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Category: Algebra

Three-interior-angles-of-a-nonagon-are-equal-and-the-sum-of-the-other-six-is-1050-Find-the-size-of-one-of-the-equal-angles-

Question Number 71533 by pete last updated on 16/Oct/19 $$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{nonagon}\:\mathrm{are} \\ $$$$\mathrm{equal}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{six}\:\mathrm{is}\:\mathrm{1050}° \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{size}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equal}\:\mathrm{angles}. \\ $$ Answered by MJS last updated on 17/Oct/19 $$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{is}\:\mathrm{1260}° \\…

a-number-consists-of-digits-1-and-2-the-sum-of-its-digits-is-2018-if-the-number-is-multiplied-with-5-the-sum-of-the-digits-will-be-10000-find-how-many-digits-this-number-has-

Question Number 71534 by mr W last updated on 16/Oct/19 $${a}\:{number}\:{consists}\:{of}\:{digits}\:\mathrm{1}\:{and}\:\mathrm{2}. \\ $$$${the}\:{sum}\:{of}\:{its}\:{digits}\:{is}\:\mathrm{2018}. \\ $$$${if}\:{the}\:{number}\:{is}\:{multiplied}\:{with}\:\mathrm{5},\: \\ $$$${the}\:{sum}\:{of}\:{the}\:{digits}\:{will}\:{be}\:\mathrm{10000}. \\ $$$${find}\:{how}\:{many}\:{digits}\:{this}\:{number} \\ $$$${has}. \\ $$ Answered by…

Express-28-as-continued-fraction-

Question Number 71518 by TawaTawa last updated on 16/Oct/19 $$\mathrm{Express}\:\:\sqrt{\mathrm{28}}\:\:\mathrm{as}\:\mathrm{continued}\:\mathrm{fraction} \\ $$ Commented by Prithwish sen last updated on 16/Oct/19 $$\sqrt{\mathrm{28}}\:=\:\mathrm{1}+\:\sqrt{\mathrm{28}}−\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:=\:\mathrm{1}+\:\:\frac{\mathrm{27}}{\:\sqrt{\mathrm{28}}+\mathrm{1}}\:=\:\mathrm{1}+\frac{\mathrm{27}}{\mathrm{2}+\sqrt{\mathrm{28}}−\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:=\:\mathrm{1}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\:\sqrt{\mathrm{28}}+\mathrm{1}}}\:=\:\mathrm{1}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\mathrm{2}+\frac{\mathrm{27}}{\mathrm{2}+._{._{..}…

f-1-f-1-0-Is-this-true-When-is-this-not-true-

Question Number 5978 by FilupSmith last updated on 08/Jun/16 $${f}\left(\mathrm{1}\right){f}\left(−\mathrm{1}\right)\leqslant\mathrm{0} \\ $$$$\mathrm{Is}\:\mathrm{this}\:\mathrm{true}? \\ $$$$\mathrm{When}\:\mathrm{is}\:\mathrm{this}\:\mathrm{not}\:\mathrm{true}? \\ $$ Commented by Yozzii last updated on 09/Jun/16 $${If}\:{x}\in\mathbb{R},\:{f}\left({x}\right)\in\mathbb{R}\:{is}\:{odd}\:\Rightarrow{f}\left({x}\right){f}\left(−{x}\right)=−\left({f}\left({x}\right)\right)^{\mathrm{2}} \leqslant\mathrm{0}…

Question-137037

Question Number 137037 by JulioCesar last updated on 29/Mar/21 Answered by mathmax by abdo last updated on 29/Mar/21 $$\mathrm{I}=\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{3}} −\mathrm{8}\right)^{\mathrm{2}} }\:\left(\mathrm{compolex}\:\mathrm{method}\right)\:\Rightarrow\mathrm{I}=\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{4}\right)^{\mathrm{2}} } \\…