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Question Number 12292 by sin (x) last updated on 18/Apr/17 Answered by mrW1 last updated on 18/Apr/17 $${S}=\frac{\mathrm{1}}{\mathrm{6}}×\pi{r}^{\mathrm{2}} +\frac{{r}^{\mathrm{2}} }{\mathrm{2}}\left(\frac{\pi}{\mathrm{3}}−\mathrm{sin}\:\frac{\pi}{\mathrm{3}}\right) \\ $$$$=\frac{\pi{r}^{\mathrm{2}} }{\mathrm{3}}−\frac{{r}^{\mathrm{2}} }{\mathrm{2}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\…
Question Number 77819 by aliesam last updated on 10/Jan/20 Answered by lémùst last updated on 10/Jan/20 $${posons}\:{t}=\:^{\mathrm{3}} \sqrt{{r}}\:,\:{ainsi}\:{t}\:−\:\frac{\mathrm{1}}{{t}}\:=\:\mathrm{1} \\ $$$$\Rightarrow{t}^{\mathrm{2}} −{t}−\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow{t}=\pm\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${donc}\:{r}=\pm\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{\mathrm{3}}…
Question Number 77804 by BK last updated on 10/Jan/20 Commented by MJS last updated on 10/Jan/20 $$\mathrm{is}\:\mathrm{2}^{\mid{x}\mid} \:\mathrm{positive}\:\mathrm{or}\:\mathrm{negative}? \\ $$$$\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{sin}\:{x}^{\mathrm{2}} \:? \\ $$$$\mathrm{what}\:\mathrm{are}\:{your}\:\mathrm{thoughts},\:\mathrm{Sir}\:\mathrm{BK}? \\ $$…
Question Number 77800 by mr W last updated on 10/Jan/20 $${if}\:{a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}} =\sqrt{{a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} }\:{with}\:{n}\geqslant\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:{in}\:{explicit}\:{form}. \\ $$ Terms of…
Question Number 77799 by mr W last updated on 10/Jan/20 $${if}\:{a}_{\mathrm{1}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +\mathrm{6}{n}^{\mathrm{2}} −\mathrm{12}{n}+\mathrm{2} \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$ Answered by mr…
Question Number 143329 by Huy last updated on 13/Jun/21 $$\mathrm{log}_{\mathrm{2x}+\mathrm{1}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{log}_{\mathrm{x}+\mathrm{1}} \left(\mathrm{3}\sqrt{\mathrm{2x}+\mathrm{5}}+\mathrm{18}\right)=\mathrm{2x} \\ $$ Answered by Olaf_Thorendsen last updated on 13/Jun/21 $$\mathrm{log}_{\mathrm{2}{x}+\mathrm{1}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{log}_{{x}+\mathrm{1}}…
Question Number 12261 by frank ntulah last updated on 17/Apr/17 $${find}\:{the}\:{value}\:{of}\:{a}\:{b}\:{and}\:{c} \\ $$$$\:{a}+{b}+{c}=\mathrm{4} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{66} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} =\mathrm{280} \\ $$…
Question Number 12257 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by sma3l2996 last updated on 17/Apr/17 $$\left({a}+{b}−\mathrm{2}{ab}\right)^{\mathrm{2}} +\left({a}+{b}−\mathrm{1}\right)^{\mathrm{2}} =\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{4}{a}^{\mathrm{2}} {b}^{\mathrm{2}} −\mathrm{4}{ab}^{\mathrm{2}} +\mathrm{2}{a}\left({b}−\mathrm{2}{ab}\right)\right)+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 12255 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by mrW1 last updated on 16/Apr/17 $$\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)\left({x}+\mathrm{4}\right)+\mathrm{1} \\ $$$$=\left({x}+\frac{\mathrm{5}}{\mathrm{2}}−\frac{\mathrm{3}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}}\right)+\mathrm{1} \\ $$$$=\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} \right]\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \right]+\mathrm{1}…