Question Number 4592 by love math last updated on 09/Feb/16 $$\frac{\mathrm{1}}{\mathrm{2}}+{log}_{\mathrm{9}} {x}−{log}_{\mathrm{3}} \mathrm{5}{x}>{log}_{\frac{\mathrm{1}}{\mathrm{3}}} \left({x}+\mathrm{1}\right) \\ $$ Answered by Rasheed Soomro last updated on 10/Feb/16 $$\frac{\mathrm{1}}{\mathrm{2}}+{log}_{\mathrm{9}}…
Question Number 4589 by FilupSmith last updated on 09/Feb/16 $${a}_{{n}} =\sqrt{\mathrm{2}+{a}_{{n}−\mathrm{1}} } \\ $$$${a}_{\mathrm{1}} =\sqrt{\mathrm{2}} \\ $$$$ \\ $$$${L}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} =\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+…}}}} \\ $$$${L}=? \\ $$…
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Question Number 4587 by FilupSmith last updated on 09/Feb/16 $${L}=\underset{{i}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {i}}{{i}+\mathrm{1}} \\ $$$${L}=? \\ $$ Commented by Yozzii last updated on 14/Feb/16 $${L}\:{does}\:{not}\:{exist}.\:{While}\:\mid{L}\mid=\underset{{i}\rightarrow\infty} {\mathrm{lim}}\frac{{i}}{{i}+\mathrm{1}}…
Question Number 135656 by otchereabdullai@gmail.com last updated on 14/Mar/21 $$\mathrm{500},\:\mathrm{108},\mathrm{54}\:\mathrm{and}\:\mathrm{15}\:\mathrm{are}\:\mathrm{are}\:\mathrm{not}\: \\ $$$$\mathrm{perfect}\:\mathrm{cubes}\:\mathrm{how}\:\mathrm{do}\:\mathrm{we}\:\mathrm{factorize} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{500X}^{\mathrm{3}} −\mathrm{108Y}^{\mathrm{3}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{54X}^{\mathrm{3}} +\mathrm{15Y}^{\mathrm{3}} \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{well}\:\mathrm{explained}\: \\ $$$$\mathrm{steps}\:\mathrm{or}\:\mathrm{shortcut}\:\mathrm{thanks} \\ $$ Commented…
Question Number 135658 by I want to learn more last updated on 14/Mar/21 Answered by mr W last updated on 15/Mar/21 Commented by mr W…
Question Number 70121 by ahmadshahhimat775@gmail.com last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $${let}\:{a}\:{angle}\:{left}\:−,{c}\:{side}\:{of}\:{squar} \\ $$$$\Rightarrow{c}=\mathrm{6}{sin}\left({a}\right) \\ $$$$\frac{\mathrm{6}{sin}\left({a}\right)+\mathrm{6}{cos}\left({a}\right)}{{sin}\left(\mathrm{45}\right)}=\frac{\mathrm{10}}{{sin}\left(\mathrm{45}+{a}\right)} \\ $$$$\Rightarrow\mathrm{6}.\left({sin}\left({a}\right)+{cos}\left({a}\right)\right).{sin}\left(\mathrm{45}+{a}\right)=\mathrm{10}{sin}\left(\mathrm{45}\right)…
Question Number 4584 by MrGreg last updated on 08/Feb/16 $$ \\ $$ Answered by FilupSmith last updated on 09/Feb/16 $$\:\:\:\:{S}=\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+\mathrm{64}−… \\ $$$$+{S}=\mathrm{0}+\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+\mathrm{64}−… \\ $$$$\mathrm{2}{S}=\mathrm{1}+\left(−\mathrm{1}+\mathrm{2}−\mathrm{4}+\mathrm{8}−\mathrm{16}+…\right) \\…
Question Number 135653 by I want to learn more last updated on 14/Mar/21 Commented by mr W last updated on 14/Mar/21 $${question}\:{is}\:{wrong}.\:{just}\:{check}\:{again}. \\ $$ Commented…
Question Number 4582 by FilupSmith last updated on 08/Feb/16 $${S}=\mathrm{log}_{{a}} {i} \\ $$$${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$${a}\in\mathbb{R} \\ $$$${Solve}\:{S} \\ $$$$ \\ $$$${extra}: \\ $$$$\mathrm{what}\:\mathrm{if}\:\:{a}\in\mathbb{C}? \\…