Question Number 190339 by mr W last updated on 01/Apr/23 $${solve}\:{for}\:{x}\:\in\mathbb{R} \\ $$$$\sqrt{{x}−\mathrm{1}}+\sqrt{\mathrm{3}{x}−\mathrm{5}}+\sqrt{\mathrm{4}{x}−\mathrm{7}}=\mathrm{4}{x}−\mathrm{5} \\ $$ Answered by ajfour last updated on 01/Apr/23 $$\sqrt{{x}−\mathrm{1}}+\sqrt{\mathrm{3}{x}−\mathrm{5}}+\sqrt{\mathrm{4}{x}−\mathrm{7}} \\ $$$$\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}+\mathrm{3}{x}−\mathrm{5}+\mathrm{4}{x}−\mathrm{7}\right)+\frac{\mathrm{3}}{\mathrm{2}}…
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Question Number 190192 by mr W last updated on 29/Mar/23 $${if}\:{a}>{b}>\mathrm{0},\:{find}\:{the}\:{minimum}\:{of} \\ $$$${a}^{\mathrm{2}} +\frac{\mathrm{1}}{\left({a}−{b}\right){b}}=? \\ $$ Commented by Frix last updated on 29/Mar/23 $$\mathrm{Minimum}=\mathrm{4}\:\mathrm{at}\:{a}=\sqrt{\mathrm{2}}\wedge{b}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\…
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Question Number 189977 by cherokeesay last updated on 25/Mar/23 Answered by a.lgnaoui last updated on 26/Mar/23 $${the}\:\:{totale}\:{Area}: \\ $$$$\mathrm{2}\left(\mathrm{12}×\mathrm{3},\mathrm{5}+\mathrm{9}×\mathrm{3},\mathrm{5}\right)=\mathrm{147}{m}^{\mathrm{2}} \\ $$$${Area}\:{of}\:{windows}=\mathrm{21}{m}^{\mathrm{2}} \\ $$$${Area}\:{of}\:{tiles}=\mathrm{147}−\mathrm{21}=\mathrm{126}{m}^{\mathrm{2}} =\mathrm{126}×\mathrm{10}^{\mathrm{2}} {cm}^{\mathrm{2}}…
Question Number 189970 by Rupesh123 last updated on 25/Mar/23 Answered by Rasheed.Sindhi last updated on 25/Mar/23 $${x},{y},{x}+{y},{x}−{y}\:\in\mathbb{P}\:\:;\:{x},{y}=? \\ $$$$\bullet{If}\:\:{x}\:{and}\:{y}\:{were}\:{both}\:{odd}\:{primes} \\ $$$$\Rightarrow\mathrm{2}\:\mid\:\left({x}+{y}\right)\Rightarrow{x}+{y}\:\notin\mathbb{P}\:{or}\:{x}+{y}=\mathrm{2} \\ $$$${x}+{y}=\mathrm{2}\:{has}\:{no}\:{solution}\:{in}\:{prime} \\ $$$$\bullet{If}\:{x}={y}=\mathrm{2}\Rightarrow\:{x}+{y},{x}−{y}\:\notin\mathbb{P}…
Question Number 189901 by cherokeesay last updated on 23/Mar/23 Answered by BaliramKumar last updated on 24/Mar/23 $$\mathrm{4}.\:\left(\mathrm{i}\right)\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\infty}\right]\:=\:\mathrm{2}\left[\frac{\mathrm{1}}{\mathrm{2}}\:−\:\mathrm{0}\right]\:=\:\mathrm{1} \\ $$ Answered by talminator2856792 last updated on…
Question Number 58804 by Tawa1 last updated on 30/Apr/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}:\:\:\:\:\mathrm{4}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{3}\:\mathrm{sin}\:\mathrm{x}\:\:=\:\:\mathrm{2} \\ $$ Commented by MJS last updated on 30/Apr/19 $$\mathrm{generally} \\ $$$${a}\mathrm{cos}\:{x}\:+{b}\mathrm{sin}\:{x}\:={c} \\ $$$${x}=\mathrm{2arctan}\:{t} \\…
Question Number 124141 by nico last updated on 01/Dec/20 Answered by Lordose last updated on 01/Dec/20 $$ \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \mathrm{e}^{−\mathrm{ix}^{\mathrm{2}} } \mathrm{dx}\:\:\:\:\: \\ $$$$\mathrm{Set}\:\mathrm{u}=\mathrm{x}\sqrt{\mathrm{i}}\:\:\Rightarrow\:\mathrm{du}\:=\:\sqrt{\mathrm{i}}\mathrm{dx}…
Question Number 124116 by danielasebhofoh last updated on 30/Nov/20 Answered by Dwaipayan Shikari last updated on 01/Dec/20 $$\int{x}^{−{x}} {dx} \\ $$$$=\underset{{n}\geqslant\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \int\frac{\left({xlogx}\right)^{{n}} }{{n}!}{dx}…