Question Number 207943 by hardmath last updated on 31/May/24 $$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mid\mathrm{x}\:+\:\mathrm{2}\mid}\:\:=\:\:? \\ $$ Commented by mr W last updated on 31/May/24 $$=\frac{\left(\mathrm{2}+\mathrm{2}\right)\left(\mathrm{2}+\mathrm{1}\right)}{\mid\mathrm{2}+\mathrm{2}\mid}=\mathrm{3}…
Question Number 207937 by efronzo1 last updated on 31/May/24 $$\:\:\mathrm{An}\:\mathrm{ordered}\:\mathrm{data}\:\mathrm{consists}\:\mathrm{of}\: \\ $$$$\:\mathrm{6}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{and}\:\mathrm{4}\:\mathrm{odd}\:\mathrm{numbers}. \\ $$$$\:\mathrm{The}\:\mathrm{average}\:\mathrm{of}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{numbers}\: \\ $$$$\:\mathrm{is}\:\mathrm{2022}.\:\mathrm{The}\:\mathrm{3rd},\:\mathrm{5th},\:\mathrm{6th}\:\mathrm{and} \\ $$$$\:\mathrm{8}\:\mathrm{th}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{odd}.\: \\ $$$$\:\mathrm{The}\:\mathrm{data}\:\mathrm{range}\:\mathrm{is}\:\mathrm{24}\:,\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\:\mathrm{interquartile}\:\mathrm{range}\:\mathrm{is}\:\mathrm{14}.\: \\ $$$$\:\mathrm{The}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{average} \\…
Question Number 207938 by necx122 last updated on 31/May/24 $${what}\:{is}\:{the}\:{area}\:{bounded}\:{by}\:{the}\:{curve} \\ $$$${y}={x}\left({x}−\mathrm{2}\right)\left({x}−\mathrm{5}\right)\:{and}\:{the}\:{x}\:{axis}? \\ $$$$ \\ $$ Answered by mr W last updated on 31/May/24 $${A}=\int_{\mathrm{0}}…
Question Number 207930 by hardmath last updated on 30/May/24 $$\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:\:\:\mathrm{number}\:\mathrm{series} \\ $$$$\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{3}} ^{\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}} \:\:=\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{7}} \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{k}}\:=\:? \\ $$ Commented by mr W…
Question Number 207924 by AliJumaa last updated on 31/May/24 $$\int{f}\left({x}\right){g}\left({x}\right){dx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{{n}} \:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{h}^{{n}} }\:\underset{{i}={o}} {\overset{{n}} {\sum}}\left[\:\left(−\mathrm{1}\right)^{{i}} \left(\frac{{n}!}{{i}!\left({n}−{i}\right)!}\right){f}\left({x}+\left({n}−{i}\right){h}\right)\right]\:\frac{\mathrm{1}}{{n}!}\underset{{a}} {\overset{{x}} {\int}}\left({x}−{t}\right)^{{n}} {g}\left({t}\right){dt}\: \\ $$$${prove}\:{that}\:{right} \\ $$$${its}\:{a}\:{relation}\:{that}\:{i}\:{have}\:{derrived}…
Question Number 207925 by lmcp1203 last updated on 30/May/24 Commented by lmcp1203 last updated on 31/May/24 $${proof}\:\alpha\:=\mathrm{20} \\ $$ Answered by Frix last updated on…
Question Number 207920 by efronzo1 last updated on 30/May/24 $$\:\:\:\:\mathrm{Given}\:\mathrm{p},\mathrm{q}\:,\mathrm{r}\:\mathrm{and}\:\mathrm{s}\:\mathrm{real}\:\mathrm{positive}\: \\ $$$$\:\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\begin{cases}{\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} =\:\mathrm{r}^{\mathrm{2}} +\mathrm{s}^{\mathrm{2}} }\\{\mathrm{p}^{\mathrm{2}} +\mathrm{s}^{\mathrm{2}} −\mathrm{ps}\:=\:\mathrm{q}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} +\mathrm{qr}.}\end{cases} \\ $$$$\:\:\mathrm{Find}\:\:\frac{\mathrm{pq}+\mathrm{rs}}{\mathrm{ps}+\mathrm{qr}}\:. \\…
Question Number 207919 by efronzo1 last updated on 30/May/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Commented by Frix last updated on 30/May/24 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{0}\vee\mathrm{15} \\ $$…
Question Number 207909 by Ismoiljon_008 last updated on 30/May/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 207910 by Ismoiljon_008 last updated on 30/May/24 Answered by A5T last updated on 30/May/24 Commented by A5T last updated on 30/May/24 $${AB}=\sqrt{\left(\mathrm{2}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}}…