Question Number 142208 by ZiYangLee last updated on 27/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{orthogonal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{circles}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{7}{x}−{y}=\mathrm{0} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{6}{y}+\mathrm{5}=\mathrm{0}\:\mathrm{and}\:\mathrm{which}\:\mathrm{passes} \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(−\mathrm{3},\mathrm{0}\right). \\ $$ Answered by mr…
Question Number 142205 by mohammad17 last updated on 27/May/21 Commented by mohammad17 last updated on 27/May/21 $${help}\:{me}\:{sir}\:? \\ $$ Commented by mohammad17 last updated on…
Question Number 142204 by mnjuly1970 last updated on 27/May/21 Answered by MJS_new last updated on 28/May/21 $$\mathrm{what}\:\mathrm{are}\:\mathrm{you}\:\mathrm{waiting}\:\mathrm{for}? \\ $$$${A}^{\mathrm{2}} =\begin{bmatrix}{\mathrm{7}}&{\mathrm{2}{m}−\mathrm{5}}&{\mathrm{5}}\\{\mathrm{2}}&{{m}^{\mathrm{2}} −\mathrm{1}}&{{m}+\mathrm{2}}\\{\mathrm{2}}&{\mathrm{2}−{m}}&{\mathrm{9}}\end{bmatrix} \\ $$$${A}^{\mathrm{4}} =\begin{bmatrix}{\mathrm{4}{m}+\mathrm{49}}&{\mathrm{2}{m}^{\mathrm{3}} −\mathrm{5}{m}^{\mathrm{2}}…
Question Number 142207 by 777316 last updated on 27/May/21 Answered by mr W last updated on 28/May/21 $${say}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}} ={L} \\ $$$${L}=\frac{\mathrm{3}{L}+\mathrm{4}}{\mathrm{2}{L}+\mathrm{3}} \\ $$$$\mathrm{2}{L}^{\mathrm{2}} +\mathrm{3}{L}=\mathrm{3}{L}+\mathrm{4}…
Question Number 76669 by aliesam last updated on 29/Dec/19 Commented by benjo 1/2 santuyy last updated on 29/Dec/19 $${what}\:{Li}^{\mathrm{2}} \left({sin}\left({x}\right)\right)\:{sir}? \\ $$ Commented by aliesam…
Question Number 11131 by Joel576 last updated on 13/Mar/17 $$\mathrm{Proof}\:\mathrm{with}\:\mathrm{induction},\:\mathrm{for}\:\mathrm{every}\:{n}\:\in\:\mathbb{N} \\ $$$$\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{2}^{{i}\:+\:\mathrm{2}} \:=\:\mathrm{2}^{{n}\:+\:\mathrm{3}} \:−\:\mathrm{8} \\ $$ Commented by Joel576 last updated on 13/Mar/17…
Question Number 142200 by liberty last updated on 27/May/21 $$\:{Let}\:{p}\:\&\:{q}\:{real}\:{positive}\:{number} \\ $$$$\:\:{what}\:{the}\:{minimum}\:{of}\:\left(\frac{{p}^{\mathrm{2}} }{{q}^{\mathrm{2}} }\:+\frac{{q}}{{p}}\right)^{\mathrm{3}} . \\ $$ Answered by MJS_new last updated on 27/May/21 $$\mathrm{let}\:{q}={pt}\wedge{t}>\mathrm{0}…
Question Number 76667 by naka3546 last updated on 29/Dec/19 Commented by benjo 1/2 santuyy last updated on 29/Dec/19 $${using}\:{L}'{Hopital}\:{Rule}\: \\ $$ Answered by john santu…
Question Number 76664 by aliesam last updated on 29/Dec/19 $$\int_{\mathrm{0}} ^{+\infty} \frac{{t}\:{ln}\left({t}\right)}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dt} \\ $$ Commented by mathmax by abdo last updated on 29/Dec/19…
Question Number 76663 by aliesam last updated on 29/Dec/19 Answered by benjo 1/2 santuyy last updated on 29/Dec/19 $$\mathrm{2}^{\mathrm{3}{n}\:} \:? \\ $$ Answered by mind…