Question Number 35512 by Rio Mike last updated on 19/May/18 $$\:{Given}\:{that}\:\left({x}+\mathrm{1},\mathrm{3},{x}\right)\:{are}\:{lengths} \\ $$$${of}\:{the}\:{sides}\:{of}\:{a}\:{right}\:{angled} \\ $$$${triangle}\left({pythagoras}\:{tripple}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{x}. \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 35513 by Rio Mike last updated on 19/May/18 $${g}\left({x}\right)=\:\mathrm{6}{x}^{\mathrm{2}} −\:\mathrm{5}{ax}\:+\:{b}^{\mathrm{2}} \\ $$$${given}\:{that}\:{g}\left({x}\right)\:{has}\:{only}\:{two}\:{roots} \\ $$$${and}\:{are}\:\left({x}−\mathrm{1}\right)\:{and}\:\left({x}−\mathrm{2}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}.{Using} \\ $$$$\left({x}−\mathrm{1}\right)\:{as}\:{a}\:{root}\:{detemine}\:{the}\: \\ $$$${extend}\:{to}\:{which}\:\left({x}−\mathrm{2}\right)\:{is}\:{a}\:{root} \\ $$$$\left({occurance}\:{as}\:{a}\:{root}\right). \\…
Question Number 166573 by Rasheed.Sindhi last updated on 22/Feb/22 Commented by henderson last updated on 22/Feb/22 $$\mathrm{very}\:\mathrm{nice} \\ $$ Answered by peter frank last updated…
Question Number 101026 by 175 last updated on 29/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}}{{e}^{\:\mathrm{sin}{x}\:−{x}} } \\ $$ Answered by mathmax by abdo last updated on 29/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}}{\mathrm{e}^{\mathrm{sinx}−\mathrm{x}} }\:=\mathrm{x}\:\mathrm{e}^{\mathrm{x}}…
Question Number 35482 by Joel579 last updated on 19/May/18 $$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{3}\:×\mathrm{3}\:\mathrm{matrices}.\:\mathrm{The}\:\mathrm{statements}\:\mathrm{below} \\ $$$$\mathrm{which}\:\mathrm{is}\:{True}\:\mathrm{is}\:… \\ $$$$\left(\mathrm{A}\right)\:{AB}\:=\:{BA} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{If}\:{AB}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{only}\:{A}\:=\:\mathrm{0}\:\mathrm{or}\:{B}\:=\:\mathrm{0}\:\mathrm{is}\:\mathrm{true} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{If}\:{AB}\:=\:{I},\:\mathrm{then}\:\mathrm{only}\:{A}\:=\:{I}\:\mathrm{or}\:{A}\:=\:−{I}\:\mathrm{is}\:\mathrm{true} \\ $$$$\left(\mathrm{D}\right)\:\mathrm{There}\:\mathrm{exist}\:{A}\:\mathrm{where}\:{A}\:\neq\:\mathrm{0},\:\mathrm{and}\:\mathrm{yet}\:{A}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\left(\mathrm{E}\right)\:\mid{A}\:+\:{B}\mid\:=\:\mid{A}\mid\:+\:\mid{B}\mid \\ $$…
Question Number 35478 by 7991 last updated on 19/May/18 $$\sqrt[{\mathrm{5}}]{\mathrm{3}\sqrt{\mathrm{2}}\left(\mathrm{2}−{i}\right)}=…?? \\ $$ Commented by MJS last updated on 19/May/18 $$\mathrm{these}\:\mathrm{are}\:\mathrm{all}\:\mathrm{the}\:\mathrm{same} \\ $$$${z}={a}+{b}\mathrm{i}={r}\mathrm{e}^{\varphi\mathrm{i}} ={r}\mathrm{cos}\left(\varphi\right)+{r}\mathrm{sin}\left(\varphi\right)\mathrm{i} \\ $$$${z}^{\frac{{p}}{{q}}}…
Question Number 35460 by Rio Mike last updated on 19/May/18 $${Find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which} \\ $$$${the}\:{equation}\: \\ $$$$\begin{pmatrix}{{k}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\\{\mathrm{10}\:\:\:\:\:\:\:−{k}+\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{k}−\mathrm{1}}\\{\mathrm{8}}\end{pmatrix} \\ $$$${have} \\ $$$$\left.{a}\right)\:{a}\:\:{unique}\:{solution} \\ $$$$\left.{b}\right)\:{no}\:{solution} \\ $$$$\left.{c}\right){an}\:{infinite}\:{solution} \\ $$$${hence}…
Question Number 100986 by Dwaipayan Shikari last updated on 29/Jun/20 Commented by bachamohamed last updated on 29/Jun/20 $$\boldsymbol{{look}}\:\boldsymbol{{this}}\: \\ $$$$\mathrm{2}=\sqrt{\mathrm{1}+\sqrt{\mathrm{9}}}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{8}}}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{64}}}}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{63}}}} \\ $$$$\:\:=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{63}^{\mathrm{2}} }}}}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\left(\mathrm{63}^{\mathrm{2}} −\mathrm{1}\right)}}}} \\…
Question Number 100985 by Dwaipayan Shikari last updated on 29/Jun/20 Commented by Dwaipayan Shikari last updated on 29/Jun/20 $${is}\:{this}\:{a}\:{solution}? \\ $$ Commented by Dwaipayan Shikari…
Question Number 35426 by Rio Mike last updated on 18/May/18 $${find}\:{the}\:{value}\:{of}\:{x}\:{if}\:{the}\:{inverse} \\ $$$${of}\:{the}\:{matrix}\:\begin{pmatrix}{{x}+\mathrm{5}\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{7}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}}\end{pmatrix}\:{is} \\ $$$$\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix} \\ $$ Commented by prof Abdo imad last updated on…