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AllQuestion and Answers: Page 62

Question Number 218119    Answers: 2   Comments: 0

determinant ((ε,1,0,0,0,1),(1,ε,1,0,0,0),(0,1,ε,1,0,0),(0,0,1,ε,1,0),(0,0,0,1,ε,1),(1,0,0,0,1,ε))=?

$$\begin{vmatrix}{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}&{\varepsilon}\end{vmatrix}=? \\ $$$$ \\ $$

Question Number 218115    Answers: 1   Comments: 0

Question Number 218148    Answers: 2   Comments: 0

I=∫_0 ^( ∞) ((sin((√( x ))))/( (( e^x ))^(1/4) ))dx=?

$$ \\ $$$$\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{sin}\left(\sqrt{\:{x}\:}\right)}{\:\sqrt[{\mathrm{4}}]{\:{e}^{{x}} }}{dx}=? \\ $$$$ \\ $$

Question Number 218103    Answers: 2   Comments: 0

x+(1/x)=3 , x^5 +(1/x^5 )=?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:,\:{x}^{\mathrm{5}} +\frac{\mathrm{1}}{{x}^{\mathrm{5}} }=? \\ $$

Question Number 218099    Answers: 5   Comments: 0

x^2 +x+1=0 , x^4 +x^2 +1=?

$${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0}\:,\:{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}=? \\ $$

Question Number 218093    Answers: 2   Comments: 0

Solve for x (√(2x+3)) −(√(x−2)) =(√(x+2))

$${Solve}\:{for}\:{x} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{3}}\:−\sqrt{{x}−\mathrm{2}}\:=\sqrt{{x}+\mathrm{2}}\: \\ $$

Question Number 218088    Answers: 3   Comments: 0

Solve (√(x+5)) +(√(x−3)) =4

$${Solve} \\ $$$$\sqrt{{x}+\mathrm{5}}\:+\sqrt{{x}−\mathrm{3}}\:=\mathrm{4} \\ $$

Question Number 218076    Answers: 2   Comments: 0

How many ways to arrnge the letters ABCCCDEFG (1) in general . (2) all 3 Cs must be together (3) only 2 Cs must be together (4) no 2 or 3 Cs be together (5) no letter still in its original place .

$${How}\:{many}\:{ways}\:{to}\:{arrnge} \\ $$$${the}\:{letters}\:{ABCCCDEFG} \\ $$$$\left(\mathrm{1}\right)\:{in}\:{general}\:. \\ $$$$\left(\mathrm{2}\right)\:{all}\:\mathrm{3}\:{Cs}\:{must}\:{be}\:{together} \\ $$$$\left(\mathrm{3}\right)\:{only}\:\mathrm{2}\:{Cs}\:{must}\:{be}\:{together} \\ $$$$\left(\mathrm{4}\right)\:{no}\:\mathrm{2}\:{or}\:\mathrm{3}\:{Cs}\:{be}\:{together} \\ $$$$\left(\mathrm{5}\right)\:{no}\:{letter}\:{still}\:\:{in}\:{its} \\ $$$${original}\:{place}\:. \\ $$

Question Number 218066    Answers: 1   Comments: 2

If Alphaprime borrows 25$ from LYCONTRIX at the rzte of 12% p.a. How much does the former owe to the other in a span of 8years?

$${If}\:{Alphaprime}\:{borrows}\:\mathrm{25\$}\:{from} \\ $$$${LYCONTRIX}\:{at}\:{the}\:{rzte}\:{of}\:\mathrm{12\%}\:{p}.{a}. \\ $$$${How}\:{much}\:{does}\:{the}\:{former}\:{owe}\:{to}\:{the} \\ $$$${other}\:{in}\:{a}\:{span}\:{of}\:\mathrm{8}{years}? \\ $$

Question Number 218063    Answers: 2   Comments: 0

∫_0 ^(2π) cos x^2

$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mathrm{cos}\:{x}^{\mathrm{2}} \\ $$

Question Number 218057    Answers: 1   Comments: 0

Solve (x−3)^(5/3) −6(x−3)^(2/3) −8=0

$${Solve} \\ $$$$\left({x}−\mathrm{3}\right)^{\mathrm{5}/\mathrm{3}} −\mathrm{6}\left({x}−\mathrm{3}\right)^{\mathrm{2}/\mathrm{3}} −\mathrm{8}=\mathrm{0} \\ $$

Question Number 218055    Answers: 1   Comments: 1

Question Number 218054    Answers: 0   Comments: 0

Question Number 218047    Answers: 3   Comments: 0

Determine x: (√(x+3)) + ((x+1))^(1/3) =2

$${Determine}\:{x}: \\ $$$$\sqrt{{x}+\mathrm{3}}\:+\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}\:=\mathrm{2} \\ $$

Question Number 218046    Answers: 0   Comments: 0

Question Number 218045    Answers: 0   Comments: 0

Question Number 218041    Answers: 1   Comments: 0

find (x,y,z)/such as (x+y+z=1 (x^2 +y^2 +z^2 =9 ((1/x)+(1/y)+(1/z)=1

$${find}\:\left({x},{y},{z}\right)/{such}\:{as} \\ $$$$\left({x}+{y}+{z}=\mathrm{1}\right. \\ $$$$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:=\mathrm{9}\right. \\ $$$$\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=\mathrm{1}\right. \\ $$

Question Number 218036    Answers: 2   Comments: 0

Solve x^2 + y^2 + xy = 19 x + y= 5

$${Solve} \\ $$$$\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}\:=\:\mathrm{19}\: \\ $$$$\:\mathrm{x}\:+\:\mathrm{y}=\:\mathrm{5} \\ $$

Question Number 218030    Answers: 1   Comments: 5

Question Number 218025    Answers: 0   Comments: 0

I=∫_0 ^( ∞) te^(−t) J_(−(1/2)) (t ) dt =?

$$ \\ $$$$\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} {te}^{−{t}} {J}_{−\frac{\mathrm{1}}{\mathrm{2}}} \:\left({t}\:\right)\:{dt}\:=? \\ $$$$ \\ $$

Question Number 218021    Answers: 1   Comments: 0

Question Number 218019    Answers: 2   Comments: 0

x^2 +y^2 +x+y=18 xy+x+y=7 Solve.

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{x}+{y}=\mathrm{18} \\ $$$${xy}+{x}+{y}=\mathrm{7} \\ $$$${Solve}. \\ $$

Question Number 218013    Answers: 1   Comments: 0

Question Number 218005    Answers: 0   Comments: 2

if x^2 +y^2 +z^2 =1, maximum value xy+2yz = ...

$$\: \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{1},\: \\ $$$$\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{x}}\mathrm{y}+\mathrm{2yz}\:=\:... \\ $$

Question Number 218003    Answers: 0   Comments: 6

1. ∫ ((x dx)/((x + 2)∙(x + 4))) 2. ∫ ((x + 2)/(x^3 − 2x^2 )) dx 3. ∫ ((2x + 7)/(x^2 − 4x + 3)) dx

$$\mathrm{1}.\:\:\:\int\:\:\frac{\mathrm{x}\:\mathrm{dx}}{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{4}\right)} \\ $$$$\mathrm{2}.\:\:\:\int\:\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{2x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$\mathrm{3}.\:\:\:\int\:\:\frac{\mathrm{2x}\:+\:\mathrm{7}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}}\:\mathrm{dx} \\ $$

Question Number 217992    Answers: 0   Comments: 0

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