Question Number 1395 by Rasheed Soomro last updated on 28/Jul/15 $$\:\:\:\:\:\:\:\:\:\:\mathrm{C}{onsider}\:\boldsymbol{\mathrm{quadrilateral}}\:\boldsymbol{\mathrm{ABCD}}\:\:{same}\:{as}\:{in}\:{Q}\:\mathrm{1378}\:{with}\: \\ $$$${same}\:{conditions}/{restrictions}\:\left({Pl}\:\:{refer}\:\:{the}\:{Question}\:{again}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\bullet\:{What}\:{could}\:{be}\:{possible}\:\boldsymbol{\mathrm{minimum}}\:{and}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}} \\ $$$${of}\:{the}\:{quadrilateral}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\bullet{When}\:{qusdrilateral}\:{has}\:\boldsymbol{\mathrm{minimum}}\:\boldsymbol{\mathrm{area}}\:{what}\:{is}\:{the}\:{value}/{s} \\ $$$${of}\:\boldsymbol{{m}}\angle\boldsymbol{\mathrm{A}}?\:{Similarly}\:{what}\:{is}\:{value}/{s}\:\:{of}\:\boldsymbol{{m}}\angle\boldsymbol{\mathrm{A}}\:{in}\:{case}\:{of} \\ $$$$\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}}? \\ $$$$…
Question Number 66928 by mr mondo last updated on 20/Aug/19 $$\frac{\mathrm{3}^{\mathrm{120}} }{\mathrm{6}^{\mathrm{60}} } \\ $$$$\mathrm{express}\:\mathrm{in}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in} \\ $$$$\mathrm{3}\:\mathrm{significant}\:\mathrm{figure} \\ $$ Answered by mr W last updated…
Question Number 66927 by Cmr 237 last updated on 21/Aug/19 $${calcul}\:{la}\:{limite}\:{suivante}: \\ $$$${lim}\:\:\:\:\:\:\:\left(\frac{\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\mathrm{3}^{{x}} +……+{n}^{{x}} }{{n}}\right)^{\frac{\mathrm{1}}{{x}}} =\mathrm{A} \\ $$$${x}\rightarrow\mathrm{0} \\ $$$$\mathrm{trouve}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\boldsymbol{\mathrm{A}} \\ $$$$\mathrm{trouve}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\boldsymbol{\mathrm{P}}\:\mathrm{definir}\:\mathrm{par}: \\…
Question Number 132463 by EDWIN88 last updated on 14/Feb/21 $$\:\mathrm{Given}\:\int_{{a}} ^{\:{b}} \:\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}}{\mid{x}−\mathrm{3}\mid}\:\mathrm{dx}\:=\:\frac{\mathrm{11}}{\mathrm{2}}\:\mathrm{where}\:\begin{cases}{{a}<\mathrm{3}<{b}}\\{{a}+\mathrm{2}{b}=\mathrm{8}}\end{cases} \\ $$$$\:\mathrm{Find}\:\int_{{a}} ^{{b}} \:\mid{x}\mid\:\mathrm{dx}.\: \\ $$ Answered by bemath last updated on…
Question Number 66922 by paro123 last updated on 20/Aug/19 Commented by paro123 last updated on 20/Aug/19 $$\mathrm{No}.\mathrm{8} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 1387 by navajyoti.tamuli.tamuli@gmail. last updated on 27/Jul/15 $${Q}.\:{is}\:{there}\:{any}\:{angle}\:{in}\:{a}\:{circle}? \\ $$ Commented by Rasheed Soomro last updated on 28/Jul/15 $${Two}\:{answers}\:{can}\:{be}\:{given}.{Each}\:{has}\:\:{its}\:\:{own}\:{reasoning}. \\ $$$$\left({i}\right)\:{There}\:{are}\:{infinity}\:{number}\:{of}\:{angles}. \\ $$$${Consider}\:{a}\:{polygon}\:{of}\:{n}\:{angles}\:{inscribed}\:{in}\:{a}\:{circle}:…
Question Number 132459 by mnjuly1970 last updated on 14/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:\:{calculus}\:…. \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}^{\mathrm{2}} \right){ln}\left({x}\right)}{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx}= \\ $$$$\:\:{solution}: \\ $$$$\boldsymbol{\phi}\overset{{x}^{\mathrm{2}} ={t}} {=}\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}\right){ln}\left(\sqrt{{t}}\:\right)}{{t}^{\frac{\mathrm{3}}{\mathrm{4}}} }\:\frac{{dt}}{{t}^{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 1379 by 314159 last updated on 27/Jul/15 $${Find}\:{all}\:{positive}\:{integers}\:{n}\:{such}\:{that}\:\: \\ $$$${n}\leqslant\mathrm{2014}\:{and}\:\mathrm{3}^{{n}−\mathrm{1}} .{n}\:\:{will}\:{be}\:{a}\:{perfect}\:{square}\:{integer}. \\ $$ Commented by 123456 last updated on 26/Jul/15 $${m}\equiv\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$${n}={m}^{\mathrm{2}}…
Question Number 1378 by Rasheed Soomro last updated on 28/Jul/15 $$\:\:\:\:\:{Four}\:{sides}\:{m}\overline {\boldsymbol{\mathrm{AB}}}\:,\:{m}\overline {\boldsymbol{\mathrm{BC}}}\:,\:{m}\overline {\boldsymbol{\mathrm{CD}}}\:\:{and}\:\:{m}\overline {\boldsymbol{\mathrm{DA}}}\:{of}\:{a}\:\boldsymbol{\mathrm{quadrilateral}}\: \\ $$$$\boldsymbol{\mathrm{ABCD}}\:\:{have}\:{measurement}\:\boldsymbol{{a}}\:,\:\boldsymbol{{b}}\:,\:\boldsymbol{{c}}\:\:{and}\:\boldsymbol{{d}}\:{units}\:{respectively}. \\ $$$$\:\:\:\:\:{Let}\:{the}\:{sum}\:{of}\:{any}\:{adjacent}\:{sides}\:{is}\:{not}\:{equal}\:{to}\:{the}\:{sum}\:{of} \\ $$$${remaining}\:{adjacent}\:{sides}\:\:{and}\:{measurement}\:{of}\:{all}\:{the}\:{sides}\: \\ $$$${is}\:{positive}\:{and}\:{real}. \\ $$$$\:\:\:\:\:\:{What}\:{could}\:{be}\:{the}\:{possible}\:{minimum}\:{and}\:{maximum}\:{values}…
Question Number 66910 by naka3546 last updated on 20/Aug/19 $${P}\:\:=\:\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{999}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}\right)} \\ $$$${Q}\:\:=\:\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{999}} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{999}+{n}\right)\left(\mathrm{1999}−{n}\right)} \\ $$$$\frac{{P}}{{Q}}\:\:=\:\:? \\ $$ Commented by naka3546 last updated…