Question Number 16086 by Tinkutara last updated on 17/Jun/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation}\:\mid{x}\:+\:\mathrm{4}\mid\:=\:\mathrm{8}\left[{x}\right] \\ $$$$+\:{x}\:−\:\mathrm{4}\:\mathrm{is}?\:\left(\mathrm{where}\:\left[\centerdot\right]\:\mathrm{Greatest}\:\mathrm{Integer}\right. \\ $$$$\left.\mathrm{Function}\right) \\ $$ Commented by prakash jain last updated on…
Question Number 16085 by Tinkutara last updated on 18/Jun/17 $$\mathrm{Let}\:{f}\left(\mathrm{sin}\:{x}\right)\:+\:\mathrm{2}{f}\left(\mathrm{cos}\:{x}\right)\:=\:\mathrm{3}\:\forall\:{x}\:\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$$$\mathrm{Then} \\ $$$$\left(\mathrm{1}\right)\:{f}\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2}\right)\:{f}\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(−\mathrm{1},\:\mathrm{0}\right) \\ $$$$\left(\mathrm{3}\right)\:{f}\left(\mathrm{cos}\:{x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right) \\ $$$$\left(\mathrm{4}\right)\:{f}\left({x}\right)\:=\:\mathrm{1},\:{x}\:\in\:\left(\mathrm{0},\:\mathrm{1}\right) \\ $$ Commented by prakash…
Question Number 147158 by puissant last updated on 18/Jul/21 Answered by Olaf_Thorendsen last updated on 18/Jul/21 $$\left.\mathrm{A}\right) \\ $$$$\mathrm{I}. \\ $$$$\mathrm{1}.\:\mathrm{Quel}\:\mathrm{est}\:\mathrm{le}\:\mathrm{nombre}\:\mathrm{de}\:\mathrm{tirages} \\ $$$$\mathrm{possibles}\:? \\ $$$$\mathrm{Dans}\:\mathrm{chaque}\:\mathrm{triplet},\:\mathrm{le}\:\mathrm{chiffre}\:\mathrm{de}…
Question Number 16082 by Tinkutara last updated on 17/Jun/17 $$\mathrm{Solution}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{2}\left[{x}\right]\:+\:\mathrm{4}\left\{{x}\right\}\:=\:\mathrm{3}{x} \\ $$$$+\:\mathrm{2}\:\left(\mathrm{where}\:\left\{\centerdot\right\}\:\mathrm{denotes}\:\mathrm{fractional}\right. \\ $$$$\left.\mathrm{function}\:\mathrm{and}\:\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{G}.\mathrm{I}.\mathrm{F}\right)\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left\{−\mathrm{2}\right\} \\ $$$$\left(\mathrm{2}\right)\:\left\{−\mathrm{2},\:−\:\frac{\mathrm{3}}{\mathrm{2}}\right\} \\ $$$$\left(\mathrm{3}\right)\:\phi \\ $$$$\left(\mathrm{4}\right)\:{R} \\ $$ Commented…
Question Number 16081 by Tinkutara last updated on 17/Jun/17 $$\mathrm{A}\:\mathrm{spherical}\:\mathrm{balloon}\:\mathrm{of}\:\mathrm{21}\:\mathrm{cm}\:\mathrm{diameter} \\ $$$$\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{filled}\:\mathrm{with}\:\mathrm{hydrogen}\:\mathrm{at}\:\mathrm{NTP} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{cylinder}\:\mathrm{containing}\:\mathrm{the}\:\mathrm{gas}\:\mathrm{at} \\ $$$$\mathrm{20}\:\mathrm{atmosphere}\:\mathrm{at}\:\mathrm{27}°\mathrm{C}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{cylinder} \\ $$$$\mathrm{can}\:\mathrm{hold}\:\mathrm{2}.\mathrm{82}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{water},\:\mathrm{calculate} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{balloons}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{filled}\:\mathrm{up}. \\ $$ Answered…
Question Number 147149 by nadovic last updated on 18/Jul/21 $$\:\mathrm{Two}\:\mathrm{concurrent}\:\mathrm{forces}\:\boldsymbol{{F}}_{\mathrm{1}} \:=\:\mathrm{12N}\:\mathrm{and} \\ $$$$\:\boldsymbol{{F}}_{\mathrm{2}} \:=\:\mathrm{30N}\:\mathrm{are}\:\mathrm{150}°\:\mathrm{apart}.\:\mathrm{Calculate}\: \\ $$$$\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\boldsymbol{{F}}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{resultant} \\ $$$$\:\mathrm{force}. \\ $$ Answered by Olaf_Thorendsen last…
Question Number 16079 by Tinkutara last updated on 17/Jun/17 $$\mathrm{An}\:\mathrm{open}\:\mathrm{flask}\:\mathrm{contains}\:\mathrm{air}\:\mathrm{at}\:\mathrm{27}°\mathrm{C}.\:\mathrm{To} \\ $$$$\mathrm{what}\:\mathrm{temperature}\:\mathrm{it}\:\mathrm{must}\:\mathrm{be}\:\mathrm{heated}\:\mathrm{to} \\ $$$$\mathrm{expel}\:\mathrm{one}-\mathrm{fourth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{air}? \\ $$ Commented by ajfour last updated on 18/Jun/17 $${is}\:{it}\:\mathrm{127}°{C}\:? \\…
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Question Number 16077 by Tinkutara last updated on 17/Jun/17 $$\mathrm{Let}\:{ABCDE}\:\mathrm{be}\:\mathrm{an}\:\mathrm{equiangular} \\ $$$$\mathrm{pentagon}\:\mathrm{whose}\:\mathrm{side}\:\mathrm{lengths}\:\mathrm{are} \\ $$$$\mathrm{rational}\:\mathrm{numbers}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{pentagon}\:\mathrm{is}\:\mathrm{regular}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 81610 by TawaTawa last updated on 14/Feb/20 Answered by MJS last updated on 14/Feb/20 $$\mathrm{2}\leqslant{x}\leqslant\mathrm{4} \\ $$$$\mathrm{let}\:{x}={t}^{\mathrm{2}} +\mathrm{2}\:\Rightarrow\:\mathrm{0}\leqslant{t}^{\mathrm{2}} \leqslant\mathrm{2} \\ $$$$\mathrm{3}{t}−\mathrm{12}\sqrt{\mathrm{2}−{t}^{\mathrm{2}} }+\mathrm{21}{t}^{\mathrm{2}} −\mathrm{40}+{t}\sqrt{\mathrm{2}−{t}^{\mathrm{2}}…