Question Number 186099 by akuba last updated on 01/Feb/23 $$\mathrm{1}.\:{Solve}\:{for}\:{the}\:{linear}\:{system}: \\ $$$${x}−\mathrm{2}{y}+\mathrm{3}{z}=\mathrm{5} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{4}{z}=\mathrm{0} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}−\mathrm{11}{z}=−\mathrm{5} \\ $$$$\mathrm{2}.\:{Ghana}\:{railways}\:{co}−{operation}\:{has}\:\mathrm{20}\: \\ $$$${trains}\:{for}\:{it}'{s}\:{operations}.\:{It}\:{is}\:{observed}\:{that} \\ $$$${x}\:{trains}\:{can}\:{accommodate}\:\mathrm{2}\:{passengers}, \\ $$$${y}\:{trains}\:\mathrm{3}\:{passengers}\:{and}\:{z}\:{trains}\:\mathrm{5}\: \\…
Question Number 120558 by peter frank last updated on 01/Nov/20 Answered by mr W last updated on 01/Nov/20 $${from} \\ $$$${e}^{{i}\theta} =\mathrm{cos}\:\theta+{i}\:\mathrm{sin}\:\theta \\ $$$${e}^{−{i}\theta} =\mathrm{cos}\:\theta−{i}\:\mathrm{sin}\:\theta…
Question Number 120556 by bobhans last updated on 01/Nov/20 Commented by bobhans last updated on 01/Nov/20 $$\mathrm{The}\:\mathrm{graph}\:\mathrm{y}=\sqrt{\mathrm{x}}\:\mathrm{and}\:\mathrm{y}=\mathrm{5}−\mathrm{x}^{\mathrm{2}} \:\mathrm{intersect}\:\mathrm{at} \\ $$$$\mathrm{one}\:\mathrm{point}\:\mathrm{x}=\mathrm{r}\:.\:\mathrm{use}\:\mathrm{newton}\:\mathrm{method} \\ $$$$\mathrm{to}\:\mathrm{estimate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{r}\:\mathrm{to} \\ $$$$\mathrm{four}\:\mathrm{decimal}\:\mathrm{places} \\…
Question Number 55014 by Rio Mike last updated on 16/Feb/19 $${what}\:{is}\:{the}\:{value}\:{of}\:{t}\:{that}\:{makes}\: \\ $$$${x}^{\mathrm{2}} +\mathrm{10}{x}+{t}\:{a}\:{perfect}\:{square}? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Answered by peter…
Question Number 55011 by tm888 last updated on 16/Feb/19 $$\underset{{k}={o}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}−{x}^{{k}} }\:\:\:\:{find}\:{out}\:{the}\:{summetion} \\ $$$$ \\ $$ Commented by Meritguide1234 last updated on 16/Feb/19 $$\mathrm{no}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{possible}…
Question Number 120545 by pooooop last updated on 01/Nov/20 $$\left(\sqrt{\boldsymbol{{x}}}\right)^{\frac{\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{x}}}}} \:=\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\:\:\:\boldsymbol{{x}}=? \\ $$ Commented by pooooop last updated on 01/Nov/20 $$ \\ $$$$\:\:\:\left(\sqrt{{x}}\right)^{\frac{{x}\sqrt{{x}}}{{x}}} =\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\…
Question Number 120529 by bemath last updated on 01/Nov/20 Commented by bemath last updated on 01/Nov/20 Answered by Dwaipayan Shikari last updated on 01/Nov/20 $$\:\:\:\:\:\:\:{S}=\mathrm{1}+\mathrm{2}{a}+\mathrm{3}{a}^{\mathrm{2}}…
Question Number 186053 by Rupesh123 last updated on 31/Jan/23 Answered by SEKRET last updated on 31/Jan/23 $$\:\:\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{a}}−\mathrm{1}=\mathrm{0}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\mathrm{5}\boldsymbol{\mathrm{a}}+\mathrm{1} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{a}}^{\mathrm{3}} =\mathrm{5}\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}=\mathrm{5}\left(\mathrm{5}\boldsymbol{\mathrm{a}}+\mathrm{1}\right)+\boldsymbol{\mathrm{a}}=\mathrm{26}\boldsymbol{\mathrm{a}}+\mathrm{5} \\ $$$$\:\:\:\left(\mathrm{26}\boldsymbol{\mathrm{a}}+\mathrm{5}\right)^{\mathrm{2}}…
Question Number 54983 by ajfour last updated on 15/Feb/19 $${Find}\:{shortest}\:{distance}\:{from}\:{origin} \\ $$$${to}\:{the}\:{cubic}\:\:\:{y}={x}^{\mathrm{3}} −\mathrm{10}{x}^{\mathrm{2}} +\mathrm{27}{x}−\mathrm{18}. \\ $$ Commented by mr W last updated on 15/Feb/19 $${you}\:{can}\:{apply}\:{your}\:{solution}\:{method}\:{for}…
Question Number 186025 by SAMIRA last updated on 31/Jan/23 $$\boldsymbol{\mathrm{P}}\left(\boldsymbol{{x}}\right)\:=\:−\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{x}}−\mathrm{2} \\ $$$${division}\:{euclidienne}\:{par}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last updated…