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Question Number 43463 Answers: 0 Comments: 1

Question Number 43461 Answers: 0 Comments: 1

found something (others have found before) which I thought might be of interest, especially for Sir Tanmay Chaudhury: take any polynome of degree 4 with 2 real inflection points y=ax^4 +bx^3 +cx^2 +dx+e y′′=12ax^2 +6bx+2c=0 has got 2 real solutions x_1 and x_2 the line connecting the inflection points intersects the curve in 2 more points P and Q, their x−values are p and q let p<x_1 <x_2 <q ⇒ ((x_2 −x_1 )/(x_1 −p))=((x_2 −x_1 )/(q−x_2 ))=(1/2)+((√5)/2) which is the Golden Ratio

$$\mathrm{found}\:\mathrm{something}\:\left(\mathrm{others}\:\mathrm{have}\:\mathrm{found}\:\mathrm{before}\right) \\ $$$$\mathrm{which}\:\mathrm{I}\:\mathrm{thought}\:\mathrm{might}\:\mathrm{be}\:\mathrm{of}\:\mathrm{interest}, \\ $$$$\mathrm{especially}\:\mathrm{for}\:\mathrm{Sir}\:\mathrm{Tanmay}\:\mathrm{Chaudhury}: \\ $$$$\mathrm{take}\:\mathrm{any}\:\mathrm{polynome}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{4}\:\mathrm{with}\:\mathrm{2}\:\mathrm{real} \\ $$$$\mathrm{inflection}\:\mathrm{points} \\ $$$${y}={ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e} \\ $$$${y}''=\mathrm{12}{ax}^{\mathrm{2}} +\mathrm{6}{bx}+\mathrm{2}{c}=\mathrm{0}\:\mathrm{has}\:\mathrm{got}\:\mathrm{2}\:\mathrm{real}\:\mathrm{solutions} \\ $$$${x}_{\mathrm{1}} \:\mathrm{and}\:{x}_{\mathrm{2}} \\ $$$$\mathrm{the}\:\mathrm{line}\:\mathrm{connecting}\:\mathrm{the}\:\mathrm{inflection}\:\mathrm{points} \\ $$$$\mathrm{intersects}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{in}\:\mathrm{2}\:\mathrm{more}\:\mathrm{points} \\ $$$${P}\:\mathrm{and}\:{Q},\:\mathrm{their}\:{x}−\mathrm{values}\:\mathrm{are}\:{p}\:\mathrm{and}\:{q} \\ $$$$\mathrm{let}\:{p}<{x}_{\mathrm{1}} <{x}_{\mathrm{2}} <{q} \\ $$$$\Rightarrow\:\frac{{x}_{\mathrm{2}} −{x}_{\mathrm{1}} }{{x}_{\mathrm{1}} −{p}}=\frac{{x}_{\mathrm{2}} −{x}_{\mathrm{1}} }{{q}−{x}_{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}\:\mathrm{which}\:\mathrm{is}\:\mathrm{the}\:\mathrm{Golden}\:\mathrm{Ratio} \\ $$

Question Number 43454 Answers: 0 Comments: 0

qn: There is a group of 50 people who are patriotic out of which 20 believes in non violence. Two persons are selected at rondom out of them. write the probability distribution for the selected persons who are non violent. also find the mean of the distribution. explain the importance of non violence in patriotism.

$$\mathrm{qn}:\:\mathrm{There}\:\mathrm{is}\:\mathrm{a}\:\mathrm{group}\:\mathrm{of}\:\mathrm{50}\:\mathrm{people} \\ $$$$\mathrm{who}\:\mathrm{are}\:\mathrm{patriotic}\:\mathrm{out}\:\mathrm{of}\:\mathrm{which}\:\mathrm{20} \\ $$$$\mathrm{believes}\:\mathrm{in}\:\mathrm{non}\:\mathrm{violence}.\:\mathrm{Two}\:\mathrm{persons} \\ $$$$\mathrm{are}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{rondom}\:\mathrm{out}\:\mathrm{of}\:\mathrm{them}. \\ $$$$\mathrm{write}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{distribution}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{selected}\:\mathrm{persons}\:\mathrm{who}\:\mathrm{are}\:\mathrm{non}\:\mathrm{violent}. \\ $$$$\mathrm{also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{the}\:\mathrm{distribution}. \\ $$$$\mathrm{explain}\:\mathrm{the}\:\mathrm{importance}\:\mathrm{of}\:\mathrm{non}\:\mathrm{violence}\:\mathrm{in}\:\mathrm{patriotism}. \\ $$$$ \\ $$$$ \\ $$

Question Number 43452 Answers: 1 Comments: 0

prove that tanhx=itanx

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{tanh}{x}}=\boldsymbol{{i}\mathrm{tan}{x}} \\ $$

Question Number 43449 Answers: 1 Comments: 0

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Question Number 43438 Answers: 2 Comments: 0

Question Number 43434 Answers: 0 Comments: 1

Let P and Q be statements. If (∼P) ∨ Q is true, then P ∨ Q is false. True or False?

$$\mathrm{Let}\:{P}\:\mathrm{and}\:{Q}\:\mathrm{be}\:\mathrm{statements}.\:\mathrm{If}\:\left(\sim{P}\right)\:\vee\:{Q}\:\mathrm{is}\:\mathrm{true}, \\ $$$$\mathrm{then}\:{P}\:\:\vee\:{Q}\:\mathrm{is}\:\mathrm{false}. \\ $$$$\mathrm{True}\:\mathrm{or}\:\mathrm{False}? \\ $$

Question Number 43419 Answers: 0 Comments: 2

Question Number 43418 Answers: 1 Comments: 0

Question Number 43417 Answers: 1 Comments: 2

Question Number 43416 Answers: 0 Comments: 1

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Question Number 43395 Answers: 1 Comments: 2

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Question Number 43391 Answers: 1 Comments: 0

x^2 +x=y^4 +y^3 +y^2 +y x^4 +(x+1)^4 =y^2 +(y+1)^2 find x and y of is…

$${x}^{\mathrm{2}} +{x}={y}^{\mathrm{4}} +{y}^{\mathrm{3}} +{y}^{\mathrm{2}} +{y} \\ $$$${x}^{\mathrm{4}} +\left({x}+\mathrm{1}\right)^{\mathrm{4}} ={y}^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}\:{x}\:\mathrm{and}\:{y}\:\:\mathrm{of}\:\mathrm{is}\ldots \\ $$$$ \\ $$

Question Number 43386 Answers: 4 Comments: 4

Question Number 43384 Answers: 1 Comments: 0

Question Number 43374 Answers: 1 Comments: 0

A drawer contains 5 brown socks and 4 blue socks well mixed. A man reaches the drawer and pulls out 2 socks at random. What is the probability that they match?

$$\mathrm{A}\:\mathrm{drawer}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{brown}\:\mathrm{socks}\:\mathrm{and}\:\mathrm{4} \\ $$$$\mathrm{blue}\:\mathrm{socks}\:\mathrm{well}\:\mathrm{mixed}.\:\mathrm{A}\:\mathrm{man}\:\mathrm{reaches} \\ $$$$\mathrm{the}\:\mathrm{drawer}\:\mathrm{and}\:\mathrm{pulls}\:\mathrm{out}\:\mathrm{2}\:\mathrm{socks}\:\mathrm{at} \\ $$$$\mathrm{random}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{they}\:\mathrm{match}? \\ $$

Question Number 43365 Answers: 0 Comments: 0

Question Number 43363 Answers: 3 Comments: 1

If z= cos θ + isin θ , 0<θ<(π/6) , then prove that argument of 1−z^4 = 2θ − (π/2) .

$$\mathrm{If}\:\mathrm{z}=\:\mathrm{cos}\:\theta\:+\:\mathrm{isin}\:\theta\:,\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{6}}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{argument}\:\mathrm{of}\:\:\mathrm{1}−\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{2}\theta\:−\:\frac{\pi}{\mathrm{2}}\:. \\ $$

Question Number 43360 Answers: 0 Comments: 9

Question Number 43354 Answers: 1 Comments: 0

A particle starts from rest with acceleration(30+6t) ms^(−2) at time t. Where will the particle come to rest again?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{with}\:\mathrm{acceleration}\left(\mathrm{30}+\mathrm{6t}\right) \\ $$$$\mathrm{ms}^{−\mathrm{2}} \:\mathrm{at}\:\mathrm{time}\:\mathrm{t}.\:\mathrm{Where}\:\mathrm{will}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{come}\:\mathrm{to}\:\mathrm{rest} \\ $$$$\mathrm{again}? \\ $$

Question Number 43353 Answers: 2 Comments: 1

Given the functions f(x)=2x−1 and f•g(x)=x^2 −x+2, find g(x)

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{functions}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}\:\mathrm{and}\:\mathrm{f}\bullet\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{2}, \\ $$$$\mathrm{find}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$

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