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Question Number 114236 Answers: 2 Comments: 0

70% of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACs and 85% have washing machines. At least what percentage of employees has all four gadgets?

$$\mathrm{70\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{employees}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{multinational}\:\mathrm{corporation}\:\mathrm{have}\:\mathrm{VCD} \\ $$$$\mathrm{players},\:\mathrm{75\%}\:\mathrm{have}\:\mathrm{microwave}\:\mathrm{ovens}, \\ $$$$\mathrm{80\%}\:\mathrm{have}\:\mathrm{ACs}\:\mathrm{and}\:\mathrm{85\%}\:\mathrm{have}\:\mathrm{washing} \\ $$$$\mathrm{machines}.\:\mathrm{At}\:\mathrm{least}\:\mathrm{what}\:\mathrm{percentage}\:\mathrm{of} \\ $$$$\mathrm{employees}\:\mathrm{has}\:\mathrm{all}\:\mathrm{four}\:\mathrm{gadgets}? \\ $$

Question Number 114235 Answers: 2 Comments: 0

Let A={(n,2n):n∈N} and B={(2n,3n):n∈N}. Then A∩B is equal to

$$\mathrm{Let}\:\mathrm{A}=\left\{\left(\mathrm{n},\mathrm{2n}\right):\mathrm{n}\in\mathrm{N}\right\}\:\mathrm{and} \\ $$$$\mathrm{B}=\left\{\left(\mathrm{2n},\mathrm{3n}\right):\mathrm{n}\in\mathrm{N}\right\}.\:\mathrm{Then}\:\mathrm{A}\cap\mathrm{B}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 114233 Answers: 1 Comments: 0

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A×B and B×A is

$$\mathrm{If}\:\mathrm{two}\:\mathrm{sets}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{having}\:\mathrm{99} \\ $$$$\mathrm{elements}\:\mathrm{in}\:\mathrm{common},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{common}\:\mathrm{to}\:\mathrm{each} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{sets}\:\mathrm{A}×\mathrm{B}\:\mathrm{and}\:\mathrm{B}×\mathrm{A}\:\mathrm{is} \\ $$

Question Number 114223 Answers: 1 Comments: 0

Question Number 114219 Answers: 0 Comments: 0

Question Number 114212 Answers: 1 Comments: 0

Question Number 114208 Answers: 0 Comments: 18

find the greatest coeeficient in the expansion of (3+4x)^(−5)

$${find}\:{the}\:{greatest}\:{coeeficient}\:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{3}+\mathrm{4}{x}\right)^{−\mathrm{5}} \\ $$

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

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

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