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AllQuestion and Answers: Page 506

Question Number 166223    Answers: 0   Comments: 0

Question Number 166258    Answers: 0   Comments: 0

Question Number 166257    Answers: 1   Comments: 2

⌊x⌋⌊2x⌋⌊3x⌋= 6 x=?^

$$ \\ $$$$\:\:\:\lfloor{x}\rfloor\lfloor\mathrm{2}{x}\rfloor\lfloor\mathrm{3}{x}\rfloor=\:\mathrm{6} \\ $$$$\:\:\:\:\:\:\:{x}=\overset{} {?}\: \\ $$

Question Number 166212    Answers: 1   Comments: 0

x, y , z ∈R^( +) and x≥y≥z and x^2 +y^( 2) +z^( 2) ≥ 2xy +2xz+2yz Find Min((x/z) )=?

$$ \\ $$$$\:\:\:{x},\:{y}\:,\:{z}\:\in\mathbb{R}^{\:+} \:{and}\:\:{x}\geqslant{y}\geqslant{z} \\ $$$$\:\:\:\:{and}\:\: \\ $$$$\:\:\:\:{x}^{\mathrm{2}} +{y}^{\:\mathrm{2}} +{z}^{\:\mathrm{2}} \geqslant\:\mathrm{2}{xy}\:+\mathrm{2}{xz}+\mathrm{2}{yz} \\ $$$$\:\:\:\:\:\:\mathrm{F}{ind}\:\:\:\:\:\mathrm{M}{in}\left(\frac{{x}}{{z}}\:\right)=? \\ $$

Question Number 166210    Answers: 1   Comments: 0

Question Number 166208    Answers: 2   Comments: 1

Question Number 166246    Answers: 1   Comments: 0

Question Number 166195    Answers: 3   Comments: 0

Question Number 166192    Answers: 1   Comments: 0

∫ (dx/(5+4sin x)) =?

$$\:\:\:\:\int\:\frac{{dx}}{\mathrm{5}+\mathrm{4sin}\:{x}}\:=? \\ $$

Question Number 166191    Answers: 1   Comments: 0

∫^( (π/2)) _(−(π/2)) ((sin x)/(x^4 +x^2 +1)) dx=?

$$\:\:\:\:\:\:\:\underset{−\frac{\pi}{\mathrm{2}}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}=? \\ $$

Question Number 166186    Answers: 2   Comments: 0

if sinθ = (1/2) find cosθ

$${if}\:{sin}\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:{cos}\theta \\ $$

Question Number 166182    Answers: 2   Comments: 0

calculer la primitive de ∫(t^2 /((1+t^2 )^2 ))dt

$${calculer}\:{la}\:{primitive}\:{de} \\ $$$$\int\frac{{t}^{\mathrm{2}} }{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$

Question Number 166181    Answers: 0   Comments: 0

Question Number 166177    Answers: 1   Comments: 0

help me please A cone 9 cm high and 8 cm in base diameter is filled with ice. a) vanilla for 2/5 of the height, b) chocolate for the remaining part 1. Calculate the volume of ice it contains. 2. Calculate the volume of the vanilla ice cream and the volume of the chocolate. By what fractions must the total volume of ice be multiplied to obtain these two volumes? The different volumes will be rounded to the nearest cm³.

$$ \\ $$help me please A cone 9 cm high and 8 cm in base diameter is filled with ice. a) vanilla for 2/5 of the height, b) chocolate for the remaining part 1. Calculate the volume of ice it contains. 2. Calculate the volume of the vanilla ice cream and the volume of the chocolate. By what fractions must the total volume of ice be multiplied to obtain these two volumes? The different volumes will be rounded to the nearest cm³.

Question Number 166176    Answers: 0   Comments: 0

Question Number 166170    Answers: 2   Comments: 0

tan(a+b)=(1/(17)) , tan(a−b)=((11)/(13)) tan2a=? tan2b=?

$${tan}\left({a}+{b}\right)=\frac{\mathrm{1}}{\mathrm{17}}\:\:\:,\:\:\:{tan}\left({a}−{b}\right)=\frac{\mathrm{11}}{\mathrm{13}} \\ $$$${tan}\mathrm{2}{a}=?\:\:\:\:\:\:{tan}\mathrm{2}{b}=? \\ $$

Question Number 166169    Answers: 1   Comments: 0

sin^7 (x)+(1/(sin^3 (x)))=cos^7 (x)+(1/(cos^3 (x)))

$$\:\:\mathrm{sin}^{\mathrm{7}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)}=\mathrm{cos}\:^{\mathrm{7}} \left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{x}\right)} \\ $$$$ \\ $$

Question Number 166168    Answers: 0   Comments: 0

prove Σ_(r=−∞) ^∞ (1/(x + (r+(1/2))π)) = tan(x) (Σ_(r=−∞) ^∞ (1/(x + r)))(Σ_(r=−∞) ^∞ (1/(x + r))) = −(π^2 /4) ( r = odd) (r = even)

$${prove} \\ $$$$\underset{{r}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{x}\:+\:\left({r}+\frac{\mathrm{1}}{\mathrm{2}}\right)\pi}\:=\:{tan}\left({x}\right) \\ $$$$\left(\underset{{r}=−\infty} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{x}\:+\:{r}}\right)\left(\underset{{r}=−\infty} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{x}\:+\:{r}}\right)\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{4}} \\ $$$$\:\:\:\:\:\left(\:{r}\:=\:{odd}\right)\:\:\:\:\:\:\:\:\left({r}\:=\:{even}\right) \\ $$

Question Number 166167    Answers: 0   Comments: 0

Question Number 166163    Answers: 0   Comments: 0

Question Number 166215    Answers: 1   Comments: 0

Question Number 166260    Answers: 1   Comments: 0

∫_0 ^(π/2) ln(sinx+cosx)dx=? −−−−−−−−−−−−by M.A

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}\right)\boldsymbol{\mathrm{dx}}=? \\ $$$$−−−−−−−−−−−−\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$

Question Number 166160    Answers: 3   Comments: 0

Σ_(n=1) ^∞ Σ_(m=1) ^∞ (1/(m^2 n+mn^2 +2mn))=?

$$\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{m}^{\mathrm{2}} \mathrm{n}+\mathrm{mn}^{\mathrm{2}} +\mathrm{2mn}}=? \\ $$

Question Number 166143    Answers: 1   Comments: 0

Question Number 166141    Answers: 2   Comments: 0

∫_0 ^x (t^2 /( (√(a+2t^2 ))))dt

$$\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\:\sqrt{\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\: \\ $$

Question Number 166137    Answers: 2   Comments: 0

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