Question Number 66759 by aliesam last updated on 19/Aug/19 Commented by mr W last updated on 19/Aug/19 $${question}\:{is}\:{wrong}. \\ $$$${there}\:{is}\:{no}\:{x}\:{which}\:{fulfills}\:\mid\frac{\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\mid>\mathrm{2}, \\ $$$${but}\:{such}\:{that}\:{e}^{{x}} >\mathrm{2016},\:{x}>\mathrm{ln}\:\mathrm{2016}\approx\mathrm{7}.\mathrm{6} \\…
Question Number 132294 by Algoritm last updated on 13/Feb/21 Commented by mr W last updated on 13/Feb/21 $${x}={y}=\mathrm{1} \\ $$$${the}\:{proof}\:{you}\:{may}\:{ask}\:{for}\:{is}\:{thinking}. \\ $$ Terms of Service…
Question Number 66751 by John Kaloki Musau last updated on 19/Aug/19 $${A}\:{rostum}\:{is}\:{made}\:{by}\:{cutting}\:{off} \\ $$$${the}\:{upper}\:{part}\:{of}\:{a}\:{cone}\:{along}\:{a} \\ $$$${plane}\:{parallel}\:{to}\:{the}\:{base}\:{at}\:\frac{\mathrm{2}}{\mathrm{3}}\:{up}\: \\ $$$${the}\:{height}.\:{What}\:{fraction}\:{of}\:{the}\: \\ $$$${volume}\:{of}\:{the}\:{cone}\:{does}\:{the} \\ $$$${rostum}\:{represent}? \\ $$ Answered…
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Question Number 132261 by muneer0o0 last updated on 12/Feb/21 Answered by Olaf last updated on 13/Feb/21 $$\Omega\:=\:\int_{−\mathrm{1}} ^{+\mathrm{1}} \int_{−\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} ^{+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \mathrm{sec}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}…
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Question Number 66718 by otchereabdullai@gmail.com last updated on 18/Aug/19 Commented by Tony Lin last updated on 19/Aug/19 Commented by Tony Lin last updated on 19/Aug/19…
Question Number 132255 by aurpeyz last updated on 12/Feb/21 $${A}\:{ray}\:{of}\:{light}\:{is}\:{incident}\:{at}\:\mathrm{60}^{\mathrm{0}} \:{at}\:{an} \\ $$$${air}−{glass}\:{plane}\:{surface}.\:{find}\:{the}\: \\ $$$${angle}\:{of}\:{refraction}\:{in}\:{the}\:{glass}\left(\right. \\ $$$$\left.{refractive}\:{index}\:{for}\:{glass}=\mathrm{1}.\mathrm{5}\right) \\ $$$$\left({a}\right)\:\mathrm{25}.\mathrm{3}\:\left({b}\right)\:\mathrm{35}.\mathrm{3}\:\left({c}\right)\:\mathrm{15}.\mathrm{3}\:\left({d}\right)\mathrm{30} \\ $$ Commented by Dwaipayan Shikari…
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…