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Question Number 96428 Answers: 2 Comments: 0

Question Number 96427 Answers: 0 Comments: 0

Question Number 96419 Answers: 5 Comments: 3

Question Number 96410 Answers: 0 Comments: 4

Question Number 96407 Answers: 1 Comments: 4

Question Number 96397 Answers: 1 Comments: 0

Hello If 5000F is the price to carry 5 tonnes of water on 5 kilometers, what is the price to carry 60 tonnes on 70.5 kilometers? please explain if possible...

$${Hello} \\ $$$${If}\:\:\mathrm{5000}{F}\:{is}\:{the}\:{price}\:{to}\:{carry}\:\mathrm{5}\:{tonnes} \\ $$$${of}\:{water}\:{on}\:\mathrm{5}\:{kilometers},\:{what}\:{is}\:{the} \\ $$$${price}\:{to}\:{carry}\:\mathrm{60}\:{tonnes}\:{on}\:\mathrm{70}.\mathrm{5}\: \\ $$$${kilometers}? \\ $$$${please}\:{explain}\:{if}\:{possible}... \\ $$

Question Number 96394 Answers: 0 Comments: 0

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

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

Question Number 96392 Answers: 1 Comments: 0

solve (dy/dx) = (4x+y+1)^2 , when y(0) = 1

$$\mathrm{solve}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\left(\mathrm{4x}+\mathrm{y}+\mathrm{1}\right)^{\mathrm{2}} \:,\:\mathrm{when}\: \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$

Question Number 96383 Answers: 1 Comments: 0

Find domain & range of function f(x) = (1/(x^2 −5x+6))

$$\mathrm{Find}\:\mathrm{domain}\:\&\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}}\: \\ $$

Question Number 96377 Answers: 1 Comments: 0

if tan(x+iy)=a+ib determine x and y interms of a and b

$$\mathrm{if}\:\mathrm{tan}\left(\mathrm{x}+\mathrm{iy}\right)=\mathrm{a}+\mathrm{ib}\:\:\:\mathrm{determine}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{interms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b} \\ $$

Question Number 96375 Answers: 2 Comments: 0

let P(x) =(1+x^2 )(1+x^4 )...(1+x^2^n ) 1) solve inside C the equation P(x)=0 2) factorize P(x) inside C[x] 3) calvulate P^′ (x) 4) decompose F =(1/(P(x)))

$$\mathrm{let}\:\mathrm{P}\left(\mathrm{x}\right)\:=\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)...\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}^{\mathrm{n}} } \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{solve}\:\mathrm{inside}\:\mathrm{C}\:\:\mathrm{the}\:\mathrm{equation}\:\mathrm{P}\left(\mathrm{x}\right)=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calvulate}\:\mathrm{P}^{'} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{4}\right)\:\mathrm{decompose}\:\mathrm{F}\:=\frac{\mathrm{1}}{\mathrm{P}\left(\mathrm{x}\right)} \\ $$

Question Number 96373 Answers: 2 Comments: 0

1. find ∫_1 ^(+∞) (dx/(x^2 −i)) and ∫_1 ^(+∞) (dx/(x^2 +i)) (i=(√(−1))) 2. find the value of ∫_1 ^(+∞) (dx/(x^4 +1))

$$\mathrm{1}.\:\mathrm{find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} −\mathrm{i}}\:\:\mathrm{and}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{i}}\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$$$\mathrm{2}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$

Question Number 96365 Answers: 2 Comments: 0

Question Number 96358 Answers: 0 Comments: 0

Question Number 96350 Answers: 1 Comments: 2

Question Number 96349 Answers: 0 Comments: 1

Question Number 96390 Answers: 1 Comments: 0

Question Number 96346 Answers: 1 Comments: 4

∫(1/(ln(x)))dx

$$\int\frac{\mathrm{1}}{\mathfrak{ln}\left(\mathfrak{x}\right)}\boldsymbol{\mathrm{d}}\mathfrak{x} \\ $$

Question Number 96342 Answers: 2 Comments: 2

∫e^(sin(x)) dx

$$\int\mathfrak{e}^{\mathfrak{sin}\left(\mathfrak{x}\right)} \boldsymbol{\mathrm{d}}\mathfrak{x} \\ $$

Question Number 96340 Answers: 0 Comments: 4

The equations of two circles S_1 and S_2 are given by S_1 : x^2 + y^2 +2x +2y + 1 = 0 S_2 : x^2 + y^2 −4x + 2y +1 = 0. Show that S_1 and S_2 touch each other externally and obtain the equation of the common tangent T at the point of contact.

$$\mathrm{The}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{two}\:\mathrm{circles}\:{S}_{\mathrm{1}} \:\mathrm{and}\:{S}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{given}\:\mathrm{by} \\ $$$$\:{S}_{\mathrm{1}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\mathrm{2}{x}\:+\mathrm{2}{y}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\:\:\:{S}_{\mathrm{2}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{4}{x}\:+\:\mathrm{2}{y}\:+\mathrm{1}\:=\:\mathrm{0}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:{S}_{\mathrm{1}} \:\mathrm{and}\:{S}_{\mathrm{2}} \:\mathrm{touch}\:\mathrm{each}\:\mathrm{other}\:\mathrm{externally}\:\mathrm{and}\:\mathrm{obtain} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{tangent}\:{T}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{contact}. \\ $$

Question Number 96335 Answers: 0 Comments: 0

∫(((3x^3 −x^2 +2x−4))/(√(x^3 −3x+4)))dx

$$\int\frac{\left(\mathrm{3}\mathfrak{x}^{\mathrm{3}} −\mathfrak{x}^{\mathrm{2}} +\mathrm{2}\mathfrak{x}−\mathrm{4}\right)}{\sqrt{\mathfrak{x}^{\mathrm{3}} −\mathrm{3}\mathfrak{x}+\mathrm{4}}}\boldsymbol{\mathrm{d}}\mathfrak{x} \\ $$

Question Number 96330 Answers: 0 Comments: 2