Question Number 151216 by liberty last updated on 19/Aug/21 $$\:\:\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\:\:\sqrt[{\mathrm{7}}]{\mathrm{x}+\mathrm{3}}\:+\sqrt[{\mathrm{7}}]{\mathrm{6}−\mathrm{x}}\:=\:\sqrt[{\mathrm{7}}]{\mathrm{9}}\: \\ $$ Answered by MJS_new last updated on 19/Aug/21 $$\mathrm{very}\:\mathrm{obviously}\:{x}=−\mathrm{3}\vee{x}=\mathrm{6} \\ $$ Commented…
Question Number 85588 by TawaTawa1 last updated on 23/Mar/20 Commented by john santu last updated on 23/Mar/20 $$\mathrm{14},\mathrm{450}\:=\:\frac{{a}\left(\mathrm{4}^{{n}} −\mathrm{1}\right)}{\mathrm{3}} \\ $$$$\mathrm{43},\mathrm{350}\:=\:{a}\:\left(\mathrm{4}^{{n}} −\mathrm{1}\right) \\ $$$${a}\:=\:\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}} −\mathrm{1}}\:\Rightarrow\:\mathrm{100}<\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}}…
Question Number 85546 by TawaTawa1 last updated on 22/Mar/20 Commented by TawaTawa1 last updated on 23/Mar/20 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum},\:\mathrm{S},\:\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{with}\:\mathrm{a}\:\mathrm{common} \\ $$$$\mathrm{ratio}\:\:\mathrm{4}\:\:\mathrm{is}\:\:\mathrm{14},\mathrm{450}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{and}\:\mathrm{lies}\:\mathrm{between}\:\mathrm{100}\:\mathrm{and}\:\mathrm{500}. \\ $$$$\mathrm{Does}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{agree}\:\mathrm{with}\:\mathrm{output}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\left(\mathrm{given}\:\mathrm{below}\right)?.\:\mathrm{Show}\:\mathrm{your}\:\mathrm{workings}…
Question Number 151079 by mathdanisur last updated on 18/Aug/21 Answered by dumitrel last updated on 18/Aug/21 Commented by dumitrel last updated on 18/Aug/21 Commented by…
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Question Number 150903 by puissant last updated on 16/Aug/21 $${let}\:{x},{y}>\mathrm{0}\:,\:{n}\in\mathbb{N}, \\ $$$${show}\:{that}\:\left({x}+{y}\right)^{{n}} \leqslant\mathrm{2}^{{n}−\mathrm{1}} \left({x}^{{n}} +{y}^{{n}} \right).. \\ $$ Answered by qaz last updated on 16/Aug/21…
Question Number 19812 by Joel577 last updated on 16/Aug/17 $$\mathrm{If}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{of}\:\mathrm{equation}\:{y}\:=\:\frac{{x}}{\mathrm{3}\:−\:{x}}\:\mathrm{at}\: \\ $$$${x}\:=\:{a}\:\mathrm{crossed}\:\mathrm{line}\:{y}\:=\:{x}\:\mathrm{at}\:\left({b},{b}\right) \\ $$$$\mathrm{Find}\:{b}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a} \\ $$ Answered by ajfour last updated on 16/Aug/17 $$\mathrm{y}=−\mathrm{1}−\frac{\mathrm{3}}{\mathrm{x}−\mathrm{3}}\:\:\:\:\:\Rightarrow\:\:\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{3}}{\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} }…
Question Number 19704 by Tinkutara last updated on 14/Aug/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\left(\mathrm{in}\:\mathrm{base}\:\mathrm{10}\right)\:\mathrm{of}\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{natural}\:\mathrm{numbers}\:\mathrm{less}\:\mathrm{than}\:\mathrm{64}\:\mathrm{which} \\ $$$$\mathrm{have}\:\mathrm{exactly}\:\mathrm{three}\:\mathrm{ones}\:\mathrm{in}\:\mathrm{their}\:\mathrm{base}\:\mathrm{2} \\ $$$$\mathrm{representation}? \\ $$ Answered by mrW1 last updated on 15/Aug/17…
Question Number 19683 by 786786AM last updated on 14/Aug/17 $$\mathrm{In}\:\mathrm{an}\:\mathrm{A}.\mathrm{P};\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{is}\:−\mathrm{2}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{term}\:\:\mathrm{exceeds}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{by}\:\mathrm{58}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$ Answered by Rasheed.Sindhi last updated on 15/Aug/17 $$\mathrm{Let}\:\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{middle}\:\mathrm{term} \\ $$$$\mathrm{m}+\mathrm{58}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{term}. \\…
Question Number 85184 by Serlea last updated on 19/Mar/20 $$\mathrm{Serlea} \\ $$$$\mathrm{Shows}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digit}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{100}^{\mathrm{25}} −\mathrm{25} \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{4}. \\ $$ Commented by mr W last updated…