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Question Number 114202 Answers: 0 Comments: 1

pls suggest to me a meaningful nickname in physics.

$${pls}\:{suggest}\:{to}\:{me}\:{a}\:{meaningful}\:{nickname}\:{in} \\ $$$${physics}. \\ $$

Question Number 114201 Answers: 1 Comments: 3

find the greatest coefficient of (3y−8x)^(−6)

$${find}\:{the}\:{greatest}\:{coefficient}\:{of}\:\left(\mathrm{3}{y}−\mathrm{8}{x}\right)^{−\mathrm{6}} \\ $$

Question Number 114225 Answers: 1 Comments: 0

y^(′′) −3y^′ +2y=xsin(x)

$${y}^{''} −\mathrm{3}{y}^{'} +\mathrm{2}{y}={xsin}\left({x}\right) \\ $$

Question Number 114196 Answers: 1 Comments: 1

solve ∫_0 ^(π/4) ln(1+sinx)dx

$${solve} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{1}+\mathrm{sin}{x}\right){dx} \\ $$

Question Number 114253 Answers: 1 Comments: 0

For a cubic function in the form: f(x) = ax^3 +bx^2 +cx+d What must be true of a, b, c, and d in order for the function to be able to be converted to the form: f(x) = a(x−h)^3 +k

$$\mathrm{For}\:\mathrm{a}\:\mathrm{cubic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}: \\ $$$${f}\left({x}\right)\:=\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d} \\ $$$$\mathrm{What}\:\mathrm{must}\:\mathrm{be}\:\mathrm{true}\:\mathrm{of}\:{a},\:{b},\:{c},\:\mathrm{and}\:{d}\:\mathrm{in} \\ $$$$\mathrm{order}\:\mathrm{for}\:\mathrm{the}\:\mathrm{function}\:\mathrm{to}\:\mathrm{be}\:\mathrm{able}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{converted}\:\mathrm{to}\:\mathrm{the}\:\mathrm{form}: \\ $$$${f}\left({x}\right)\:=\:{a}\left({x}−{h}\right)^{\mathrm{3}} +{k} \\ $$

Question Number 114189 Answers: 0 Comments: 6

Question Number 114185 Answers: 5 Comments: 0

Question Number 114181 Answers: 3 Comments: 0

Given a function f(x) = x^2 +(1/x^2 )+4x+(4/x) ; where x>0. find the minimum value of f(x)

$${Given}\:{a}\:{function}\: \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{4}{x}+\frac{\mathrm{4}}{{x}}\:;\:{where}\:{x}>\mathrm{0}. \\ $$$${find}\:{the}\:{minimum}\:{value}\:{of}\:{f}\left({x}\right) \\ $$

Question Number 114176 Answers: 3 Comments: 1

(1) 3x^2 ln (y) dx + (x^3 /y)dy = 0 (2) (e^(2x) +4)y ′= y (3) dz = t(t^2 +1).e^(2z) dt

$$\left(\mathrm{1}\right)\:\mathrm{3}{x}^{\mathrm{2}} \:\mathrm{ln}\:\left({y}\right)\:{dx}\:+\:\frac{{x}^{\mathrm{3}} }{{y}}{dy}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\left({e}^{\mathrm{2}{x}} +\mathrm{4}\right){y}\:'=\:{y}\: \\ $$$$\left(\mathrm{3}\right)\:{dz}\:=\:{t}\left({t}^{\mathrm{2}} +\mathrm{1}\right).{e}^{\mathrm{2}{z}} \:{dt}\: \\ $$

Question Number 114167 Answers: 0 Comments: 2

if f(x)=x^2 ,∀x∈R then (1) the function is( one −to−one) (2) the function is not (one−to−one) chose (1) or (2)

$${if}\:{f}\left({x}\right)={x}^{\mathrm{2}} \:\:\:,\forall{x}\in{R} \\ $$$${then}\: \\ $$$$\left(\mathrm{1}\right)\:{the}\:{function}\:{is}\left(\:{one}\:−{to}−{one}\right) \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:{the}\:{function}\:{is}\:{not}\:\left({one}−{to}−{one}\right) \\ $$$$ \\ $$$${chose}\:\left(\mathrm{1}\right)\:{or}\:\left(\mathrm{2}\right) \\ $$

Question Number 114161 Answers: 2 Comments: 0

∫ (dx/(x^4 −5x^2 −16))

$$\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} −\mathrm{5}{x}^{\mathrm{2}} −\mathrm{16}} \\ $$

Question Number 114166 Answers: 0 Comments: 2

if u=5x^2 +1 , y=u^3 then (dy/dx)=? (1) (dy/du).(du/dx) (2)(dy/du)/(du/dx) chose (1) or (2)

$${if}\:{u}=\mathrm{5}{x}^{\mathrm{2}} +\mathrm{1}\:,\:{y}={u}^{\mathrm{3}} \:{then}\:\frac{{dy}}{{dx}}=? \\ $$$$\left(\mathrm{1}\right)\:\frac{{dy}}{{du}}.\frac{{du}}{{dx}}\:\:\:\:\:\left(\mathrm{2}\right)\frac{{dy}}{{du}}/\frac{{du}}{{dx}} \\ $$$$ \\ $$$${chose}\:\left(\mathrm{1}\right)\:{or}\:\left(\mathrm{2}\right) \\ $$

Question Number 114163 Answers: 0 Comments: 0

Question Number 114158 Answers: 2 Comments: 0

Question Number 114152 Answers: 2 Comments: 0

if f(x)=3x−2 find f^(−1) (x) ? (2)if f(x)=3x^2 −x+10 ,g(x)=1−20x find (fog)(5)

$${if}\:{f}\left({x}\right)=\mathrm{3}{x}−\mathrm{2}\:\:{find}\:{f}^{−\mathrm{1}} \left({x}\right)\:? \\ $$$$ \\ $$$$\left(\mathrm{2}\right){if}\:{f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −{x}+\mathrm{10}\:,{g}\left({x}\right)=\mathrm{1}−\mathrm{20}{x}\:{find}\: \\ $$$$\left({fog}\right)\left(\mathrm{5}\right) \\ $$

Question Number 114146 Answers: 0 Comments: 2

prove ∫_0 ^1 ((t^(n+2) φ(t,1,n+2)+ln(1−t)+t H_(n+1) )/(t(t−1)))dt =((H_(n+1) ^((2)) −(H_n )^2 )/2)

$${prove} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}^{{n}+\mathrm{2}} \phi\left({t},\mathrm{1},{n}+\mathrm{2}\right)+{ln}\left(\mathrm{1}−{t}\right)+{t}\:{H}_{{n}+\mathrm{1}} }{{t}\left({t}−\mathrm{1}\right)}{dt} \\ $$$$=\frac{{H}_{{n}+\mathrm{1}} ^{\left(\mathrm{2}\right)} −\left({H}_{{n}} \right)^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 114145 Answers: 1 Comments: 0

A particle moves along a straight line such that its velocity, v m s^(−1) , is given by v=t^3 −4t^2 +3t, where t is time, in seconds, after passing through fixed point O. Find the total distance, in m, travelled by the particle until the particle returned to the fixed point O for the second time.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{velocity},\:{v}\:\mathrm{m}\:\mathrm{s}^{−\mathrm{1}} ,\:\mathrm{is}\:\mathrm{given} \\ $$$$\mathrm{by}\:{v}={t}^{\mathrm{3}} −\mathrm{4}{t}^{\mathrm{2}} +\mathrm{3}{t},\:\mathrm{where}\:{t}\:\mathrm{is}\:\mathrm{time},\:\mathrm{in}\: \\ $$$$\mathrm{seconds},\:\mathrm{after}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{fixed} \\ $$$$\mathrm{point}\:\mathrm{O}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{distance},\:\mathrm{in}\:\mathrm{m},\:\mathrm{travelled} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{until}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{returned} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{fixed}\:\mathrm{point}\:\mathrm{O}\:\mathrm{for}\:\mathrm{the}\:\mathrm{second}\:\mathrm{time}. \\ $$

Question Number 114135 Answers: 2 Comments: 0

....Advanced mathematics ... i:: prove that : Ω=(1/π)∫_0 ^( ∞) (1/((x^2 −x+1)^2 (√x)))dx =1 ii::evaluate :: Φ = ∫_0 ^( 1) x^2 ln(x) ln(1−x)dx=??? ....m.n.july. 1970....

$$\:\:\:\:\:\:\:\:\:\:\:\:....\mathscr{A}{dvanced}\:\:{mathematics}\:... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{i}::\:{prove}\:\:{that}\::\:\:\:\:\Omega=\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} \sqrt{{x}}}{dx}\:=\mathrm{1}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{ii}::{evaluate}\:::\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{\mathrm{2}} \:{ln}\left({x}\right)\:{ln}\left(\mathrm{1}−{x}\right){dx}=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:....{m}.{n}.{july}.\:\mathrm{1970}.... \\ $$$$\: \\ $$

Question Number 114134 Answers: 1 Comments: 4

(m^2 −n^2 +6(n+m)/(m^2 −(6−n)^2 m+n=12

$$\left({m}^{\mathrm{2}} −{n}^{\mathrm{2}} +\mathrm{6}\left({n}+{m}\right)/\left({m}^{\mathrm{2}} −\left(\mathrm{6}−{n}\right)^{\mathrm{2}} \right.\right. \\ $$$${m}+{n}=\mathrm{12} \\ $$

Question Number 114130 Answers: 1 Comments: 5

Question Number 114122 Answers: 1 Comments: 0

find the value sin (cos^(−1) ((3/5))+tan^(−1) ((7/(13))))

$${find}\:{the}\:{value}\:\mathrm{sin}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{5}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{7}}{\mathrm{13}}\right)\right) \\ $$

Question Number 114114 Answers: 1 Comments: 1

A 50g golf ball is struck with a club moving with a velocity of 22m/s after it moves 4cm and ball accelerates with a velocity of 44m/s. estimate the average force exerted by the club on the ball.

$$ \\ $$$$\mathrm{A}\:\mathrm{50g}\:\mathrm{golf}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{struck}\:\mathrm{with}\:\mathrm{a}\:\mathrm{club}\:\mathrm{moving} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{22m}/\mathrm{s}\:\mathrm{after}\:\mathrm{it}\:\mathrm{moves}\:\mathrm{4cm}\:\mathrm{and} \\ $$$$\mathrm{ball}\:\mathrm{accelerates}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{44m}/\mathrm{s}. \\ $$$$\mathrm{estimate}\:\mathrm{the}\:\mathrm{average}\:\mathrm{force}\:\mathrm{exerted}\:\mathrm{by}\:\mathrm{the}\:\mathrm{club} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{ball}. \\ $$

Question Number 114110 Answers: 1 Comments: 2

(4/(1!)) + ((11)/(2!)) + ((22)/(3!)) + ((37)/(4!)) + ... = ?

$$\frac{\mathrm{4}}{\mathrm{1}!}\:+\:\frac{\mathrm{11}}{\mathrm{2}!}\:+\:\frac{\mathrm{22}}{\mathrm{3}!}\:+\:\frac{\mathrm{37}}{\mathrm{4}!}\:+\:...\:=\:? \\ $$

Question Number 114108 Answers: 3 Comments: 0

prove that 2 tan^(−1) ((2/3))=sin^(−1) (((12)/(13)))

$${prove}\:{that}\:\mathrm{2}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{12}}{\mathrm{13}}\right) \\ $$

Question Number 114107 Answers: 1 Comments: 2

prove that ∫_0 ^(π/2) [((ln(((1−sinx)/(1+sinx)))(√(cosx)))/((1+sinx)(√(1−sinx))))]dx=−8

$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left[\frac{\mathrm{ln}\left(\frac{\mathrm{1}−\mathrm{sin}{x}}{\mathrm{1}+\mathrm{sin}{x}}\right)\sqrt{\mathrm{cos}{x}}}{\left(\mathrm{1}+\mathrm{sin}{x}\right)\sqrt{\mathrm{1}−\mathrm{sin}{x}}}\right]{dx}=−\mathrm{8} \\ $$

Question Number 114105 Answers: 0 Comments: 1

∫ ((arctan(e^x ))/( (√x))) dx

$$\int\:\frac{{arctan}\left({e}^{{x}} \right)}{\:\sqrt{{x}}}\:{dx} \\ $$

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