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If a petrol tank costs σ2000.00 to fill it up at 10°C,how much extra must I pay to fill up the tank at 50°C if the petrol costs σ50.00 per litre and its cubic expansivity is 9.5×10^(−4) K^(−1) ?

$${If}\:{a}\:{petrol}\:{tank}\:{costs}\:\sigma\mathrm{2000}.\mathrm{00}\:{to} \\ $$$${fill}\:{it}\:{up}\:{at}\:\mathrm{10}°{C},{how}\:{much}\:{extra} \\ $$$${must}\:{I}\:{pay}\:{to}\:{fill}\:{up}\:{the}\:{tank}\:{at}\:\mathrm{50}°{C} \\ $$$${if}\:{the}\:{petrol}\:{costs}\:\sigma\mathrm{50}.\mathrm{00}\:{per}\:{litre} \\ $$$${and}\:{its}\:{cubic}\:{expansivity}\:{is} \\ $$$$\mathrm{9}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} {K}^{−\mathrm{1}} ? \\ $$

Question Number 42118 Answers: 1 Comments: 0

x−4=−(1/x) then . prove x^4 −194=−(1/x^4 )

$$\mathrm{x}−\mathrm{4}=−\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{then}\:.\:\mathrm{prove}\:\mathrm{x}^{\mathrm{4}} −\mathrm{194}=−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} } \\ $$

Question Number 42112 Answers: 1 Comments: 1

Question Number 42110 Answers: 1 Comments: 1

Question Number 42107 Answers: 0 Comments: 0

Question Number 42106 Answers: 1 Comments: 0

Question Number 42098 Answers: 0 Comments: 1

let S_(n,p) =Σ_(k=1) ^n (1/(√(k+p))) find a equivalent of S_(n,p) when n→+∞ p integr ≥1.

$${let}\:{S}_{{n},{p}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{\sqrt{{k}+{p}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{S}_{{n},{p}} \:{when}\:{n}\rightarrow+\infty \\ $$$${p}\:{integr}\:\geqslant\mathrm{1}. \\ $$

Question Number 42096 Answers: 0 Comments: 2

let S_n =Σ_(k=1) ^n (1/(√k)) find a ewuivalent of S_n when n→+∞

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{\sqrt{{k}}} \\ $$$${find}\:{a}\:{ewuivalent}\:\:{of}\:\:{S}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$

Question Number 42094 Answers: 1 Comments: 0

If 7 points out of 12 are in the same straight line, then the number of triangles formed is

$$\mathrm{If}\:\:\mathrm{7}\:\mathrm{points}\:\mathrm{out}\:\mathrm{of}\:\:\mathrm{12}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{straight}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{triangles}\:\mathrm{formed}\:\mathrm{is} \\ $$

Question Number 42089 Answers: 0 Comments: 1

let f(x) =Σ_(n=1) ^∞ ((sin(nx))/n) x^n with −1<x<1 1) find a explicite form of f(x) 2) find the value of Σ_(n=1) ^∞ (1/(n2^n ))sin((n/2))

$${let}\:{f}\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({nx}\right)}{{n}}\:{x}^{{n}} \:\:\:\:\:{with}\:\:−\mathrm{1}<{x}<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{a}\:{explicite}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}\mathrm{2}^{{n}} }{sin}\left(\frac{{n}}{\mathrm{2}}\right) \\ $$

Question Number 42088 Answers: 1 Comments: 1

find ∫ (1+(1/x^2 ))ln(1−(1/x))dx .

$${find}\:\:\:\:\:\int\:\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){ln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx}\:\:. \\ $$

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