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} \\ $$…
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Question Number 207910 by Ismoiljon_008 last updated on 30/May/24 Answered by A5T last updated on 30/May/24 Commented by A5T last updated on 30/May/24 $${AB}=\sqrt{\left(\mathrm{2}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}}…
Question Number 207904 by Ahmed777hamouda last updated on 30/May/24 Commented by Ahmed777hamouda last updated on 30/May/24 $$\mathrm{H}{ow}\:\boldsymbol{\mathrm{prove}}\:\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} =\mathrm{2}\boldsymbol{\mathrm{I}}_{{o}} \boldsymbol{\mathrm{J}}_{{n}} \left(\boldsymbol{\mathrm{nx}}\right)\mathrm{cos}\:\left(\boldsymbol{\mathrm{n}}\theta_{\boldsymbol{\mathrm{g}}} +\boldsymbol{\mathrm{n}\theta}_{\boldsymbol{\mathrm{n}}} \right) \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{fourier}}\:\boldsymbol{\mathrm{series}} \\…
Question Number 207906 by nachosam last updated on 30/May/24 $${help} \\ $$$$\int_{\mathrm{1}} ^{\:\infty} {x}^{−{ln}\left({x}\right)} {dx} \\ $$$$ \\ $$ Answered by Berbere last updated on…
Question Number 207901 by Tawa11 last updated on 29/May/24 Answered by mr W last updated on 30/May/24 $$\boldsymbol{{v}}=\frac{{d}\boldsymbol{{r}}}{{dt}}={e}^{{t}} \left(\mathrm{cos}\:{t}−\mathrm{sin}\:{t}\right)\:\boldsymbol{{i}}+{e}^{{t}} \left(\mathrm{sin}\:{t}+\:\mathrm{cos}\:{t}\right)\:\boldsymbol{{j}} \\ $$$$\boldsymbol{{a}}=\frac{{d}\boldsymbol{{v}}}{{dt}}=−\mathrm{2}{e}^{{t}} \:\mathrm{sin}\:{t}\:\boldsymbol{{i}}+\mathrm{2}{e}^{{t}} \:\mathrm{cos}\:{t}\:\boldsymbol{{j}} \\…