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AllQuestion and Answers: Page 1341

Question Number 79462 Answers: 1 Comments: 0

prove p⇒q and ∼q⇒∼p are logicaly equivalent with out truth table

$${prove}\:{p}\Rightarrow{q}\:{and}\:\sim{q}\Rightarrow\sim{p}\:{are}\:{logicaly}\: \\ $$$${equivalent}\:{with}\:{out}\:{truth}\:{table} \\ $$$$ \\ $$

Question Number 79456 Answers: 0 Comments: 2

If A and B are acute positive angles satisfying the equations 3 sin^2 A+2 sin^2 B=1 and 3 sin 2A−2 sin 2B=0, then A+2B=

$$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{acute}\:\mathrm{positive}\:\mathrm{angles} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equations}\: \\ $$$$\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} {A}+\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} {B}=\mathrm{1}\:\mathrm{and}\: \\ $$$$\mathrm{3}\:\mathrm{sin}\:\mathrm{2}{A}−\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{B}=\mathrm{0},\:\mathrm{then}\:{A}+\mathrm{2}{B}= \\ $$

Question Number 79455 Answers: 1 Comments: 0

If sin θ_1 +sin θ_2 +sin θ_3 = 3, then cos θ_1 +cos θ_2 +cos θ_3 =

$$\mathrm{If}\:\:\mathrm{sin}\:\theta_{\mathrm{1}} +\mathrm{sin}\:\theta_{\mathrm{2}} +\mathrm{sin}\:\theta_{\mathrm{3}} \:=\:\mathrm{3},\:\mathrm{then} \\ $$$$\mathrm{cos}\:\theta_{\mathrm{1}} +\mathrm{cos}\:\theta_{\mathrm{2}} +\mathrm{cos}\:\theta_{\mathrm{3}} \:= \\ $$

Question Number 79453 Answers: 1 Comments: 0

If in a triangle ABC 2 ((cos A)/a)+((cos B)/b)+2((cos C)/c) = (a/(bc)) + (b/(ca)) then the value of the angle A is

$$\mathrm{If}\:\mathrm{in}\:\mathrm{a}\:\mathrm{triangle}\:{ABC} \\ $$$$\mathrm{2}\:\frac{\mathrm{cos}\:{A}}{{a}}+\frac{\mathrm{cos}\:{B}}{{b}}+\mathrm{2}\frac{\mathrm{cos}\:{C}}{{c}}\:=\:\frac{{a}}{{bc}}\:+\:\frac{{b}}{{ca}} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle}\:{A}\:\mathrm{is} \\ $$

Question Number 79452 Answers: 1 Comments: 1

∫_( 1) ^(2)^(1/7) (1/(x(2x^7 + 1))) dx =

$$\:\:\underset{\:\mathrm{1}} {\overset{\sqrt[{\mathrm{7}}]{\mathrm{2}}} {\int}}\:\frac{\mathrm{1}}{{x}\left(\mathrm{2}{x}^{\mathrm{7}} +\:\mathrm{1}\right)}\:{dx}\:= \\ $$

Question Number 79449 Answers: 1 Comments: 6

Question Number 79443 Answers: 1 Comments: 1

lim_(x→0) [(sin x)^(1/x) +((1/x))^(sin x) ] =

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} +\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{sin}\:\mathrm{x}} \right]\:= \\ $$

Question Number 79437 Answers: 0 Comments: 2

The value of tan 1° tan 2° tan 3°...tan 89° is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{1}°\:\mathrm{tan}\:\mathrm{2}°\:\mathrm{tan}\:\mathrm{3}°...\mathrm{tan}\:\mathrm{89}° \\ $$$$\mathrm{is} \\ $$

Question Number 79435 Answers: 0 Comments: 1

16 cos ((2π)/(15)) cos ((4π)/(15)) cos ((8π)/(15)) cos ((14π)/(15)) =____.

$$\mathrm{16}\:\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{8}\pi}{\mathrm{15}}\:\mathrm{cos}\:\frac{\mathrm{14}\pi}{\mathrm{15}}\:=\_\_\_\_. \\ $$

Question Number 79424 Answers: 0 Comments: 0

Derive the width of the diffraction pattern for the case of (i)single slits (ii)double slits

$${Derive}\:{the}\:{width}\:{of}\:{the} \\ $$$${diffraction}\:{pattern}\:{for} \\ $$$${the}\:{case}\:{of} \\ $$$$\left({i}\right){single}\:{slits} \\ $$$$\left({ii}\right){double}\:{slits} \\ $$

Question Number 79423 Answers: 1 Comments: 0

solve for x and y sinh x − 2cosh y = 0 3cosh x + 6 sihn y = 5

$${solve}\:{for}\:{x}\:{and}\:{y}\: \\ $$$$\:\:\:{sinh}\:{x}\:−\:\mathrm{2}{cosh}\:{y}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{3}{cosh}\:{x}\:+\:\mathrm{6}\:{sihn}\:{y}\:=\:\mathrm{5} \\ $$

Question Number 79419 Answers: 0 Comments: 6

given f(x)=f(x+5) ∀x∈R If ∫ _7^9 f(x)=t and ∫ _2^6 f(x)dx = t^2 +4t−3 . find the value of t.

$$\mathrm{given}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}+\mathrm{5}\right)\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{If}\:\int\:_{\mathrm{7}} ^{\mathrm{9}} \:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{t}\:\mathrm{and}\:\int\:_{\mathrm{2}} ^{\mathrm{6}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\:= \\ $$$$\mathrm{t}^{\mathrm{2}} +\mathrm{4t}−\mathrm{3}\:.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{t}. \\ $$

Question Number 79417 Answers: 2 Comments: 3

For x,y∈R find the minimum and maximum of 2x^2 −3x+4y if x^2 +2y^2 −xy−5x−7y−30=0.

$${For}\:{x},{y}\in\mathbb{R}\:{find}\:{the}\:{minimum}\:{and} \\ $$$${maximum}\:{of}\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4}{y} \\ $$$${if}\:{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} −{xy}−\mathrm{5}{x}−\mathrm{7}{y}−\mathrm{30}=\mathrm{0}. \\ $$

Question Number 79413 Answers: 0 Comments: 1

Question Number 79404 Answers: 0 Comments: 4

for every real number a , b such that a^2 +b^2 −4a−6b=2. what is the maximum and minimum value of the expression (√(a^2 +b^2 −8a−10b+41)) ?

$$\mathrm{for}\:\mathrm{every}\:\mathrm{real}\:\mathrm{number}\:\mathrm{a}\:,\:\mathrm{b}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{4a}−\mathrm{6b}=\mathrm{2}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\: \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{expression}\: \\ $$$$\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{8a}−\mathrm{10b}+\mathrm{41}}\:? \\ $$

Question Number 79398 Answers: 0 Comments: 1

((x^2 −1)/(x^2 +1))dx

$$\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 79395 Answers: 0 Comments: 2

given (x,y) is a point on circle x^2 +y^2 −6x+4y−23=0. find minimum and maximum value of 4x+3y

$$\mathrm{given}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{is}\:\mathrm{a}\:\:\mathrm{point}\:\mathrm{on}\:\mathrm{circle} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{6x}+\mathrm{4y}−\mathrm{23}=\mathrm{0}. \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{4x}+\mathrm{3y}\: \\ $$

Question Number 79394 Answers: 1 Comments: 0

Question Number 79377 Answers: 1 Comments: 3

Question Number 79374 Answers: 1 Comments: 0

Question Number 79373 Answers: 0 Comments: 0

find ∫_0 ^∞ e^(−(x^3 +(1/x^3 ))) dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)} {dx} \\ $$

Question Number 79368 Answers: 2 Comments: 6

Question Number 79365 Answers: 1 Comments: 1

Question Number 79361 Answers: 1 Comments: 1

Question Number 79359 Answers: 0 Comments: 1

Question Number 79357 Answers: 0 Comments: 1

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