Question Number 33184 by Rio Mike last updated on 12/Apr/18 $${describe}\:{geometrically}\:{the}\:{matrice} \\ $$$$\:\:\:\:\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33158 by Rio Mike last updated on 11/Apr/18 $${the}\:{matrice}\:{which}\:{comes}\:{from} \\ $$$${the}\:{transformation}\:{matrix}\: \\ $$$$\:\begin{pmatrix}{{cos}\theta\:\:\:\:\:\:\:\:\:−{sin}\theta}\\{{sin}\:\theta\:\:\:\:\:\:\:\:\:\:\:\:\:\:{cos}\theta}\end{pmatrix} \\ $$$${at}\:\mathrm{90}°\:{is}? \\ $$ Commented by Joel578 last updated on…
Question Number 33159 by Rio Mike last updated on 11/Apr/18 $${if}\:{y}=\:\mathrm{3}{x}^{\mathrm{4}} \:{find}\:{the}\:{percentage}\:{increase}\:{in}\:{y} \\ $$$${if}\:{x}\:{increases}\:{at}\:\frac{\mathrm{5}}{\mathrm{2}}\%\:{or}\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\overset{} {\%} \\ $$$${use}\:{the}\:{Binomial}\:{Expansion}\:{method} \\ $$$$\left({that}\:{is}\:{find}\:{new}\:{y}\:{and}\:{new}\:{x}\:{and}\:{simplify}\right) \\ $$ Terms of Service Privacy…
Question Number 33157 by Rio Mike last updated on 11/Apr/18 $${find}\:{k}\:{if} \\ $$$${kloga}=\:{loga}\:+\:{log}\:{a}^{\mathrm{2}} +\:{log}\:{a}^{\mathrm{3}\:} +\:{log}\:{a}^{\mathrm{4}} \\ $$ Commented by Joel578 last updated on 11/Apr/18 $$\mathrm{log}\:{a}^{{m}}…
Question Number 33153 by Rio Mike last updated on 11/Apr/18 $${it}\:{is}\:{given}\:{that} \\ $$$$\:\:\underset{{r}=\mathrm{1}\:} {\overset{\mathrm{20}} {\sum}}\left[{f}\left({r}\right)−\mathrm{10}\right]=\mathrm{200} \\ $$$${and} \\ $$$$\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\left[{f}\left({r}\right)−\mathrm{10}\right]^{\mathrm{2}} =\mathrm{2800} \\ $$$${find}\:{the}\:{value}\:{of} \\…
Question Number 33154 by Rio Mike last updated on 11/Apr/18 $${it}\:{is}\:{given}\:{that}\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{U}_{{n}} =\:\frac{\mathrm{1}+\mathrm{3}^{\mathrm{2}{n}+\mathrm{2}} −\mathrm{2}×\mathrm{5}^{{n}+\mathrm{1}} }{\mathrm{8}} \\ $$$${where}\:{U}_{{n}} \:{is}\:{the}\:{n}^{{th}} \:{term}\:{of}\:{a}\:{sequence} \\ $$$${find}\:{the}\:{simplified}\:{expression}\:{for}\:{U}_{{n}} \\ $$ Commented…
Question Number 33152 by Rio Mike last updated on 11/Apr/18 $${it}\:{is}\:{given}\:{that} \\ $$$$\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{x}^{{r}} =\mathrm{2}\:{and}\:\sqrt{\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\left({x}_{{r}} \right)^{\mathrm{2}} −\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left(\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\right)^{\mathrm{2}} }=\:\mathrm{3} \\…
Question Number 33139 by Rio Mike last updated on 11/Apr/18 $$\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\: \\ $$$$\:{ax}^{\mathrm{2}} +{bx}\:+{c}=\mathrm{0} \\ $$$${show}\:{that}\:\alpha+\beta=\:\frac{−{b}}{{a}}\:{and}\:\alpha\beta=\:\frac{{c}}{{a}} \\ $$$${hence}\:{form}\:{an}\:{equation}\:{whose} \\ $$$${sum}\:{of}\:{roots}\:{and}\:{product}\:{of}\:{roots} \\ $$$${are}\:{respectively}\: \\ $$$$\:\:\:−\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:\mathrm{2}. \\…
Question Number 98673 by MJS last updated on 15/Jun/20 $$\mathrm{find}\:{a}_{{n}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n} \\ $$$$\left(\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{find}\:\mathrm{it}…\right) \\ $$$${a}_{\mathrm{1}} =\mathrm{1};\:{a}_{\mathrm{2}} =\mathrm{4} \\ $$$${a}_{\mathrm{3}} ={a}_{\mathrm{2}} ×\mathrm{4}×\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}^{\mathrm{2}} } \\ $$$${a}_{\mathrm{4}}…
Question Number 33135 by Rio Mike last updated on 11/Apr/18 $${the}\:{triangle}\:{with}\:{vertices}\:{A}\left(−\mathrm{1},−\mathrm{3}\right) \\ $$$$,{B}\left(\mathrm{2},\mathrm{1}\right),{and}\:{C}\left(−\mathrm{2},\mathrm{2}\right),\:{is}\:{transformed} \\ $$$${by}\:{matrix}\:\begin{pmatrix}{{a}\:\:\:\:\:\:{b}}\\{{c}\:\:\:\:\:\:\:{d}}\end{pmatrix}\:{into}\:{the}\:{triangle}\:{with}\:{vertices} \\ $$$${A}\left(−\mathrm{2},−\mathrm{3}\bar {\right)},\:{B}\left(\mathrm{4},\mathrm{1}\right),{C}\left(−\bar {\mathrm{4}},\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\: \\ $$$${a},{b},{c}\:{and}\:{d} \\ $$$$ \\ $$…