Question Number 5935 by Master Tria last updated on 05/Jun/16 $$\mathrm{If}\:{a},\:{b},\:{c},\:{x},\:{y},\:{z}\:\in\:{R}\:\mathrm{be}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\left({a}+{b}+{c}\right)^{\mathrm{2}} =\mathrm{3}\left({ab}+{bc}+{ca}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −{z}^{\mathrm{2}} \right), \\ $$$$\mathrm{then} \\ $$ Commented by prakash jain…
Question Number 5917 by Summaira last updated on 05/Jun/16 $$\mathrm{If}\:\begin{vmatrix}{{x}+{a}}&{\:\:\:{b}}&{\:\:\:{c}}\\{\:\:\:{a}}&{{x}+{b}}&{\:\:\:{c}}\\{\:\:\:{a}}&{\:\:\:{b}}&{{x}+{c}}\end{vmatrix}=\:\mathrm{0},\:\mathrm{then}\:{x}\:\mathrm{equals} \\ $$ Answered by sanusihammed last updated on 05/Jun/16 Terms of Service Privacy Policy Contact:…
Question Number 136901 by nadovic last updated on 27/Mar/21 $${A}\:{gold}\:{ore}\:{is}\:{found}\:{to}\:{have}\:{a}\:{purity} \\ $$$${of}\:\mathrm{70}{ppm}.\:{How}\:{much}\:{gold}\:{in}\:{grams} \\ $$$${can}\:{be}\:{recovered}\:{from}\:\mathrm{5}{kg}\:{of}\:{the}\:{ore}? \\ $$ Answered by Olaf last updated on 27/Mar/21 $${m}_{{pure}\:{gold}} \:=\:\tau{m}_{{ore}}…
Question Number 5824 by Bc160200609 last updated on 30/May/16 $$\mathrm{The}\:\mathrm{exponent}\:\mathrm{of}\:\:\mathrm{12}\:\mathrm{in}\:\:\mathrm{100}!\:\:\mathrm{is}\: \\ $$ Commented by Yozzii last updated on 30/May/16 $$\mathrm{12}^{\mathrm{48}} =\mathrm{2}^{\mathrm{96}} \mathrm{3}^{\mathrm{48}} \:{but}\:{I}\:{haven}'{t}\:{figured} \\ $$$${out}\:{yet}\:{how}\:{to}\:{show}\:{this}.…
Question Number 5639 by Daily last updated on 23/May/16 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{negative}\:\mathrm{real}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\:\:{x}^{\mathrm{4}} −\mathrm{4}{x}−\mathrm{1}=\mathrm{0}\:\mathrm{is} \\ $$ Commented by Yozzii last updated on 23/May/16 $${Descartes}\:{rule}\:{of}\:{signs}\:{may}\:{help}. \\ $$…
Question Number 5638 by Daily last updated on 23/May/16 $$\mathrm{If}\:{a}\leqslant\:\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{real}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{satisfying}\:{x}^{\mathrm{2}} −\mathrm{2}{a}\:\mid\:{x}−{a}\:\mid−\mathrm{3}{a}^{\mathrm{2}} =\mathrm{0}\:\mathrm{are} \\ $$ Answered by Yozzii last updated on 23/May/16 $${We}\:{can}\:{look}\:{for}\:{solutions}\:{based}\:{on} \\…
Question Number 5358 by realmath last updated on 11/May/16 $$\mathrm{The}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{the}\:\mathrm{simultaneous} \\ $$$$\mathrm{occurrence}\:\mathrm{of}\:\mathrm{two}\:\mathrm{events}\:{A}\:\mathrm{and}\:{B}\:\mathrm{is}\:{p}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{exactly}\:\mathrm{one}\:\mathrm{of} \\ $$$${A},\:{B}\:\mathrm{occurs}\:\mathrm{is}\:{q},\:\mathrm{then} \\ $$ Commented by Yozzii last updated on 11/May/16…
Question Number 5321 by qw last updated on 07/May/16 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{sin}^{\mathrm{2}} {x}} {\int}}\:\mathrm{sin}^{−\mathrm{1}} \sqrt{{t}}\:{dt}\:+\underset{\:\mathrm{0}} {\overset{\mathrm{cos}^{\mathrm{2}} {x}} {\int}}\mathrm{cos}^{−\mathrm{1}} \sqrt{{t}}\:{dt}\:= \\ $$ Commented by Yozzii last updated…
Question Number 5313 by qw last updated on 06/May/16 $$\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{{a}\left({a}+{b}+{c}\right)}{{bc}}}\:+\:\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{{b}\left({a}+{b}+{c}\right)}{{ca}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\mathrm{tan}^{−\mathrm{1}} \sqrt{\frac{{c}\left({a}+{b}+{c}\right)}{{ab}}}\:\:= \\ $$ Commented by Yozzii last updated on 07/May/16 $${Let}\:{j}={tan}\left({tan}^{−\mathrm{1}}…
Question Number 5206 by ´[ last updated on 30/Apr/16 $$\mathrm{If}\:\alpha,\:\beta\:\in\:{R},\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0},\:{k}\:\in\:{R}\:\mathrm{lies}\:\mathrm{between}\:\alpha\:\mathrm{and} \\ $$$$\beta,\:\mathrm{if} \\ $$ Commented by prakash jain last updated on 30/Apr/16…