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If a bag contains 6 green balls and 3 red balls, what the probability of picking out 2 red, with and without replacement.

For the first ball the probability we pick a red ball is the same, it's the number of red balls divided by the total number of balls. Which in this case is 3/9. If we replace the balls the chance of picking ...
TF
Answered by Toby F. • Maths tutor
23283 Views

Find where the curve 2x^2 + xy + y^2 = 14 has stationary points

d/dx (xy) = x dy/dx + y d/dx (y^2) = 2y dy/dx [This is from the chain rule] So, d/dx (2x^2 + xy + y^2 = 14) => 4x + x dy/dx + y + 2y dy/dx = 0 set dy/dx = 0 as stationary point has gradient 0 Obtains 4x+y...
MH
Answered by Matthew H. • Maths tutor
9102 Views

Remove the brackets: −{−2[x−3(y−4)]−5(z+6)}

First Step: - {-2[x-3y+12]-5z-30} Second Step: - {-2x+6y-24-5z-30} Third Step (Order is x,y, then z) : - {-2x+6y-5z-54} Final Step: 2x-6y+5z+30
VZ
Answered by Victoria Z. • Maths tutor
5564 Views

Using complex numbers, derive the trigonometric identities for cos(2θ) and sin(2θ).

When dealing with complex numbers and trigonometric functions, always turn to DeMoivre's Theorem that states [cos(θ)+isin(θ)] n = [cos(nθ)+ i sin(nθ)]. If we set n=2, the we see a combination of cos(2θ) and ...
TK
Answered by Thomas K. • Maths tutor
9452 Views

Integrate (x+3)^(1/2) .dx

[whiteboard feature does not seam to be working here] Here we need to make a U sibstitution. So we take (x+3) and make this equal U so we now have the integral of u^1/2 . dx In order to switch to .du and do ...
CZ
Answered by Callum Z. • Maths tutor
5125 Views