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Question Number 94868    Answers: 0   Comments: 5

Question Number 94862    Answers: 0   Comments: 4

Show that cos^6 x+sin^6 x=(1/8)(5+3cos(4x)) By using the formula: a^3 +b^3 =(a+b)(a^2 −ab+b^2 )

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cos}^{\mathrm{6}} {x}+{sin}^{\mathrm{6}} {x}=\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{5}+\mathrm{3}{cos}\left(\mathrm{4}{x}\right)\right) \\ $$$$\mathrm{By}\:\mathrm{using}\:\mathrm{the}\:\mathrm{formula}: \\ $$$$\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} =\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}^{\mathrm{2}} −\mathrm{ab}+\mathrm{b}^{\mathrm{2}} \right) \\ $$

Question Number 94861    Answers: 0   Comments: 1

Show that (g○f)′(x)=g′(f(x))∙f′(x)

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{g}\circ\mathrm{f}\right)'\left(\mathrm{x}\right)=\mathrm{g}'\left(\mathrm{f}\left(\mathrm{x}\right)\right)\centerdot\mathrm{f}'\left(\mathrm{x}\right) \\ $$

Question Number 94857    Answers: 2   Comments: 7

Question Number 94855    Answers: 1   Comments: 0

Solve for x in R x(√(x+3))−4(√(x+3))+2x−8=0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{in}\:\mathbb{R} \\ $$$${x}\sqrt{{x}+\mathrm{3}}−\mathrm{4}\sqrt{{x}+\mathrm{3}}+\mathrm{2}{x}−\mathrm{8}=\mathrm{0} \\ $$

Question Number 94849    Answers: 1   Comments: 0

Calculate limits of f at +∞; −1 and 1 f(x)=2x+3−(x/(1−x^2 ))

$$\mathrm{Calculate}\:\mathrm{limits}\:\mathrm{of}\:{f}\:\mathrm{at}\:+\infty;\:−\mathrm{1}\:\mathrm{and}\:\mathrm{1} \\ $$$${f}\left({x}\right)=\mathrm{2}{x}+\mathrm{3}−\frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$

Question Number 94847    Answers: 2   Comments: 0

Question Number 94835    Answers: 0   Comments: 0

proof or disproof that if a quotient group (G/H) is abelian then G must be abelian.

$$\mathrm{proof}\:\mathrm{or}\:\mathrm{disproof}\:\mathrm{that}\:\mathrm{if}\:\mathrm{a}\:\mathrm{quotient} \\ $$$$\mathrm{group}\:\frac{\mathrm{G}}{\mathrm{H}}\:\mathrm{is}\:\mathrm{abelian}\:\mathrm{then}\:\mathrm{G}\:\mathrm{must}\:\mathrm{be}\:\mathrm{abelian}. \\ $$

Question Number 94820    Answers: 1   Comments: 0

A train which travels at a uniform speed due to mechanical fault after traveling for an hour goes at 3/5 th of the original speed and reaches the destination 2 hours late. If the fault occured after traveling another 50 miles the train would have reached 40 minutes earlier. What is the distance between the two stations ?

$${A}\:{train}\:{which}\:{travels}\:{at}\:{a}\:{uniform}\:{speed}\:{due}\:{to}\:{mechanical}\:{fault}\:{after}\: \\ $$$${traveling}\:{for}\:{an}\:{hour}\:{goes}\:{at}\:\mathrm{3}/\mathrm{5}\:{th}\:{of}\:{the}\:{original}\:{speed}\:{and}\:{reaches}\:{the}\: \\ $$$${destination}\:\mathrm{2}\:{hours}\:{late}.\:{If}\:{the}\:{fault}\:{occured}\:{after}\:{traveling}\:{another}\:\mathrm{50} \\ $$$${miles}\:{the}\:{train}\:{would}\:{have}\:{reached}\:\mathrm{40}\:{minutes}\:{earlier}.\:{What}\:{is}\:{the}\: \\ $$$${distance}\:{between}\:{the}\:{two}\:{stations}\:? \\ $$

Question Number 94818    Answers: 1   Comments: 7

find such a polynomial if is divided by (x−2) then the remainder is 5, if it isdivided by (x−3) the remainder is 9, if it is divided by (x−4) the remainder is 13, if divide by (x−10) and the remaider becomes 37 and if (x−(3/4)) divided by the remainder becomes zero?

$$\:\mathrm{find}\:\mathrm{such}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{if}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{2}\right)\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{remainder}\:\mathrm{is}\:\mathrm{5},\:\mathrm{if}\:\mathrm{it}\:\mathrm{isdivided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{3}\right)\:\mathrm{the}\:\mathrm{remainder} \\ $$$$\mathrm{is}\:\mathrm{9},\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{4}\right)\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{13},\:\mathrm{if}\: \\ $$$$\mathrm{divide}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{10}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaider}\:\mathrm{becomes}\:\mathrm{37}\:\mathrm{and} \\ $$$$\mathrm{if}\:\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)\:\mathrm{divided}\:\mathrm{by}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{becomes}\:\mathrm{zero}? \\ $$

Question Number 94816    Answers: 1   Comments: 2

Question Number 94811    Answers: 3   Comments: 0

∫(dx/(x+(√x))) (2,3)=?

$$\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}}}\:\:\:\left(\mathrm{2},\mathrm{3}\right)=? \\ $$

Question Number 94806    Answers: 0   Comments: 2

Question Number 94803    Answers: 1   Comments: 0

Question Number 94801    Answers: 0   Comments: 0

Question Number 94797    Answers: 1   Comments: 0

Question Number 94786    Answers: 0   Comments: 1

x, y ∈N\{0, 1} ∧ x≤y find z∈N with z!=x!y!

$${x},\:{y}\:\in\mathbb{N}\backslash\left\{\mathrm{0},\:\mathrm{1}\right\}\:\wedge\:{x}\leqslant{y} \\ $$$$\mathrm{find}\:{z}\in\mathbb{N}\:\mathrm{with}\:{z}!={x}!{y}! \\ $$

Question Number 94782    Answers: 1   Comments: 0

The velocity of physical quantities is given by v = (√((P + (1/n))/x)) , where P is the pressure. Find the dimention of n and x.

$$\mathrm{The}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{physical}\:\mathrm{quantities}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:\:\mathrm{v}\:\:=\:\:\sqrt{\frac{\mathrm{P}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{n}}}{\mathrm{x}}}\:,\:\:\mathrm{where}\:\:\mathrm{P}\:\mathrm{is}\:\mathrm{the}\:\mathrm{pressure}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{dimention}\:\mathrm{of}\:\:\:\mathrm{n}\:\:\mathrm{and}\:\:\mathrm{x}. \\ $$

Question Number 94780    Answers: 0   Comments: 1

x!(x−4)!=12(2x−7)! x=?

$$\mathrm{x}!\left(\mathrm{x}−\mathrm{4}\right)!=\mathrm{12}\left(\mathrm{2x}−\mathrm{7}\right)! \\ $$$$\mathrm{x}=? \\ $$

Question Number 94776    Answers: 0   Comments: 0

Question Number 94774    Answers: 2   Comments: 1

Question Number 94773    Answers: 1   Comments: 0

Question Number 94772    Answers: 0   Comments: 0

Question Number 94769    Answers: 2   Comments: 0

Question Number 94768    Answers: 1   Comments: 0

Question Number 94767    Answers: 1   Comments: 0

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