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Question Number 79491 Answers: 0 Comments: 4
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{used}\:\mathrm{place} \\ $$
Question Number 79485 Answers: 1 Comments: 0
$$\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx} \\ $$
Question Number 79480 Answers: 0 Comments: 3
Question Number 79479 Answers: 0 Comments: 1
$$\mathrm{how}\:\mathrm{do}\:\mathrm{16}\:\mathrm{people}\:\mathrm{play}\:\mathrm{3}\:\mathrm{matches} \\ $$$$\mathrm{in}\:\mathrm{teams}\:\mathrm{of}\:\mathrm{4}\:\mathrm{but}\:\mathrm{must}\:\mathrm{only}\:\mathrm{be} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{team}\:\mathrm{once}\:?\: \\ $$
Question Number 79497 Answers: 1 Comments: 0
$$\frac{\left(\mathrm{4}{x}−\mid{x}−\mathrm{6}\mid\right)\left(\mathrm{log}_{\frac{\mathrm{1}}{\mathrm{3}}} \left({x}+\mathrm{4}\right)+\mathrm{1}\right)}{\mathrm{2}^{{x}^{\mathrm{2}} −\mathrm{2}^{\mid{x}\mid} } }\geqslant\mathrm{0} \\ $$
Question Number 79472 Answers: 0 Comments: 5
$$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}}\:+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{14x}+\mathrm{65}} \\ $$
Question Number 79469 Answers: 0 Comments: 0
$${Q}.{solve} \\ $$$$−\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }−{coth}\left({t}\right)\frac{{dy}}{{dt}}+\left(\mathrm{20}+\frac{\mathrm{4}}{{sinh}^{\mathrm{2}} \left({t}\right)}\right){y}=\mathrm{0} \\ $$
Question Number 79462 Answers: 1 Comments: 0
$${prove}\:{p}\Rightarrow{q}\:{and}\:\sim{q}\Rightarrow\sim{p}\:{are}\:{logicaly}\: \\ $$$${equivalent}\:{with}\:{out}\:{truth}\:{table} \\ $$$$ \\ $$
Question Number 79456 Answers: 0 Comments: 2
$$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{acute}\:\mathrm{positive}\:\mathrm{angles} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equations}\: \\ $$$$\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} {A}+\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} {B}=\mathrm{1}\:\mathrm{and}\: \\ $$$$\mathrm{3}\:\mathrm{sin}\:\mathrm{2}{A}−\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{B}=\mathrm{0},\:\mathrm{then}\:{A}+\mathrm{2}{B}= \\ $$
Question Number 79455 Answers: 1 Comments: 0
$$\mathrm{If}\:\:\mathrm{sin}\:\theta_{\mathrm{1}} +\mathrm{sin}\:\theta_{\mathrm{2}} +\mathrm{sin}\:\theta_{\mathrm{3}} \:=\:\mathrm{3},\:\mathrm{then} \\ $$$$\mathrm{cos}\:\theta_{\mathrm{1}} +\mathrm{cos}\:\theta_{\mathrm{2}} +\mathrm{cos}\:\theta_{\mathrm{3}} \:= \\ $$
Question Number 79453 Answers: 1 Comments: 0
$$\mathrm{If}\:\mathrm{in}\:\mathrm{a}\:\mathrm{triangle}\:{ABC} \\ $$$$\mathrm{2}\:\frac{\mathrm{cos}\:{A}}{{a}}+\frac{\mathrm{cos}\:{B}}{{b}}+\mathrm{2}\frac{\mathrm{cos}\:{C}}{{c}}\:=\:\frac{{a}}{{bc}}\:+\:\frac{{b}}{{ca}} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle}\:{A}\:\mathrm{is} \\ $$
Question Number 79452 Answers: 1 Comments: 1
$$\:\:\underset{\:\mathrm{1}} {\overset{\sqrt[{\mathrm{7}}]{\mathrm{2}}} {\int}}\:\frac{\mathrm{1}}{{x}\left(\mathrm{2}{x}^{\mathrm{7}} +\:\mathrm{1}\right)}\:{dx}\:= \\ $$
Question Number 79449 Answers: 1 Comments: 6
Question Number 79443 Answers: 1 Comments: 1
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} +\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{sin}\:\mathrm{x}} \right]\:= \\ $$
Question Number 79437 Answers: 0 Comments: 2
$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{1}°\:\mathrm{tan}\:\mathrm{2}°\:\mathrm{tan}\:\mathrm{3}°...\mathrm{tan}\:\mathrm{89}° \\ $$$$\mathrm{is} \\ $$
Question Number 79435 Answers: 0 Comments: 1
$$\mathrm{16}\:\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{14}\pi}{\mathrm{15}}\:=\_\_\_\_. \\ $$
Question Number 79424 Answers: 0 Comments: 0
$${Derive}\:{the}\:{width}\:{of}\:{the} \\ $$$${diffraction}\:{pattern}\:{for} \\ $$$${the}\:{case}\:{of} \\ $$$$\left({i}\right){single}\:{slits} \\ $$$$\left({ii}\right){double}\:{slits} \\ $$
Question Number 79423 Answers: 1 Comments: 0
$${solve}\:{for}\:{x}\:{and}\:{y}\: \\ $$$$\:\:\:{sinh}\:{x}\:−\:\mathrm{2}{cosh}\:{y}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{3}{cosh}\:{x}\:+\:\mathrm{6}\:{sihn}\:{y}\:=\:\mathrm{5} \\ $$
Question Number 79419 Answers: 0 Comments: 6
$$\mathrm{given}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{5}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{If}\:\int\:_{\mathrm{7}} ^{\mathrm{9}} \:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{t}\:\mathrm{and}\:\int\:_{\mathrm{2}} ^{\mathrm{6}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:= \\ $$$$\mathrm{t}^{\mathrm{2}} +\mathrm{4t}−\mathrm{3}\:.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{t}. \\ $$
Question Number 79417 Answers: 2 Comments: 3
$${For}\:{x},{y}\in\mathbb{R}\:{find}\:{the}\:{minimum}\:{and} \\ $$$${maximum}\:{of}\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4}{y} \\ $$$${if}\:{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} −{xy}−\mathrm{5}{x}−\mathrm{7}{y}−\mathrm{30}=\mathrm{0}. \\ $$
Question Number 79413 Answers: 0 Comments: 1
Question Number 79404 Answers: 0 Comments: 4
$$\mathrm{for}\:\mathrm{every}\:\mathrm{real}\:\mathrm{number}\:\mathrm{a}\:,\:\mathrm{b}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{4a}−\mathrm{6b}=\mathrm{2}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\: \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{expression}\: \\ $$$$\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{8a}−\mathrm{10b}+\mathrm{41}}\:? \\ $$
Question Number 79398 Answers: 0 Comments: 1
$$\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$
Question Number 79395 Answers: 0 Comments: 2
$$\mathrm{given}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{is}\:\mathrm{a}\:\:\mathrm{point}\:\mathrm{on}\:\mathrm{circle} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{6x}+\mathrm{4y}−\mathrm{23}=\mathrm{0}. \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{4x}+\mathrm{3y}\: \\ $$
Question Number 79394 Answers: 1 Comments: 0
Question Number 79377 Answers: 1 Comments: 3
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