Recent content by glog

Probability (Choose) question -- marbles in a jar Simple high school question which i really forgot how to solve :( "a bowl of 50 marbles, three are blue and the rest are white, if you pick 16 marbles what's the chance you'll get at least one blue one?" any help would be appreciated...

Yeah I definitely think that change of variables is reasonable, I just think there's any easier way to turn this into a circle than this matrix approach. Hmmm...

Homework Statement \int\int x^2 dA where the area D is boundd by the ellipse 5x^2 + 4xy + y^2 = 1. Homework Equations The Attempt at a Solution I'm not sure where to start this question. A few ideas I'm exploring are: 1. rewrite in polar co-ordinates (not sure how to write an...

Nevermind... this needs to be done with polar co-ordinates. Thanks -glog

Homework Statement \int\int e^(^x^2^+^y^2^) dA where D is the region bounded by y = sqrt(1-x^2) and y = |x|. Homework Equations The Attempt at a Solution Obviously I can draw this region out and see what it looks like, and I will have to split the integral into two for negative...

Alright so perhaps the bounds are then: \int^1_0 \int^x_0 In which case, my integral simplifies to: \int^1_0 x sin(x^2) Which becomes: -1/2 cos (x^2) | 1_0 This make sense?

Homework Statement \int^1_0 \int^1_y sin(x^2) dx dy The Attempt at a Solution This equation cannot be integrated nicely, so I tried to reverse the order of integration: \int^1_0 \int^1_x sin(x^2) dy dx However this only helps for the first step, since when we intregrate by y, we...

I have a unit circle: x^2+y^2 <= 1 And I'm asked to convert it to a square with verticies (0,0),(0,1),(1,0),(1,1). Now obviously I have to do this in polar coordinates, so I've rewritten the equation as: x = cos t y = sin t I'm sort of drawing a blank after setting up these...

hey i got it! sweet! appreciate your help :)

can you elaborate on what you wrote a bit? sorry I'm just not sure how you got that theta = 0, pi, 2pi/3... since this last one does not equal 0 for sin(theta) also 3*theta = inverse sin( 0, pi, etc.) = 0 therefore, 2pi/3 works here since it becomes 2pi and sin2pi = 0...

I'm trying to plot the graph r = sin 3t and find its area. This is how far I've gotten: The graph looks like a plane propellor with one propellor pointing downward, and two pointing up-left / up-right, with the length of each equal to 1. Now to get the area... I have to figure out where...

yep makes perfect sense... only one angle is fixed :)

This should be relitively simple: y = x ... convert to spherical coords: p*sin(r)*sin(t) = p*sin(r)*cos(t) which reduces to... sin(t) = cos(t) tan(t) = 1 (is this right?) t =~ 0.78... (Can i get a nice fraction for this?) Any help is appreciated. - glog

Question Details: Convert the following equation into cylindrical coordinates... x^2 + y^2 + z^2 = 4 It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to: r^2 + z^2 = 4 ... is there a better way to do this?

sure, thanks! so i get the partial derivs: f(x,y) = e^2 fx(x,y) = 2e^2 fy(x,y) = 2e^2 fxx(x,y) = 4e^2 fxy(x,y) = 4e^2 fyy(x,y) = 4e^2 I get my linear approx: L1,1(x,y) = 2ex^2+2ey^2-3e^2 so then, by Taylor: |e^(x^2 + y^2) - (2ex^2+2ey^2-3e^2)| = 1/2[fxx(1,1) x^2 + 2fxy(1,1) xy +...