Question Number 132252 by aurpeyz last updated on 12/Feb/21 $$ \\ $$$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{glass}\:\mathrm{block}\:\left(\mathrm{n}=\mathrm{1}.\mathrm{52}\right)\:\mathrm{is} \\ $$$$\mathrm{pla}{c}\mathrm{ed}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{clean}\:\mathrm{water}\:\mathrm{contained}\: \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{basin}.\:\mathrm{A}\:\mathrm{layer}\:\mathrm{of}\:\mathrm{oil}\:\left(\mathrm{n}=\mathrm{1}.\mathrm{44}\right)\:\mathrm{floats} \\ $$$$\mathrm{o}{n}\:\mathrm{the}\:\mathrm{water}\:\mathrm{surface}.\:\mathrm{A}\:\mathrm{ray}\:\mathrm{of}\:\mathrm{light}\: \\ $$$$\mathrm{from}\:\mathrm{air}\:\mathrm{strikes}\:\mathrm{the}\:\mathrm{oil}\:\mathrm{surface}\:\mathrm{at}\:\mathrm{an} \\ $$$$\mathrm{ange}\:\mathrm{of}\:\mathrm{incidence}\:\mathrm{of}\:\mathrm{28}^{\mathrm{0}} .\:\mathrm{Calculate}\:\mathrm{the} \\ $$$$\mathrm{a}{n}\mathrm{gle}\:\mathrm{of}\:\mathrm{refraction}\:\mathrm{at}\:\mathrm{the}\:\mathrm{water}−\mathrm{glass}…
Question Number 132248 by aurpeyz last updated on 12/Feb/21 $$ \\ $$$${In}\:{a}\:\mathrm{60}^{\mathrm{0}} \:{prism}\:{of}\:{refractive}\:{index}\:\mathrm{1}.\mathrm{5} \\ $$$${calculate}\:{the}\:{angle}\:{of}\:{minimum}\: \\ $$$${deviation}\:{when}\:{light}\:{is}\:{refracted} \\ $$$${throuh}\:{the}\:{prism} \\ $$$$\left({a}\right)\:\mathrm{40}.\mathrm{2}\:\left({b}\right)\:\mathrm{37}.\mathrm{5}\:\left({c}\right)\:\mathrm{37}.\mathrm{2}\:\left({d}\right)\:\mathrm{40}.\mathrm{5}\:\left({e}\right)\mathrm{40}.\mathrm{6} \\ $$ Commented by…
Question Number 1171 by 112358 last updated on 09/Jul/15 $${What}\:{is}\:{the}\:{set}\:\mathbb{Z}_{\mathrm{8}} −\left\{\mathrm{0}\right\}?\:{I}\:{met} \\ $$$${this}\:{notation}\:{in}\:{a}\:{question}\:{asking} \\ $$$${whether}\:{or}\:{not}\:{the}\:{set}\:\mathbb{Z}_{\mathrm{8}} −\left\{\mathrm{0}\right\} \\ $$$${forms}\:{a}\:{group}\:{under}\: \\ $$$${multiplication}\:\left({mod}\:\mathrm{8}\right). \\ $$ Answered by 123456…
Question Number 66697 by naka3546 last updated on 18/Aug/19 Commented by kaivan.ahmadi last updated on 18/Aug/19 $${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{4}}} \:\frac{−{sin}\left({x}−\frac{\pi}{\mathrm{4}}\right)−\left(\mathrm{1}+{tan}^{\mathrm{2}} {x}\right)}{{cos}\left({x}−\frac{\pi}{\mathrm{4}}\right)}=\frac{\mathrm{0}−\left(\mathrm{1}+\mathrm{1}\right)}{\mathrm{1}}=−\mathrm{2} \\ $$ Answered by Cmr 237…
Question Number 132220 by aurpeyz last updated on 12/Feb/21 Answered by Olaf last updated on 12/Feb/21 $$\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6}\left(\mathrm{cos60}°\overset{\rightarrow} {{i}}+\mathrm{sin60}°\overset{\rightarrow} {{j}}\right) \\ $$$$\overset{\rightarrow} {\mathrm{P}}\:=\:\mathrm{6}\left(\frac{\mathrm{1}}{\mathrm{2}}\overset{\rightarrow} {{i}}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\overset{\rightarrow} {{j}}\right)…
Question Number 66683 by Tinkutara@ last updated on 18/Aug/19 Commented by mr W last updated on 18/Aug/19 $${each}\:{runner}\:{has}\:{two}\:{possibilities},\:{totally} \\ $$$$\mathrm{2}×\mathrm{2}×\mathrm{2}=\mathrm{8}.\:{such}\:{that}\:{they}\:{don}'{t}\:{collide}, \\ $$$${all}\:{of}\:{them}\:{must}\:{run}\:{in}\:{the}\:{same} \\ $$$${direction},\:{there}\:{are}\:{two}\:{such}\:{possibilities}. \\…
Question Number 66684 by Tinkutara@ last updated on 18/Aug/19 Answered by MJS last updated on 18/Aug/19 $$\mathrm{this}\:\mathrm{is}\:\mathrm{old}… \\ $$$$\mathrm{you}\:\mathrm{always}\:\mathrm{say}\:\mathrm{in}\:\mathrm{words}\:\mathrm{what}\:\mathrm{you}\:\mathrm{read}\:\mathrm{and} \\ $$$$\mathrm{write}\:\mathrm{down}\:\mathrm{in}\:\mathrm{numbers} \\ $$$$\mathrm{1} \\ $$$$\mathrm{one}\:“\mathrm{1}''\:=\:\mathrm{1}\:\mathrm{1}…
Question Number 66681 by Tinkutara@ last updated on 18/Aug/19 Commented by Tinkutara@ last updated on 18/Aug/19 $$?? \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 66670 by naka3546 last updated on 18/Aug/19 Commented by mathmax by abdo last updated on 18/Aug/19 $${let}\:{S}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{3}^{{n}} }{\mathrm{5}^{{n}} \left({n}^{\mathrm{2}} \:+\mathrm{3}{n}+\mathrm{2}\right)}\:\Rightarrow{S}\:=\sum_{{n}=\mathrm{0}} ^{\infty}…
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