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Question Number 55501    Answers: 0   Comments: 5

Roots of x^3 +px+q=0 are x = u+v u^3 , v^3 are roots of z^2 −α^3 z+β^6 =0 ((d^2 (y/x))/dx^2 )∣_(x=α) =0 , (dy/dx)∣_(x=β) =0 . I have noticed long way back, please hunt why (how come) ?

$${Roots}\:{of}\:{x}^{\mathrm{3}} +{px}+{q}=\mathrm{0} \\ $$$${are}\:\:{x}\:=\:{u}+{v} \\ $$$${u}^{\mathrm{3}} ,\:{v}^{\mathrm{3}} \:{are}\:{roots}\:{of} \\ $$$$\:\:\:\:\:\:\:{z}^{\mathrm{2}} −\alpha^{\mathrm{3}} {z}+\beta^{\mathrm{6}} =\mathrm{0} \\ $$$$\:\:\:\frac{{d}^{\mathrm{2}} \left({y}/{x}\right)}{{dx}^{\mathrm{2}} }\mid_{{x}=\alpha} =\mathrm{0}\:\:,\:\frac{{dy}}{{dx}}\mid_{{x}=\beta} =\mathrm{0}\:. \\ $$$${I}\:{have}\:{noticed}\:{long}\:{way}\:{back}, \\ $$$${please}\:{hunt}\:{why}\:\left({how}\:{come}\right)\:? \\ $$

Question Number 55493    Answers: 0   Comments: 6

Find intgral of tan x by parts ∫tan x dx pls help me (i am a newbie in calculus)

$${Find}\:{intgral}\:{of}\:\mathrm{tan}\:{x}\:{by}\:{parts} \\ $$$$\int{tan}\:{x}\:{dx}\:\:\:{pls}\:{help}\:{me}\:\:\left({i}\:{am}\:{a}\:{newbie}\:{in}\:{calculus}\right) \\ $$

Question Number 55491    Answers: 1   Comments: 0

Question Number 55482    Answers: 1   Comments: 0

A group of n students are numbered continously from first sdtudent as 1,2,3,...... If 1101 digits had to be used in all,what is the number of students in the group

$${A}\:{group}\:{of}\:{n}\:{students}\:{are}\:{numbered} \\ $$$${continously}\:{from}\:{first}\:{sdtudent}\:{as}\:\mathrm{1},\mathrm{2},\mathrm{3},...... \\ $$$${If}\:\mathrm{1101}\:{digits}\:{had}\:{to}\:{be}\:{used}\:{in}\:{all},{what}\:{is}\:{the}\: \\ $$$${number}\:{of}\:{students}\:{in}\:{the}\:{group} \\ $$

Question Number 55476    Answers: 1   Comments: 0

4 metal rods of length 78 cm,104 cm,117cm, a.nd 169 cm are to be cut into parts of equal length Each length must be as long as possible What is the maximum number of pieces that can be cut?

$$\mathrm{4}\:{metal}\:{rods}\:{of}\:{length}\:\mathrm{78}\:{cm},\mathrm{104}\:{cm},\mathrm{117}{cm}, \\ $$$${a}.{nd}\:\mathrm{169}\:{cm}\:{are}\:{to}\:{be}\:{cut}\:{into}\:{parts}\:{of}\:{equal}\:{length} \\ $$$${Each}\:{length}\:{must}\:{be}\:{as}\:{long}\:{as}\:{possible} \\ $$$${What}\:{is}\:{the}\:{maximum}\:{number}\:{of}\:{pieces} \\ $$$${that}\:{can}\:{be}\:{cut}? \\ $$

Question Number 55475    Answers: 1   Comments: 0

Find the equation of the plane passing through the points (1,0,0) and (0,1,0) and makes an angle of (π/4) with the plane x+y = 3

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points} \\ $$$$\left(\mathrm{1},\mathrm{0},\mathrm{0}\right)\:\mathrm{and}\:\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\mathrm{and}\:\mathrm{makes} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\:\frac{\pi}{\mathrm{4}}\:\mathrm{with}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{x}+\mathrm{y}\:=\:\mathrm{3} \\ $$

Question Number 55473    Answers: 0   Comments: 1

Question Number 55468    Answers: 1   Comments: 0

Question Number 55467    Answers: 0   Comments: 3

Question Number 55458    Answers: 1   Comments: 1

Question Number 55457    Answers: 0   Comments: 2

calculate ∫_0 ^∞ ((ln(x))/(x^2 +x+1))dx .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({x}\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}\:. \\ $$

Question Number 55449    Answers: 1   Comments: 0

Question Number 55444    Answers: 0   Comments: 0

Question Number 55433    Answers: 1   Comments: 0

Question Number 55431    Answers: 1   Comments: 1

2 plane parallel conducting plates are held horizontal,one above the other in a vacuum.Electrons having a speed of 6×10^6 m/s and moves normally to the plates enter the region between them through a hole in the lower plate which is earthed.What potential must be applied to the other plate so that the electrons just fails to reach it?What is the subsequent motion of these electrons? (ratio of charge to mass of electron= 1.8×10^(11) Ckg^(−1) )

$$\mathrm{2}\:{plane}\:{parallel}\:{conducting}\:{plates}\:{are} \\ $$$${held}\:{horizontal},{one}\:{above}\:{the}\:{other}\:{in} \\ $$$${a}\:{vacuum}.{Electrons}\:{having}\:{a}\:{speed}\:{of} \\ $$$$\mathrm{6}×\mathrm{10}^{\mathrm{6}} {m}/{s}\:{and}\:{moves}\:{normally}\:{to}\:{the} \\ $$$${plates}\:{enter}\:{the}\:{region}\:{between}\:{them} \\ $$$${through}\:{a}\:{hole}\:{in}\:{the}\:{lower}\:{plate}\:{which} \\ $$$${is}\:{earthed}.{What}\:{potential}\:{must}\:{be} \\ $$$${applied}\:{to}\:{the}\:{other}\:{plate}\:{so}\:{that}\:{the} \\ $$$${electrons}\:{just}\:{fails}\:{to}\:{reach}\:{it}?{What} \\ $$$${is}\:{the}\:{subsequent}\:{motion}\:{of}\:{these} \\ $$$${electrons}? \\ $$$$\left({ratio}\:{of}\:{charge}\:{to}\:{mass}\:{of}\:{electron}=\right. \\ $$$$\left.\mathrm{1}.\mathrm{8}×\mathrm{10}^{\mathrm{11}} {Ckg}^{−\mathrm{1}} \right) \\ $$

Question Number 55422    Answers: 0   Comments: 1

Please see these questions:

$${Please}\:{see}\:{these}\:{questions}: \\ $$

Question Number 55418    Answers: 3   Comments: 1

Question Number 55401    Answers: 0   Comments: 3

any wanna blow their mind

$${any}\:{wanna}\:{blow}\:{their}\:{mind} \\ $$

Question Number 55415    Answers: 2   Comments: 0

a, b, d are gp. such that a, b, c are real. if a + b + c = 26 and a^2 + b^2 + c^2 = 364, find b ?

$$\mathrm{a},\:\mathrm{b},\:\mathrm{d}\:\:\mathrm{are}\:\mathrm{gp}.\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\mathrm{are}\:\mathrm{real}.\:\:\mathrm{if}\:\: \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\:=\:\:\mathrm{26}\:\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{364},\:\:\:\:\:\mathrm{find}\:\:\mathrm{b}\:\:? \\ $$

Question Number 55412    Answers: 0   Comments: 0

Solve for x and y. 2^x + 2y = 1 ....... equation (i) 3^(2x) + y = 27 ..... equation (ii)

$$\mathrm{Solve}\:\mathrm{for}\:\:\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}^{\mathrm{x}} \:+\:\mathrm{2y}\:\:=\:\:\mathrm{1}\:\:\:\:\:\:\:.......\:\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{2x}} \:+\:\mathrm{y}\:\:=\:\:\mathrm{27}\:\:\:\:\:\:\:\:.....\:\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$

Question Number 55411    Answers: 1   Comments: 0

Question Number 55410    Answers: 1   Comments: 0

Question Number 55408    Answers: 1   Comments: 0

Question Number 55375    Answers: 1   Comments: 1

Question Number 55374    Answers: 1   Comments: 0

Given matrices A(x)= [((x−1),3),(4,(x+3)) ]∈ M_2 (R). The smallest det(A(x)) is..

$$\mathrm{Given}\:\mathrm{matrices}\:{A}\left({x}\right)=\begin{bmatrix}{{x}−\mathrm{1}}&{\mathrm{3}}\\{\mathrm{4}}&{{x}+\mathrm{3}}\end{bmatrix}\in\:{M}_{\mathrm{2}} \left(\mathbb{R}\right). \\ $$$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{det}\left({A}\left({x}\right)\right)\:\mathrm{is}.. \\ $$

Question Number 55373    Answers: 1   Comments: 1

lim_(n→∝) ∫_0 ^1 ((x^n e^x^n )/(cos x)) dx=...

$$\underset{{n}\rightarrow\propto} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} {e}^{{x}^{{n}} } }{\mathrm{cos}\:{x}}\:{dx}=... \\ $$

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