Question Number 72693 by Rio Michael last updated on 31/Oct/19 $${prove}\:{that}\:{the}\:{arithmetic}\:{mean}\:{of}\:{a}\:{sequence} \\ $$$${is}\:{greater}\:{or}\:{equal}\:{to}\:{the}\:{geometric}\:{mean}. \\ $$$${that}\:\:{is}\:\: \\ $$$$\:\:\:\:\frac{{a}\:+\:{b}}{\mathrm{2}}\:\geqslant\:\sqrt{{ab}}\: \\ $$ Answered by MJS last updated on…
Question Number 138224 by Bekzod Jumayev last updated on 11/Apr/21 Commented by Bekzod Jumayev last updated on 11/Apr/21 $${Help} \\ $$ Answered by MJS_new last…
Question Number 72688 by Rio Michael last updated on 31/Oct/19 $${Evaluate}\: \\ $$$$\:\underset{{t}\rightarrow\mathrm{9}} {\:{lim}}\frac{\mathrm{9}−{t}}{\mathrm{3}−\sqrt{{t}}\:} \\ $$ Answered by JDamian last updated on 01/Nov/19 $$\underset{{t}\rightarrow\mathrm{9}} {\mathrm{lim}}\left(\frac{\mathrm{9}−{t}}{\mathrm{3}−\sqrt{{t}}\:}×\frac{\mathrm{3}+\sqrt{{t}}}{\mathrm{3}+\sqrt{{t}}}\right)=\underset{{t}\rightarrow\mathrm{9}}…
Question Number 72689 by aliesam last updated on 31/Oct/19 Answered by Tanmay chaudhury last updated on 01/Nov/19 $${IMO}\:\mathrm{2001}\:{question}… \\ $$$${this}\:{question}\:{appeared}\:{in}\:{IMO}\:\mathrm{2001}…{so}\:{pls}\:{search} \\ $$$${you}\:{will}\:{get}\:{solution} \\ $$ Commented…
Question Number 7150 by Tawakalitu. last updated on 13/Aug/16 Commented by Tawakalitu. last updated on 13/Aug/16 $${how}\:{do}\:{you}\:{evaluate}\:{sir} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 138223 by mnjuly1970 last updated on 11/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}\:…\:…\:…\:{calculus}… \\ $$$$\:\:\:{evaluate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\Theta}=\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)^{\mathrm{3}} }\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……………………. \\ $$ Answered by…
Question Number 7149 by Master Moon last updated on 13/Aug/16 $$\mathrm{Find}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{P} \\ $$$$\:\mathrm{P}=\left(\mathrm{2017}^{\boldsymbol{\mathrm{k}}} +\mathrm{2016}\right)\left(\mathrm{2016}^{\boldsymbol{\mathrm{m}}} +\mathrm{2015}\right)\left(\mathrm{2015}^{\boldsymbol{\mathrm{n}}} +\mathrm{2014}\right) \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{k}},\boldsymbol{\mathrm{m}},\boldsymbol{\mathrm{n}}\in{N} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:{Help}\:{me}!!! \\ $$ Terms…
Question Number 138217 by otchereabdullai@gmail.com last updated on 11/Apr/21 $$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{water}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{being}\:\mathrm{filed} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{70lt}/\mathrm{s}.\:\mathrm{The}\: \\ $$$$\mathrm{base}\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{has}\:\mathrm{width}\:\mathrm{w}=\mathrm{9m} \\ $$$$\mathrm{and}\:\mathrm{length}\:\mathrm{length}\:\mathrm{l}=\mathrm{16m}\:\mathrm{if}\:\mathrm{the}\:\mathrm{volume} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{v}=\mathrm{w}×\mathrm{l}×\mathrm{h}\:\mathrm{where}\:\mathrm{h}\:\mathrm{is}\: \\ $$$$\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tank}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{rate} \\ $$$$\mathrm{of}\:\mathrm{change}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{tank} \\…
Question Number 7147 by Tawakalitu. last updated on 13/Aug/16 Commented by Yozzii last updated on 13/Aug/16 $${u}\left({n}\right)=\left(−\mathrm{1}+\mathrm{2}\right)+\left(−\mathrm{3}+\mathrm{4}\right)+\left(−\mathrm{5}+\mathrm{6}\right)+…+\left(−\left(\mathrm{2}{n}−\mathrm{1}\right)+\mathrm{2}{n}\right) \\ $$$${u}\left({n}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{2}{n}+\mathrm{1}+\mathrm{2}{n}\right)={n} \\ $$$${u}\left(\frac{\mathrm{10}^{\mathrm{9}} }{\mathrm{2}}\right)=\frac{\mathrm{10}^{\mathrm{9}} }{\mathrm{2}}…
Question Number 138219 by otchereabdullai@gmail.com last updated on 11/Apr/21 $$\:\mathrm{Consider}\:\mathrm{the}\:\mathrm{function}\:\mathrm{y}=\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{6}}{\mathrm{3x}−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{intercept}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{asymptotes}\:\mathrm{if}\:\mathrm{they}\:\mathrm{exist} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{turning}\:\mathrm{point}\:\mathrm{and}\: \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{type}\:\mathrm{of}\:\mathrm{turnin}\:\mathrm{point}\:\mathrm{they} \\ $$$$\mathrm{are}. \\ $$$$\left.\mathrm{4}\right)\:\mathrm{sketch}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}. \\ $$…