.{h}.{s}.={a}\left[\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}}…
Question Number 85555 by luxlavanish last updated on 22/Mar/20 $$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$ Answered by MJS last updated on 23/Mar/20 $${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\Rightarrow \\…
Question Number 151085 by mathdanisur last updated on 18/Aug/21 Answered by talminator2856791 last updated on 18/Aug/21 $$\: \\ $$$$\:\frac{{a}^{\mathrm{2}} −\left({a}+\mathrm{1}\right)^{\mathrm{2}} −\left({a}+\mathrm{2}\right)^{\mathrm{2}} +\left({a}+\mathrm{3}\right)^{\mathrm{2}} }{\left({a}+\mathrm{4}\right)^{\mathrm{2}} −\left({a}+\mathrm{3}\right)^{\mathrm{2}} −\left({a}+\mathrm{2}\right)^{\mathrm{2}}…
Question Number 85551 by jagoll last updated on 22/Mar/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$ Commented by jagoll last updated on 23/Mar/20 Terms of Service…
Question Number 20014 by Tinkutara last updated on 20/Aug/17 $$\mathrm{A}\:\mathrm{person}\:\mathrm{in}\:\mathrm{lift}\:\mathrm{is}\:\mathrm{holding}\:\mathrm{a}\:\mathrm{water}\:\mathrm{jar}, \\ $$$$\mathrm{which}\:\mathrm{has}\:\mathrm{a}\:\mathrm{small}\:\mathrm{hole}\:\mathrm{at}\:\mathrm{the}\:\mathrm{lower}\:\mathrm{end} \\ $$$$\mathrm{of}\:\mathrm{its}\:\mathrm{side}.\:\mathrm{When}\:\mathrm{the}\:\mathrm{lift}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest},\:\mathrm{the} \\ $$$$\mathrm{water}\:\mathrm{jet}\:\mathrm{coming}\:\mathrm{out}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hole}\:\mathrm{hits} \\ $$$$\mathrm{the}\:\mathrm{floor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lift}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:{d}\:\mathrm{of} \\ $$$$\mathrm{1}.\mathrm{2}\:\mathrm{m}\:\mathrm{from}\:\mathrm{the}\:\mathrm{person}.\:\mathrm{In}\:\mathrm{the}\:\mathrm{following}, \\ $$$$\mathrm{state}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lift}'\mathrm{s}\:\mathrm{motion}\:\mathrm{is}\:\mathrm{given}\:\mathrm{in}\:\mathrm{List} \\ $$$$\mathrm{I}\:\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{where}\:\mathrm{the}\:\mathrm{water}\:\mathrm{jet} \\…
Question Number 20013 by Tinkutara last updated on 20/Aug/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\frac{\mathrm{1}}{{x}\:−\:{a}}\:+\:\frac{\mathrm{1}}{{x}\:−\:{b}} \\ $$$$+\:\frac{\mathrm{1}}{{x}\:−\:{c}}\:=\:\mathrm{0}\:\mathrm{can}\:\mathrm{have}\:\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{equal} \\ $$$$\mathrm{roots}\:\mathrm{if}\:{a}\:=\:{b}\:=\:{c}. \\ $$ Commented by ajfour last updated on 20/Aug/17 $${how}\:{did}\:{u}\:{solve}\:{it}\:,\:{please}\:{let}\:{me} \\…
Question Number 151081 by malwan last updated on 18/Aug/21 $${if}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:{f}\left({x}+\mathrm{3}\right)=\mathrm{7}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\:{find} \\ $$$$\left.\mathrm{1}\left.\right)\:{a}+{b}+{c}\:\:\:\:\:\mathrm{2}\right)\:{a}−{b}+{c} \\ $$ Answered by mr W last updated on…
Question Number 85546 by TawaTawa1 last updated on 22/Mar/20 Commented by TawaTawa1 last updated on 23/Mar/20 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum},\:\mathrm{S},\:\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{with}\:\mathrm{a}\:\mathrm{common} \\ $$$$\mathrm{ratio}\:\:\mathrm{4}\:\:\mathrm{is}\:\:\mathrm{14},\mathrm{450}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{and}\:\mathrm{lies}\:\mathrm{between}\:\mathrm{100}\:\mathrm{and}\:\mathrm{500}. \\ $$$$\mathrm{Does}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{agree}\:\mathrm{with}\:\mathrm{output}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\left(\mathrm{given}\:\mathrm{below}\right)?.\:\mathrm{Show}\:\mathrm{your}\:\mathrm{workings}…