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Category: Arithmetic

Racionalizar-el-denominador-1-x-x-1-3-x-

Question Number 204841 by Simurdiera last updated on 28/Feb/24 $${Racionalizar}\:{el}\:{denominador} \\ $$$$\frac{\mathrm{1}\:−\:{x}}{\:\sqrt[{\mathrm{3}}]{{x}}\:−\:\sqrt{\sqrt{{x}}}} \\ $$ Commented by Frix last updated on 28/Feb/24 $$\frac{\mathrm{1}−{x}}{{x}^{\frac{\mathrm{1}}{\mathrm{3}}} −{x}^{\frac{\mathrm{1}}{\mathrm{4}}} }=−\left(\frac{{x}^{\frac{\mathrm{11}}{\mathrm{12}}} +{x}^{\frac{\mathrm{5}}{\mathrm{6}}}…

if-f-f-x-x-2-3x-4-find-f-1-

Question Number 204671 by mr W last updated on 25/Feb/24 $${if}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4},\:{find}\:{f}\left(\mathrm{1}\right)=? \\ $$ Answered by witcher3 last updated on 25/Feb/24 $$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{4} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{1}\right)\right)=\mathrm{2}…

If-1-1-2-1-2-2-1-3-2-1-4-2-1-5-2-pi-2-6-then-1-1-2-1-3-2-1-5-2-

Question Number 204642 by BaliramKumar last updated on 24/Feb/24 $$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\:\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:………….\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\mathrm{then}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:………….\:=\:? \\ $$$$ \\ $$…

Question-204441

Question Number 204441 by peter frank last updated on 17/Feb/24 Commented by Frix last updated on 17/Feb/24 $$\mathrm{3}\:\mathrm{circles}\:\mathrm{plus}\:\mathrm{4}\:\mathrm{times}\:\left(\mathrm{6}\:\mathrm{minus}\:\mathrm{4}\:\mathrm{radii}\right)\:\Rightarrow \\ $$$$\mathrm{perimeter}\:=\:\mathrm{6}\pi+\mathrm{8} \\ $$ Commented by peter…

3-7-11-7-11-15-11-15-19-39-43-47-

Question Number 204348 by BaliramKumar last updated on 14/Feb/24 $$\mathrm{3}×\mathrm{7}×\mathrm{11}\:+\:\mathrm{7}×\mathrm{11}×\mathrm{15}\:+\:\mathrm{11}×\mathrm{15}×\mathrm{19}\:+\:……….+\:\:\mathrm{39}×\mathrm{43}×\mathrm{47}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by MM42 last updated on 14/Feb/24 $$\underset{\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\:\left(\mathrm{4}{n}−\mathrm{1}\right)\left(\mathrm{4}{n}+\mathrm{3}\right)\left(\mathrm{4}{n}+\mathrm{7}\right) \\ $$$$=\underset{\mathrm{1}} {\overset{\mathrm{10}}…