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…
Question Number 19637 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{five}-\mathrm{digit} \\ $$$$\mathrm{integers}\:\left(\mathrm{37}{abc}\right)\:\mathrm{in}\:\mathrm{base}\:\mathrm{10}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\left(\mathrm{37}{abc}\right),\:\left(\mathrm{37}{bca}\right) \\ $$$$\mathrm{and}\:\mathrm{37}{cab}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}. \\ $$ Answered by Rasheed.Sindhi last updated on 14/Aug/17…
Question Number 84982 by M±th+et£s last updated on 18/Mar/20 $$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} \:{H}_{{n}+\mathrm{1}} }{{n}^{\mathrm{3}} −{n}} \\ $$ Answered by Kamel Kamel last updated on 18/Mar/20…
Question Number 84976 by jagoll last updated on 18/Mar/20 Commented by jagoll last updated on 18/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\: \\ $$ Commented by jagoll last updated on…
Question Number 150500 by EnterUsername last updated on 13/Aug/21 $$\mathrm{Find}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}-\mathrm{n}\:\mathrm{terms}\:\mathrm{in} \\ $$$${u}_{{n}} =\mathrm{4},\:\mathrm{9},\:\mathrm{15},\:\mathrm{23},\:\mathrm{35},\:\mathrm{55},\:\mathrm{91},\:\mathrm{159},… \\ $$ Commented by CAIMAN last updated on 13/Aug/21 Un=2^n-1+4n -1 Answered by…
Question Number 150462 by Tawa11 last updated on 12/Aug/21 Answered by puissant last updated on 12/Aug/21 $$\mathrm{I}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{ln}\left(\frac{\mathrm{2}+\mathrm{3n}}{\mathrm{1}+\mathrm{3n}}\right) \\ $$$$\mathrm{posons}\:\mathrm{U}_{\mathrm{n}} =\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{ln}\left(\frac{\mathrm{2}+\mathrm{3n}}{\mathrm{1}+\mathrm{3n}}\right) \\…
Question Number 84904 by john santu last updated on 17/Mar/20 $$\mathrm{3}^{\mathrm{2x}^{\mathrm{2}} } \:+\:\mathrm{3}^{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}} \:\geqslant\:\mathrm{10}.\:\mathrm{3}^{\mathrm{4x}+\mathrm{6}} \\ $$$$ \\ $$ Commented by john santu last updated…