Recent content by ParoXsitiC

One person said it's OK. Another said it's not. And one just gave just a general definition. If I cannot assume -R(a) is true then I need a push in the right direction on how to solve this without using this assumption, or at least a hint on how I can proof -R(a) is true using rules.

Homework Statement Using the rules of inference, prove that if ∀x(P(x) ∨ Q(x)) and ∀x((￢P(x) ∧ Q(x)) → R(x)) are true, then ∀x(￢R(x) → P(x)) is true as well. Homework Equations The Attempt at a Solution The problem arises step 5. I feel this is correct but the...

Nevermind, when evaulating both possible ways using b = 0 (just getting volume of a sphere no drill) I get 4/3 Pi R^2 when z goes from +- sqrt(R^2 - r^2) - which is the volumne of a sphere. So obviously that one is right, it makes sense visually but I know in some cases you must use the...

Homework Statement Find volume of a sphere with radius R with a hole drilled through the center of radius b. (b<R) Homework Equations cos thera = adj / hyp The Attempt at a Solution 4\,\int _{0}^{\arccos \left( {\frac {b}{R}} \right) }\!\int _{0}^{\pi }\!\int...

\left( -\sqrt {2}+t \right) ^{2}+ \left( \sqrt {2}+t \right) ^{2}=25 \, \left( \cos \left( t \right) \right) ^{2}+25\, \left( \sin \left( t \right) \right) ^{2} \left( -\sqrt {2}+t \right) ^{2}+ \left( \sqrt {2}+t \right) ^{2}=25( \, \left( \cos \left( t \right) \right) ^{2}+\left(...

http://www.wolframalpha.com/input/?i=%28-sqrt%282%29%2Bt%29%5E2+%2B+%28sqrt%282%29%2Bt%29%5E2+%3D+%285+*+cos%28t%29%29%5E2+%2B+%285+*+sin%28t%29%29%5E2 Gives me t= ± sqrt(21/2) Pluggin this into X= 5*cos(t), gives ~ -4.97 Of which according to maple the approx points of X I am...

How it relates to any mathematical formula or understanding, taking your reply literally : (-sqrt(2)+t)^2 + (sqrt(2)+t)^2 = (5 * cos(t))^2 + (5 * sin(t))^2 Yielded nothing useful.

Adding and squaring what?

Homework Statement I have a line obtained from using a slope of 1 and point (-sqrt(2),sqrt(2)): y - sqrt(2) = 1 (x+sqrt(2)) y = 2*sqrt(2) + x and a circle with radius 5 centered at origin. My thought was to solve this parametrically The line is the tangent line (blue...

x+2y+5z=1- should be x+2y+5z=10 Also I had make sure scaling was constrained, but now trying to do it in maple it looks right. so must of been a small mistake. None the less taking your advice I got t = 100/69 solving for xyz: x = 62/69 y = 64/69 z = 100/69 And it checks for all 3 planes...

Homework Statement The planes 3x+2y+z=6 and x+2y+5z=1- intersect along the line (x+2)/2 = (y-6)/(-7/2)= z. A third plane passes through the origin and is perpendicular to the intersection of the first two planes, at what point do the three planes intersect? Homework Equations...

That is how it is worded, reading it word for word. I thought it was weird too given 6 points instead of the common 3

I forgot to update the formula with -14: -2x-6y-14z = -78 Still when using (10,2,2) I get -60 and not -78

Okay I had 14 when should be -14 PQ x PR = <-2,-6,-14> Plug in point P into formula and get: -2x-6y+14z = -78 Now point Q works out to be -78 but the point (10,2,2) turns out to be -60 Is this a trick question?

Homework Statement Find equation of plane containing points: (1,1,5),(3,5,3),(8,8,1),(10,2,2),(18,6,-1),(-1,-3,6) Homework Equations Find 2 vectors given 3 points, using a common point. The cross product of these 2 vectors will be the normal vector of the plane. Use normal vector...