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Question Number 43489 Answers: 1 Comments: 0

if y=cos(logx) +3sin(logx) prove that x^2 (d^2 x/dx^2 )+x(dy/dx)+y=0

$${if}\:{y}={cos}\left({logx}\right)\:+\mathrm{3}{sin}\left({logx}\right)\:{prove}\:{that} \\ $$$${x}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {x}}{{dx}^{\mathrm{2}} }+{x}\frac{{dy}}{{dx}}+{y}=\mathrm{0} \\ $$

Question Number 43488 Answers: 1 Comments: 0

if the root of x^3 +px_ ^2 +qx+30=0 are in the ratio 2:3:5find the value of p and q

$${if}\:{the}\:{root}\:{of}\:\:{x}^{\mathrm{3}} +{px}_{} ^{\mathrm{2}} +{qx}+\mathrm{30}=\mathrm{0}\:{are} \\ $$$${in}\:{the}\:{ratio}\:\mathrm{2}:\mathrm{3}:\mathrm{5}{find}\:{the}\:{value}\:{of}\:{p}\:{and}\:{q} \\ $$

Question Number 43486 Answers: 3 Comments: 1

Question Number 43481 Answers: 1 Comments: 0

(((1+2i)^3 )/((3+i)))=

$$\frac{\left(\mathrm{1}+\mathrm{2}{i}\right)^{\mathrm{3}} }{\left(\mathrm{3}+{i}\right)}= \\ $$

Question Number 43471 Answers: 1 Comments: 0

Question Number 43470 Answers: 0 Comments: 0

Please what topic is all the question that has the summation sign. Σ. How can i study the summation by using it to solve some continuous equation.

$$\mathrm{Please}\:\mathrm{what}\:\mathrm{topic}\:\mathrm{is}\:\mathrm{all}\:\mathrm{the}\:\mathrm{question}\:\mathrm{that}\:\mathrm{has}\:\mathrm{the}\:\mathrm{summation}\:\mathrm{sign}. \\ $$$$\Sigma.\:\:\:\:\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{study}\:\mathrm{the}\:\mathrm{summation}\:\mathrm{by}\:\mathrm{using}\:\mathrm{it}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{some}\:\mathrm{continuous} \\ $$$$\mathrm{equation}. \\ $$

Question Number 43467 Answers: 2 Comments: 0

prove that tanθ+2tan2θ+4tan 4θ +8cot8θ=cotθ

$${prove}\:{th}\mathrm{at}\:\mathrm{tan}\theta+\mathrm{2}{tan}\mathrm{2}\theta+\mathrm{4}{tan}\:\:\:\mathrm{4}\theta \\ $$$$+\mathrm{8cot8}\theta={cot}\theta \\ $$

Question Number 43465 Answers: 2 Comments: 1

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