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Category: Algebra

Find-at-least-the-first-four-non-zero-term-in-a-power-series-expansion-about-x-0-for-a-general-solution-to-z-x-2-z-0-

Question Number 71761 by TawaTawa last updated on 19/Oct/19 $$\mathrm{Find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{term}\:\mathrm{in}\:\mathrm{a}\:\mathrm{power} \\ $$$$\mathrm{series}\:\mathrm{expansion}\:\mathrm{about}\:\:\mathrm{x}\:\:=\:\:\mathrm{0}\:\:\mathrm{for}\:\mathrm{a}\:\mathrm{general}\:\mathrm{solution} \\ $$$$\mathrm{to}\:\:\:\:\mathrm{z}''\:\:−\:\:\mathrm{x}^{\mathrm{2}} \mathrm{z}\:\:\:=\:\:\mathrm{0} \\ $$ Commented by mathmax by abdo last updated on…

The-side-of-a-square-is-measured-to-be-12cm-long-cofrect-to-the-nearest-cm-Find-the-maximum-absolute-error-and-the-maximum-percentage-error-for-a-The-length-of-the-square-Answer-0-5cm-

Question Number 71696 by TawaTawa last updated on 18/Oct/19 $$\mathrm{The}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{is}\:\mathrm{measured}\:\mathrm{to}\:\mathrm{be}\:\:\mathrm{12cm}\:\mathrm{long}\:\mathrm{cofrect} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\:\mathrm{cm}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{absolute}\:\mathrm{error} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{percentage}\:\mathrm{error}\:\mathrm{for} \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\:\:\:\:\left(\mathrm{Answer}:\:\:\mathrm{0}.\mathrm{5cm},\:\:\mathrm{4}.\mathrm{17\%}\right) \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}.\:\:\:\:\:\:\left(\mathrm{Answer}:\:\:\:\:\mathrm{12}.\mathrm{25cm},\:\:\:\mathrm{8}.\mathrm{5\%}\right) \\ $$ Answered by MJS last updated…

Prove-or-disprove-2ab-2bc-ca-5-3-2-abc-a-b-c-gt-0-

Question Number 6154 by Rasheed Soomro last updated on 16/Jun/16 $${Prove}\:{or}\:{disprove} \\ $$$$\left(\frac{\mathrm{2}\boldsymbol{{ab}}+\mathrm{2}\boldsymbol{{bc}}+\boldsymbol{{ca}}}{\mathrm{5}}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \geqslant\:\:\boldsymbol{{abc}}\:\:\:\forall\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}>\mathrm{0} \\ $$ Commented by Yozzii last updated on 18/Jun/16 $$\frac{\mathrm{5}\sqrt{\mathrm{5}}}{\left(\frac{\mathrm{2}}{{c}}+\frac{\mathrm{2}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\sqrt{\mathrm{2}{ab}+\mathrm{2}{bc}+{ca}}}\leqslant\mathrm{1} \\…