Question Number 30538 by SammyKT last updated on 23/Feb/18 $${A}\:{man}\:{rows}\:{a}\:{boat}\:{downstream} \\ $$$${for}\:\mathrm{3}\:{hours}\:{and}\:{then}\:{upstream} \\ $$$${for}\:\mathrm{3}\:{hours}.\:{If}\:{he}\:{covered}\:{a} \\ $$$${total}\:{distance}\:{of}\:\mathrm{12}{km},\:{find} \\ $$$${the}\:{speed}\:{of}\:{the}\:{water}\:{current}. \\ $$$$ \\ $$ Answered by mrW2…
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Question Number 95849 by bobhans last updated on 28/May/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{n}}?? \\ $$ Answered by john santu last updated on 28/May/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}}\right)\:=\:\underset{\mathrm{n}\rightarrow\infty}…
Question Number 161323 by mnjuly1970 last updated on 16/Dec/21 $$ \\ $$$$\:\:\:{prove} \\ $$$$ \\ $$$$\:\:\:\:\begin{pmatrix}{\:\:−{n}\:}\\{\:\:\:\:\:{k}}\end{pmatrix}\:\overset{?} {=}\:\left(−\mathrm{1}\right)^{\:{k}} \:\begin{pmatrix}{\:{n}\:+{k}\:−\mathrm{1}}\\{\:\:\:\:\:\:\:\:\:{k}}\end{pmatrix} \\ $$$$\:\:\:{example}\::\:\:\begin{pmatrix}{\:−\mathrm{5}}\\{\:\:\:\mathrm{4}}\end{pmatrix}\:=\:\begin{pmatrix}{\:\mathrm{8}}\\{\:\:\mathrm{4}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\: \\ $$ Commented…
Question Number 161066 by blackmamba last updated on 11/Dec/21 $$\:{x}_{\mathrm{1}} \:,{x}_{\mathrm{2}} \:{be}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$$\:\:\:\:\:\:{x}^{\mathrm{2}} +{x}+{m}=\mathrm{0}\:\&\:{x}_{\mathrm{1}} ^{\mathrm{5}} +{x}_{\mathrm{2}} ^{\mathrm{5}} \:=\:\mathrm{2021}. \\ $$$$\:{Find}\:{the}\:{sum}\:{of}\:{the}\:{possible}\:{values} \\ $$$$\:\:{of}\:{m}. \\ $$…
Question Number 161061 by cortano last updated on 11/Dec/21 Answered by MJS_new last updated on 11/Dec/21 $$\sqrt{{A}}−\sqrt{{B}}={x}\sqrt{{C}} \\ $$$${A}+{B}−\mathrm{2}\sqrt{{AB}}={x}^{\mathrm{2}} {C} \\ $$$$\mathrm{2}\left(\mathrm{2}^{\mathrm{3}/\mathrm{4}} −\sqrt{\mathrm{1}+\sqrt{\mathrm{2}}}\right)={x}^{\mathrm{2}} \left(\mathrm{2}^{\mathrm{3}/\mathrm{4}} −\sqrt{\mathrm{1}+\sqrt{\mathrm{2}}}\right)…
Question Number 29909 by *D¬ B£$T* last updated on 13/Feb/18 $${please}\:{solve}\:{this}:\:\:\sqrt{\mathrm{30}+\mathrm{12}\sqrt{\mathrm{6}}} \\ $$ Commented by rahul 19 last updated on 13/Feb/18 $$\sqrt{\mathrm{30}+\mathrm{12}\sqrt{\mathrm{6}\:}}=\:\sqrt{\mathrm{30}+\mathrm{2}\sqrt{\mathrm{216}\:\:}=}\left(\sqrt{\mathrm{a}}\:+\sqrt{\mathrm{b}}\right). \\ $$$$\mathrm{so}\:\mathrm{a}+\mathrm{b}=\mathrm{30} \\…
Question Number 160976 by alf123 last updated on 10/Dec/21 Answered by TheSupreme last updated on 10/Dec/21 $$\frac{{x}}{{y}}={s} \\ $$$$\mathrm{2}^{{sy}} +\mathrm{3}^{{y}} =\mathrm{21} \\ $$$$\mathrm{2}^{\frac{{s}}{\mathrm{2}}} =\mathrm{3}\:\rightarrow\:{s}\:=\:\mathrm{2}\:\frac{{ln}\left(\mathrm{3}\right)}{{ln}\left(\mathrm{2}\right)} \\…
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Question Number 29818 by ajfour last updated on 12/Feb/18 $$\mathrm{4},\:\mathrm{8},\:\mathrm{16},\:\mathrm{31},\:\mathrm{57},\:\mathrm{99},\:\mathrm{163},\:{T}_{\mathrm{8}} \:,{T}_{\mathrm{9}} \:,\:…. \\ $$$${Find}\:{T}_{\mathrm{8}} \:,\:{T}_{\mathrm{9}} \:. \\ $$ Answered by puneet1789 last updated on 12/Feb/18…