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Question Number 163692 Answers: 1 Comments: 0

A 10 liter bottle filled with a 20% alcohol solution. How much 75% alcohol solution should be added to obtain 45% alcohol solution? a) 1.62 lit b) 1.72 lit. c) 1.82 lit d) 1.92 lit.

$$ \\ $$A 10 liter bottle filled with a 20% alcohol solution. How much 75% alcohol solution should be added to obtain 45% alcohol solution? a) 1.62 lit b) 1.72 lit. c) 1.82 lit d) 1.92 lit.

Question Number 163690 Answers: 1 Comments: 0

lim_(x→0) ((cos 2x cos 4x cos 8x − 3x csc 2x)/(2x^2 )) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2}{x}\:\mathrm{cos}\:\mathrm{4}{x}\:\mathrm{cos}\:\mathrm{8}{x}\:−\:\mathrm{3}{x}\:\mathrm{csc}\:\mathrm{2}{x}}{\mathrm{2}{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 163688 Answers: 2 Comments: 0

Question Number 163687 Answers: 0 Comments: 0

Question Number 163682 Answers: 1 Comments: 0

Ω= ∫_0 ^( 1) (Li_( 2) ^ (x ))^( 2) dx = ? ■ m.n −−− −−−

$$ \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{Li}_{\:\mathrm{2}} ^{\:} \left({x}\:\right)\right)^{\:\mathrm{2}} {dx}\:=\:?\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\: \\ $$$$\:\:\:\:\:−−−\:−−− \\ $$$$\:\:\:\: \\ $$

Question Number 163675 Answers: 0 Comments: 1

how do we find the sum of the terms after the n^(th) term of a GP

$${how}\:{do}\:{we}\:{find}\:{the}\:{sum}\:{of}\:{the}\:{terms}\:{after}\: \\ $$$${the}\:{n}^{{th}} \:{term}\:{of}\:{a}\:{GP} \\ $$

Question Number 163666 Answers: 4 Comments: 0

lim _(x→𝛑) (((x^𝛑 − 𝛑^x )/(x−𝛑))) =?? ≪zaynal≫

$$\boldsymbol{\mathrm{lim}}\:_{\boldsymbol{{x}}\rightarrow\boldsymbol{\pi}} \:\:\left(\frac{\boldsymbol{{x}}^{\boldsymbol{\pi}} \:−\:\boldsymbol{\pi}^{\boldsymbol{{x}}} }{\boldsymbol{{x}}−\boldsymbol{\pi}}\right)\:=?? \\ $$$$\ll\mathrm{zaynal}\gg \\ $$

Question Number 163662 Answers: 1 Comments: 1

Question Number 163651 Answers: 1 Comments: 1

if (a−2b)^2 +(b−2c)^2 =0 find volve (((b+c−a)^3 )/(abc))=?

$${if}\:\:\left({a}−\mathrm{2}{b}\right)^{\mathrm{2}} +\left({b}−\mathrm{2}{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\:{volve}\:\:\frac{\left({b}+{c}−{a}\right)^{\mathrm{3}} }{{abc}}=? \\ $$

Question Number 163650 Answers: 1 Comments: 2

lim_(x→π) ((x^π^x −π^x^π )/(x−π))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{{x}^{\pi^{{x}} } −\pi^{{x}^{\pi} } }{{x}−\pi}=? \\ $$

Question Number 163642 Answers: 1 Comments: 0

lim_(x→(2/3)) ((⌊3x⌋−3x)/(9x^2 −4)) =?

$$\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\mathrm{2}}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\lfloor\mathrm{3}{x}\rfloor−\mathrm{3}{x}}{\mathrm{9}{x}^{\mathrm{2}} −\mathrm{4}}\:=? \\ $$

Question Number 163638 Answers: 0 Comments: 2

∫ (dx/( (√(2c_1 +e^(−2x) ))))

$$\int\:\frac{\boldsymbol{{dx}}}{\:\sqrt{\mathrm{2}\boldsymbol{{c}}_{\mathrm{1}} +\boldsymbol{{e}}^{−\mathrm{2}\boldsymbol{{x}}} }} \\ $$

Question Number 163632 Answers: 2 Comments: 0

(((x^2 - y^2 )∙(√3))/( (√(x^3 + 3x^2 y + 3xy^2 + y^3 )))) = -1 x^3 + y^3 = (x + y)^2 find: x and y

$$\frac{\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{y}^{\mathrm{2}} \right)\centerdot\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{3xy}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{3}} }}\:=\:-\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}} \\ $$

Question Number 163631 Answers: 2 Comments: 0

x + (1/x) = (√3) ⇒ x^(3579) + (1/x^(3579) ) = ?

$$\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\sqrt{\mathrm{3}}\:\:\Rightarrow\:\mathrm{x}^{\mathrm{3579}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3579}} }\:=\:? \\ $$

Question Number 163627 Answers: 2 Comments: 0

Question Number 163624 Answers: 1 Comments: 0

Question Number 163619 Answers: 1 Comments: 2

Prove that; ∫_(−∞) ^0 e^(−∣t∣) dt = 1

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}; \\ $$$$\:\:\int_{−\infty} ^{\mathrm{0}} \:\boldsymbol{{e}}^{−\mid\boldsymbol{{t}}\mid} \:\boldsymbol{{dt}}\:=\:\mathrm{1} \\ $$

Question Number 163618 Answers: 0 Comments: 0

Question Number 163613 Answers: 0 Comments: 0

Question Number 163614 Answers: 0 Comments: 0

∫((sec^2 x)/((secx+tanx)^(9/2) ))dx

$$\int\frac{{sec}^{\mathrm{2}} {x}}{\left({secx}+{tanx}\right)^{\mathrm{9}/\mathrm{2}} }{dx} \\ $$

Question Number 163611 Answers: 1 Comments: 0

Question Number 163610 Answers: 1 Comments: 0

Question Number 163609 Answers: 0 Comments: 0

lim_(n→∞) n[A−n(H_n −lnn−γ)]=B Find (A/B)=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}n}\left[\mathrm{A}−\mathrm{n}\left(\mathrm{H}_{\mathrm{n}} −\mathrm{lnn}−\gamma\right)\right]=\mathrm{B} \\ $$$$\mathrm{Find}\:\frac{\mathrm{A}}{\mathrm{B}}=? \\ $$

Question Number 163608 Answers: 0 Comments: 0

A_n =(n/(n^2 +1^2 ))+(n/(n^2 +2^2 ))+...+(n/(n^2 +n^2 )) Prove:: lim_(n→∞) (1/(n^4 {(1/(24))−n[n((π/4)−A_n )−(1/4)]}))=2016

$$\mathrm{A}_{\mathrm{n}} =\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} } \\ $$$$\mathrm{Prove}::\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{4}} \left\{\frac{\mathrm{1}}{\mathrm{24}}−\mathrm{n}\left[\mathrm{n}\left(\frac{\pi}{\mathrm{4}}−\mathrm{A}_{\mathrm{n}} \right)−\frac{\mathrm{1}}{\mathrm{4}}\right]\right\}}=\mathrm{2016} \\ $$

Question Number 163601 Answers: 0 Comments: 0

∫_(2/π) ^(+oo) ln(cos((1/x)))dx narure?

$$\int_{\frac{\mathrm{2}}{\pi}} ^{+{oo}} {ln}\left({cos}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$$${narure}? \\ $$

Question Number 163600 Answers: 1 Comments: 0

a line charges of charge density pl=4x^3 −x+3mc/m laying along the x−axis. determine the total charge if the line charge extends from x=2 and x=6 m

$${a}\:{line}\:{charges}\:{of}\:{charge}\:{density}\: \\ $$$${pl}=\mathrm{4}{x}^{\mathrm{3}} −{x}+\mathrm{3}{mc}/{m}\:{laying}\:{along}\:{the}\:{x}−{axis}. \\ $$$${determine}\:{the}\:{total}\:{charge}\:{if}\:{the}\:{line}\:{charge} \\ $$$${extends}\:{from}\:{x}=\mathrm{2}\:{and}\:{x}=\mathrm{6}\:{m} \\ $$

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