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Question Number 147971 Answers: 0 Comments: 6

find ∫_(−∞) ^(+∞) ((x^3 dx)/((x^2 +x+1)^4 ))

$$\mathrm{find}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{x}^{\mathrm{3}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$

Question Number 147961 Answers: 0 Comments: 0

Question Number 147948 Answers: 1 Comments: 1

Question Number 147945 Answers: 1 Comments: 2

25^x +5x=e^5 (can this be solved)

$$\mathrm{25}^{{x}} +\mathrm{5}{x}={e}^{\mathrm{5}} \:\left({can}\:{this}\:{be}\:{solved}\right) \\ $$$$ \\ $$

Question Number 147944 Answers: 1 Comments: 0

if x + y + z = 13 find x, yz^(−) + y, zx^(−) + z, xy^(−) = ?

$${if}\:\:\:{x}\:+\:{y}\:+\:{z}\:=\:\mathrm{13} \\ $$$${find}\:\:\:\overline {{x},\:{yz}}\:+\:\overline {{y},\:{zx}}\:+\:\overline {{z},\:{xy}}\:=\:? \\ $$

Question Number 147943 Answers: 0 Comments: 3

∫ (((x^2 + x)^2 )/(x + 1)) = ?

$$\int\:\frac{\left({x}^{\mathrm{2}} \:+\:{x}\right)^{\mathrm{2}} }{{x}\:+\:\mathrm{1}}\:=\:? \\ $$

Question Number 147942 Answers: 2 Comments: 0

if f(x)=f(x−4)+8 and f(2)=4 find f(10)=?

$${if}\:\:\:{f}\left({x}\right)={f}\left({x}−\mathrm{4}\right)+\mathrm{8}\:\:\:{and}\:\:\:{f}\left(\mathrm{2}\right)=\mathrm{4} \\ $$$${find}\:\:\:{f}\left(\mathrm{10}\right)=? \\ $$

Question Number 147941 Answers: 2 Comments: 0

x^2 - 6x + 3 = 0 ⇒ ((2x^2 )/3) + (6/x^2 ) = ?

$${x}^{\mathrm{2}} \:-\:\mathrm{6}{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\:\:\:\Rightarrow\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{3}}\:+\:\frac{\mathrm{6}}{{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 147936 Answers: 1 Comments: 0

Solve the inequality (π - 3)^(2sin2x) ≤ (π - 3)^2

$${Solve}\:{the}\:{inequality} \\ $$$$\left(\pi\:-\:\mathrm{3}\right)^{\mathrm{2}\boldsymbol{{sin}}\mathrm{2}\boldsymbol{{x}}} \:\leqslant\:\left(\pi\:-\:\mathrm{3}\right)^{\mathrm{2}} \\ $$

Question Number 147934 Answers: 0 Comments: 0

Question Number 147933 Answers: 1 Comments: 0

Simplify (1+ (1/(cos2x)))∙(1+(1/(cos4x)))∙(1+(1/(cos8x)))=?

$${Simplify} \\ $$$$\left(\mathrm{1}+\:\frac{\mathrm{1}}{{cos}\mathrm{2}{x}}\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{1}}{{cos}\mathrm{4}{x}}\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{1}}{{cos}\mathrm{8}{x}}\right)=? \\ $$

Question Number 147932 Answers: 1 Comments: 0

if ((1−sin2x)/(1 + sin2x)) = (√(17 + 12(√2))) find ∣((sinx + cosx)/(cosx - sinx))∣ = ?

$${if}\:\:\:\frac{\mathrm{1}−{sin}\mathrm{2}{x}}{\mathrm{1}\:+\:{sin}\mathrm{2}{x}}\:=\:\sqrt{\mathrm{17}\:+\:\mathrm{12}\sqrt{\mathrm{2}}} \\ $$$${find}\:\:\:\mid\frac{{sinx}\:+\:{cosx}}{{cosx}\:-\:{sinx}}\mid\:=\:? \\ $$

Question Number 147918 Answers: 0 Comments: 2

Question Number 147921 Answers: 0 Comments: 1

Question Number 147915 Answers: 0 Comments: 2

Question Number 147914 Answers: 0 Comments: 0

f (x ):= 3x +[ (x/4) ] , D_( f) =[ 0,∞) f^( −1) ( x )= ?

$$ \\ $$$$\:\:{f}\:\left({x}\:\right):=\:\mathrm{3}{x}\:+\left[\:\frac{{x}}{\mathrm{4}}\:\right]\:\:,\:\mathrm{D}_{\:{f}} \:=\left[\:\mathrm{0},\infty\right) \\ $$$$\:\:\:\:\:\:\:\:\:{f}^{\:−\mathrm{1}} \left(\:{x}\:\right)=\:? \\ $$$$ \\ $$

Question Number 147913 Answers: 0 Comments: 0

Question Number 147906 Answers: 1 Comments: 0

4 bad apples are mixed accidentally with 20 good apples. Obtain the probability distribution of the numbers of bad apples in a draw of 2 apples at random

$$\mathrm{4}\:{bad}\:{apples}\:{are}\:{mixed}\:{accidentally} \\ $$$${with}\:\mathrm{20}\:{good}\:{apples}.\:{Obtain}\:{the} \\ $$$$\:{probability}\:{distribution}\:{of}\:{the}\: \\ $$$${numbers}\:{of}\:{bad}\:{apples}\:{in}\:{a}\:{draw}\:{of}\: \\ $$$$\mathrm{2}\:{apples}\:{at}\:{random} \\ $$

Question Number 147905 Answers: 1 Comments: 0

Question Number 147904 Answers: 1 Comments: 0

Question Number 147895 Answers: 0 Comments: 0

Question Number 147894 Answers: 2 Comments: 0

x^2 - 3x + 4 = 0 ⇒ x^2 + ((16)/x^2 ) = ?

$${x}^{\mathrm{2}} \:-\:\mathrm{3}{x}\:+\:\mathrm{4}\:=\:\mathrm{0}\:\:\Rightarrow\:\:{x}^{\mathrm{2}} \:+\:\frac{\mathrm{16}}{{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 147893 Answers: 0 Comments: 2

x + 1 + (1/x) = 4 ⇒ x + 1 - (1/x) = ?

$${x}\:+\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{4}\:\:\Rightarrow\:\:{x}\:+\:\mathrm{1}\:-\:\frac{\mathrm{1}}{{x}}\:=\:? \\ $$

Question Number 147892 Answers: 1 Comments: 0

if x;y;z>1 then: (√((((x−1)(y−1)(z−1))/((x+1)(y+1)(z+1))) )) < ((xyz)/8)

$${if}\:\:\:{x};{y};{z}>\mathrm{1}\:\:\:{then}: \\ $$$$\sqrt{\frac{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)\left({z}−\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)\left({y}+\mathrm{1}\right)\left({z}+\mathrm{1}\right)}\:}\:<\:\frac{{xyz}}{\mathrm{8}} \\ $$

Question Number 147884 Answers: 0 Comments: 0

∫_0 ^1 e^(−x) x^a dx a>0

$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−{x}} {x}^{{a}} {dx}\:\:{a}>\mathrm{0} \\ $$$$ \\ $$

Question Number 147882 Answers: 2 Comments: 0

if ((6(√3) + 10))^(1/3) − ((6(√3) − 10))^(1/3) = x find (x^3 /(10−3x)) = ?

$${if}\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:+\:\mathrm{10}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{6}\sqrt{\mathrm{3}}\:−\:\mathrm{10}}\:=\:\boldsymbol{{x}} \\ $$$${find}\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{10}−\mathrm{3}{x}}\:=\:? \\ $$

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