Question Number 143186 by zakirullah last updated on 11/Jun/21 Commented by Canebulok last updated on 11/Jun/21 Proof: ⇒ n(n^2 +2n−8) = 0 ⇒ n(n+4)(n−2) = 0 Thus; n = 0 n = −4 n = 2 Commented by zakirullah last updated on 11/Jun/21 $$\mathrm{thank}\:\mathrm{you}…
Question Number 143165 by mohammad17 last updated on 11/Jun/21 $${solve}\:{the}\:{differention}\:{equation} \\ $$$${x}={p}^{\mathrm{3}} −{p}+\mathrm{2}\:\:\:{since}:{p}={y}' \\ $$ Commented by mohammad17 last updated on 11/Jun/21 $$???????\: \\ $$…
Question Number 143156 by mohammad17 last updated on 10/Jun/21 $${lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\left(\mathrm{1}+\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} +……+{n}^{\frac{\mathrm{1}}{{n}}} \right)\:\:? \\ $$ Answered by mr W last updated on 10/Jun/21 $$\mathrm{1}=\frac{{n}×\mathrm{1}}{{n}}<{S}_{{n}} <\frac{{n}×{n}^{\frac{\mathrm{1}}{{n}}}…
Question Number 12082 by chux last updated on 12/Apr/17 Answered by ajfour last updated on 12/Apr/17 $$\mathrm{t}=\frac{\mathrm{s}}{\mathrm{v}}=\frac{\mathrm{s}}{\left(\mathrm{c}/\mu\right)}=\frac{\mu\mathrm{s}}{\mathrm{c}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\left(\mathrm{1}.\mathrm{5}\right)\left(\mathrm{0}.\mathrm{9}×\mathrm{10}^{−\mathrm{2}} \mathrm{m}\right)}{\left(\mathrm{3}×\mathrm{10}^{\mathrm{8}} \mathrm{m}/\mathrm{s}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{45}×\mathrm{10}^{−\mathrm{12}} \mathrm{s} \\…
Question Number 143150 by ZiYangLee last updated on 10/Jun/21 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\begin{vmatrix}{{x}−\mathrm{cos}\:\theta}&{−\mathrm{sin}\:\theta}\\{\mathrm{sin}\:\theta}&{{x}−\mathrm{cos}\:\theta}\end{vmatrix}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\alpha^{{n}} +\beta^{{n}} ,\:\mathrm{where}\:{n}\in\mathbb{N}. \\ $$ Commented by mr W last updated on…
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Question Number 77607 by otchereabdullai@gmail.com last updated on 08/Jan/20 $$\mathrm{Two}\:\mathrm{bell}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{rings}\:\mathrm{in}\:\mathrm{different}\: \\ $$$$\mathrm{time}\:\mathrm{interval}.\:\mathrm{Bell}\:\mathrm{A}\:\mathrm{rings}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{interval}\:\mathrm{of}\:\mathrm{8minutes}\:\mathrm{while}\:\mathrm{Bell}\:\mathrm{B}\:\mathrm{rings} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{of}\:\mathrm{9minutes}.\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{bell}\:\mathrm{rings}\:\mathrm{together}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{time}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{time}\:\mathrm{is}\:\mathrm{10}:\mathrm{00am} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{At}\:\mathrm{what}\:\mathrm{time}\:\mathrm{will}\:\mathrm{the}\:\mathrm{two}\:\mathrm{bell}\:\mathrm{ring} \\ $$$$\mathrm{together}\:\mathrm{again}. \\…
Question Number 143131 by mohammad17 last updated on 10/Jun/21 $${find}\:{the}\:{partial}\:{sums}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)} \\ $$ Answered by qaz last updated on 10/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}}…
Question Number 77591 by naka3546 last updated on 08/Jan/20 $${x}\:+\:\frac{\mathrm{1}}{{x}}\:\:=\:\:\mathrm{1} \\ $$$${x}^{\mathrm{100}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{100}} }\:\:=\:\:? \\ $$$${x}^{\mathrm{2020}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2020}} }\:\:=\:\:? \\ $$ Commented by jagoll last updated…
Question Number 12040 by Mr Chheang Chantria last updated on 10/Apr/17 $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\:\forall\boldsymbol{{x}},\boldsymbol{{y}}\in\boldsymbol{{R}} \\ $$$$\Rightarrow\:\mathrm{1}+\:\frac{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{xy}}}{\mathrm{3}}\:\geqslant\:\boldsymbol{{x}}+\boldsymbol{{y}} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 10/Apr/17…