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Question Number 198772    Answers: 0   Comments: 1

x^4 +ax^3 +bx^2 +cx+d=0

$${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$

Question Number 198763    Answers: 3   Comments: 3

Question Number 198761    Answers: 0   Comments: 0

Question Number 198754    Answers: 1   Comments: 0

Question Number 198753    Answers: 0   Comments: 0

Question Number 198750    Answers: 1   Comments: 0

Prove the following is a tautology: [(p⊻q)∧(p⇒r)]⇒(q⊻r)

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tautology}: \\ $$$$\left[\left({p}\veebar{q}\right)\wedge\left({p}\Rightarrow{r}\right)\right]\Rightarrow\left({q}\veebar{r}\right) \\ $$

Question Number 198749    Answers: 0   Comments: 0

Find area bounded by curve below cx^3 +c^2 +y(y+1)^2 =x^2 y+cx(3y+1)

$${Find}\:{area}\:{bounded}\:{by}\:{curve}\:{below} \\ $$$${cx}^{\mathrm{3}} +{c}^{\mathrm{2}} +{y}\left({y}+\mathrm{1}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} {y}+{cx}\left(\mathrm{3}{y}+\mathrm{1}\right) \\ $$

Question Number 198743    Answers: 1   Comments: 0

Question Number 198731    Answers: 2   Comments: 2

Question Number 198722    Answers: 0   Comments: 0

I have one question. What is Exact definition of the Vector Field Form Of an Eletric Field?? for exmple.. Vector Field v^ (x,y,z)=yze_1 ^ +xze_2 ^ +xye_3 ^ i mean in physics They do all sorts of calculations using the Electrical Field but i can′t understand it cus it′s such a Abstract concept ex...▽^ ×E^ =−(∂B^ /∂t) or 𝚽=∮_A D∙dA=Q_0 ...etc help me

$$\mathrm{I}\:\mathrm{have}\:\mathrm{one}\:\mathrm{question}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{Exact}\:\mathrm{definition}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Vector}\:\mathrm{Field}\:\mathrm{Form}\:\mathrm{Of}\:\mathrm{an}\:\mathrm{Eletric}\:\mathrm{Field}?? \\ $$$$\mathrm{for}\:\mathrm{exmple}.. \\ $$$$\mathrm{Vector}\:\mathrm{Field}\: \\ $$$$\hat {\boldsymbol{\mathrm{v}}}\left({x},{y},{z}\right)={yz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} +{xz}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{2}} +{xy}\hat {\boldsymbol{\mathrm{e}}}_{\mathrm{3}} \\ $$$$\mathrm{i}\:\mathrm{mean}\:\mathrm{in}\:\mathrm{physics}\:\mathrm{They}\:\mathrm{do}\:\mathrm{all}\:\mathrm{sorts}\:\mathrm{of}\:\mathrm{calculations} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{Electrical}\:\mathrm{Field} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{understand}\:\mathrm{it} \\ $$$$\mathrm{cus}\:\mathrm{it}'\mathrm{s}\:\mathrm{such}\:\mathrm{a}\:\mathrm{Abstract}\:\mathrm{concept} \\ $$$$\mathrm{ex}...\hat {\bigtriangledown}×\hat {\boldsymbol{\mathrm{E}}}=−\frac{\partial\hat {\boldsymbol{\mathrm{B}}}}{\partial{t}}\:\:\mathrm{or}\:\boldsymbol{\Phi}=\oint_{{A}} \boldsymbol{\mathrm{D}}\centerdot\mathrm{d}\boldsymbol{\mathrm{A}}={Q}_{\mathrm{0}} ...\mathrm{etc} \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$

Question Number 211812    Answers: 1   Comments: 1

prove lim_(x→∞) ( 1 + (5/x) )^(1/x) − 1 = 5

$${prove}\:\underset{{x}\rightarrow\infty} {{lim}}\:\left(\:\mathrm{1}\:+\:\frac{\mathrm{5}}{{x}}\:\right)^{\frac{\mathrm{1}}{{x}}} −\:\mathrm{1}\:=\:\mathrm{5}\: \\ $$

Question Number 198688    Answers: 1   Comments: 0

y′′ + (2/x).y′ + y = 0 y=¿

$${y}''\:+\:\frac{\mathrm{2}}{{x}}.{y}'\:+\:{y}\:=\:\mathrm{0} \\ $$$${y}=¿ \\ $$

Question Number 198684    Answers: 3   Comments: 0

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 198604    Answers: 1   Comments: 1

Question Number 198692    Answers: 0   Comments: 0

Question Number 198695    Answers: 1   Comments: 0

∫_0 ^∞ ((e^(at) −e^(−at) )/(e^(πt) −e^(−πt) )) dt = ??

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{\mathrm{at}} −\mathrm{e}^{−\mathrm{at}} }{\mathrm{e}^{\pi\mathrm{t}} −\mathrm{e}^{−\pi\mathrm{t}} }\:\mathrm{dt}\:\:\:=\:\:\:?? \\ $$

Question Number 198647    Answers: 3   Comments: 1

Question Number 198646    Answers: 1   Comments: 0

Question Number 198576    Answers: 1   Comments: 10

How many numbers with a maximum of 5 digits, greater than 4000, can be formed with the digits 2, 3, 4, 5, 6; if repetition is allowed for 2 and 3 only?

How many numbers with a maximum of 5 digits, greater than 4000, can be formed with the digits 2, 3, 4, 5, 6; if repetition is allowed for 2 and 3 only?

Question Number 198575    Answers: 1   Comments: 3

Question Number 198572    Answers: 1   Comments: 0

lim_(x→(π/(2n))) ((√((sin 2nx)/(1+cos nx)))/(4n^2 x^2 −π^2 )) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2n}}} {\mathrm{lim}}\:\frac{\sqrt{\frac{\mathrm{sin}\:\mathrm{2nx}}{\mathrm{1}+\mathrm{cos}\:\mathrm{nx}}}}{\mathrm{4n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} −\pi^{\mathrm{2}} }\:=? \\ $$

Question Number 198566    Answers: 3   Comments: 0

((3x^2 −1)/x)+((5x)/(3x^2 −x−1))=((119)/(18))

$$\frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{{x}}+\frac{\mathrm{5}{x}}{\mathrm{3}{x}^{\mathrm{2}} −{x}−\mathrm{1}}=\frac{\mathrm{119}}{\mathrm{18}} \\ $$

Question Number 198565    Answers: 0   Comments: 0

Let a,b,c ∈ R^+ such that a+b+c=1. Prove that: b+c≥16abc

$${Let}\:{a},{b},{c}\:\in\:{R}^{+} \:{such}\:{that}\:{a}+{b}+{c}=\mathrm{1}. \\ $$$$\:{Prove}\:{that}:\:\:\:\:{b}+{c}\geqslant\mathrm{16}{abc} \\ $$

Question Number 198563    Answers: 1   Comments: 0

find all numbers (with any number of digits) satisfying (abcd...xyz)×2=(zyx...dcba)

$${find}\:{all}\:{numbers}\:\left({with}\:{any}\:{number}\right. \\ $$$$\left.{of}\:{digits}\right)\:{satisfying} \\ $$$$\left(\underline{{abcd}...{xyz}}\right)×\mathrm{2}=\left(\underline{{zyx}...{dcba}}\right) \\ $$

Question Number 198562    Answers: 1   Comments: 0

f(tan x)+ 2f(cot x) = 4x f ′(x)= ?

$$\:\:\:\mathrm{f}\left(\mathrm{tan}\:\mathrm{x}\right)+\:\mathrm{2f}\left(\mathrm{cot}\:\mathrm{x}\right)\:=\:\mathrm{4x}\: \\ $$$$\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)=\:? \\ $$

Question Number 198559    Answers: 0   Comments: 0

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