Question Number 218474 by Nicholas666 last updated on 10/Apr/25 $$ \\ $$$$\:\:\:\:{solve}\:{for}\:{real}\:\boldsymbol{{x}} \\ $$$$\:\:\:\:\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:=\:\sqrt{\mathrm{2}} \\ $$$$ \\ $$ Answered by mehdee7396 last updated on…
Question Number 218475 by lmcp1203 last updated on 10/Apr/25 Answered by Nicholas666 last updated on 10/Apr/25 $$\bullet\angle{CBD}\:+\:\angle{BDC}\:+\:\angle{BCD}\:=\mathrm{180}° \\ $$$$\bullet\boldsymbol{{x}}+\mathrm{140}°+\mathrm{30}°=\mathrm{180}° \\ $$$$\bullet\boldsymbol{{x}}+\mathrm{170}°=\mathrm{180}° \\ $$$$\bullet\boldsymbol{{x}}=\mathrm{180}°−\mathrm{170}° \\ $$$$\bullet\boldsymbol{{x}}=\mathrm{10}°…
Question Number 218462 by York12 last updated on 10/Apr/25 $$\int\frac{{dx}}{\:\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} +\mathrm{3}}} \\ $$ Answered by som(math1967) last updated on 10/Apr/25 $$\int\frac{{dx}}{\:\sqrt{\mathrm{4}−\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\right)}} \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{2}^{\mathrm{2}} −\left({x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 218456 by Spillover last updated on 10/Apr/25 Answered by vnm last updated on 10/Apr/25 $$\mathrm{d}\:\mathrm{is}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{centers} \\ $$$$\varphi\:\mathrm{is}\:\mathscr{L}\cancel{\underbrace{ }} \\ $$ Commented by Spillover…
Question Number 218459 by SdC355 last updated on 10/Apr/25 $$\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y}\right)=−\frac{\mathrm{1}}{\mathrm{2}}{y}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +\frac{\mathrm{1}}{\mathrm{2}}{x}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} \\ $$$$\overset{\rightarrow} {\bigtriangledown}×\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y}\right)=\begin{vmatrix}{\:\:\:\:\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} }&{\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} }&{\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} }\\{\:\:\:\:\:\partial_{{x}} }&{\:\partial_{{y}}…
Question Number 218445 by mr W last updated on 10/Apr/25 $${there}\:{are}\:\mathrm{100}\:{students}\:{in}\:{a}\:{school}. \\ $$$${it}\:{is}\:{found}\:{out}\:{that}\:{each}\:{student}\: \\ $$$${should}\:{select}\:{at}\:{least}\:\mathrm{4}\:{courses},\:{so}\: \\ $$$${that}\:{no}\:{two}\:{students}\:{have}\:{the}\:{same}\: \\ $$$${selection}.\: \\ $$$${how}\:{many}\:{different}\:{courses}\:{does}\: \\ $$$${the}\:{school}\:{offer}? \\ $$…
Question Number 218504 by hardmath last updated on 10/Apr/25 $$\mathrm{Let}\:\:\:\mathrm{a}>\mathrm{1}\:\:\:\mathrm{fixed} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{the}\:\mathrm{system} \\ $$$$\begin{cases}{\mathrm{a}^{\boldsymbol{\mathrm{x}}} \:\:+\:\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:=\:\:\mathrm{ay}\:+\:\mathrm{2}}\\{\mathrm{a}^{\boldsymbol{\mathrm{y}}} \:\:+\:\:\mathrm{2}^{\boldsymbol{\mathrm{y}}} \:\:=\:\:\mathrm{az}\:\:+\:\:\mathrm{2}}\\{\mathrm{a}^{\boldsymbol{\mathrm{z}}} \:\:+\:\:\mathrm{2}^{\boldsymbol{\mathrm{z}}} \:\:=\:\:\mathrm{ax}\:\:+\:\:\mathrm{2}}\end{cases}\: \\ $$ Answered by vnm…
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Question Number 218438 by Marzuk last updated on 10/Apr/25 $${An}\:{amazing}\:{thing}\:{i}\:{saw} \\ $$$${S}\:=\:\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+\:\mathrm{5}\:+\:\mathrm{6}… \\ $$$$\:\:\:\:=\:\mathrm{1}\:+\:\mathrm{2}\left(\mathrm{2}/\mathrm{2}\:+\:\mathrm{3}/\mathrm{2}\:+\:\mathrm{4}/\mathrm{2}\:+\:\mathrm{5}/\mathrm{2}\:+\mathrm{6}/\mathrm{2}….\right) \\ $$$$\:\:\:\:=\:\mathrm{1}\:+\:\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{3}/\mathrm{2}\:+\:\mathrm{2}\:+\:\mathrm{5}/\mathrm{2}\:+\:\mathrm{3}…\right) \\ $$$$\:\:\:\:=\:\mathrm{1}\:+\:\mathrm{2}\left(\mathrm{1}+\:\mathrm{2}\:+\:\mathrm{3}\:…\:+\:\mathrm{3}/\mathrm{2}\:+\:\mathrm{5}/\mathrm{2}…\right) \\ $$$$\:\:\:\:=\:\mathrm{1}\:+\:\mathrm{2}{S}\:+\:\mathrm{2}\underset{{n}=\:\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}\:+\:\mathrm{1}}{\mathrm{2}} \\ $$$${or},{S}\:−\:\mathrm{2}{S}\:=\:\mathrm{1}\:+\:\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 218503 by hardmath last updated on 10/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com