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AllQuestion and Answers: Page 17

Question Number 223619 Answers: 2 Comments: 0

Question Number 223615 Answers: 3 Comments: 0

40^(x−1) =2^(2x+1)

$$\mathrm{40}^{{x}−\mathrm{1}} =\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} \\ $$

Question Number 223595 Answers: 1 Comments: 1

Question Number 223591 Answers: 1 Comments: 12

Question Number 223585 Answers: 1 Comments: 1

Question Number 223580 Answers: 3 Comments: 0

∫_0 ^(1 ) ((e^(−r^2 ) sin(1/r^2 )ln(r+1))/r^2 ) dr

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\frac{{e}^{−\boldsymbol{{r}}^{\mathrm{2}} } \boldsymbol{\mathrm{sin}}\left(\mathrm{1}/\boldsymbol{{r}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{{r}}+\mathrm{1}\right)}{\boldsymbol{{r}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{d}{r}} \\ $$$$ \\ $$

Question Number 223571 Answers: 2 Comments: 0

S_1 = 1∙1! + 2∙2! + 3∙3! +...+ 16∙16! S_2 = 1∙1! + 2∙2! + 3∙3! +...+ 14∙14! Find: (S_1 /S_2 ) = ?

$$\mathrm{S}_{\mathrm{1}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+\:\mathrm{16}\centerdot\mathrm{16}! \\ $$$$\mathrm{S}_{\mathrm{2}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+\:\mathrm{14}\centerdot\mathrm{14}! \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{S}_{\mathrm{1}} }{\mathrm{S}_{\mathrm{2}} }\:=\:? \\ $$

Question Number 223560 Answers: 0 Comments: 15

Question Number 223570 Answers: 0 Comments: 0

demontrer que quelque soit k appartenant N l

$${demontrer}\:{que}\:{quelque}\:{soit}\:{k}\:{appartenant}\:{N}\:\:{l} \\ $$

Question Number 223569 Answers: 3 Comments: 0

Question Number 223553 Answers: 1 Comments: 1

the length of 3 meadians of a triangle is given how to calculate the area?

$${the}\:{length}\:{of}\:\mathrm{3}\:{meadians}\:{of}\:{a}\:{triangle}\:{is}\:{given} \\ $$$${how}\:{to}\:{calculate}\:{the}\:{area}? \\ $$

Question Number 223544 Answers: 1 Comments: 1

Question Number 223538 Answers: 2 Comments: 0

x+y=36 xy_(max) =??

$${x}+{y}=\mathrm{36} \\ $$$${xy}_{{max}} =?? \\ $$

Question Number 223534 Answers: 1 Comments: 0

∫_( 0) ^( 1) ((ln(x))/x) ln^3 (((1 − x)/(1 + x))) dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{ln}^{\mathrm{3}} \left(\frac{\mathrm{1}\:\:−\:\:\mathrm{x}}{\mathrm{1}\:\:+\:\:\mathrm{x}}\right)\:\mathrm{dx} \\ $$

Question Number 223529 Answers: 1 Comments: 0

Question Number 223525 Answers: 0 Comments: 0

I = ∫_0 ^(2π) ∫_0 ^(2π) ∫_0 ^(2π) ∣ cos x + cos y + cos z ∣ dxdydz

$$ \\ $$$$\:\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\mid\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:{y}\:+\:\mathrm{cos}\:{z}\:\:\mid\:\:{dxdydz}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 223523 Answers: 0 Comments: 1

Question Number 223514 Answers: 1 Comments: 0

log _8 [log _2 {log _3 (4^x +17)}]=(1/3) x=??

$$\mathrm{log}\:_{\mathrm{8}} \left[\mathrm{log}\:_{\mathrm{2}} \left\{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{4}^{{x}} +\mathrm{17}\right)\right\}\right]=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${x}=?? \\ $$

Question Number 223513 Answers: 2 Comments: 0

If x=log _a bc , y=log _b ca , z=log _c ab prove that x+y+z=xyz−2

$${If}\:{x}=\mathrm{log}\:_{{a}} {bc}\:,\:{y}=\mathrm{log}\:_{{b}} {ca}\:,\:{z}=\mathrm{log}\:_{{c}} {ab} \\ $$$${prove}\:{that}\:{x}+{y}+{z}={xyz}−\mathrm{2} \\ $$

Question Number 223512 Answers: 1 Comments: 0

If ((log x)/(y−z))=((log y)/(z−x))=((log z)/(x−y)) prove xyz=1

$${If}\:\frac{\mathrm{log}\:{x}}{{y}−{z}}=\frac{\mathrm{log}\:{y}}{{z}−{x}}=\frac{\mathrm{log}\:{z}}{{x}−{y}} \\ $$$${prove}\:{xyz}=\mathrm{1} \\ $$

Question Number 223508 Answers: 0 Comments: 0

Question Number 223490 Answers: 2 Comments: 2

Question Number 223487 Answers: 1 Comments: 0

Let Φ be the hyperbola xy = b², b ≠ 0, and P be a point on Φ. Let Q be the image of reflection of P about the origin. Construct a circle ω centred at P with radius PQ. ω cuts Φ at the points B, C, D, Q. Prove that ΔBCD is equilateral, no matter what the value of b is.

Question Number 223482 Answers: 0 Comments: 0

Question Number 223483 Answers: 1 Comments: 0

(x−1)(x−2)=1 (x−1)^(15) −(1/((x−1)^(15) ))=??

$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)=\mathrm{1} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{15}} −\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{15}} }=?? \\ $$

Question Number 223480 Answers: 0 Comments: 0

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