Recent content by Oxygenate

Homework Statement Find the equation of the plane which contains the line r(t) = (2-t, 1+t, t) and the point (1,0,1). The Attempt at a Solution Since r(t) = (2-t, 1+t, t), we know that vector a, which is parallel to the line, is (-1, 1, 1). I'm assuming that since the point is (1,0,1)...

Okay, so: Let y = z - x. Then suppose y is rational, then m/n - x = a/b, in which case x = m/n - a/b = (mb - na) / (nb), which is a rational number. But this is a contradiction to the fact that x is an irrational number. Thus the statement (for every rational number z, there exist irrational...

Okay, so suppose A is irrational number. Then let x = 1/2z – a. And let y = 1/2z + a. Then x + y = z, and x and y are irrational.

I have no idea how to begin this proof. Homework Statement Prove that for every rational number z, there exist irrational numbers x and y such that x + y = z. The Attempt at a Solution I can't think of even a way to start this proof...it's just quite obvious that the sum of two irrational...

r = 2tan(theta)sec(theta) r = 2sin(theta)/cos(theta) * 1/cos(theta) rcos^2 = 2sin(theta) r^2cos^2 = r2sin(theta) x^2 = 2y y = 1/2(x^2) It seems like this works too. Thanks! I haven't done trig in like forever...

Okay, so: r = 2sin/cos * 1/cos rcos = 2sin * 1/cos x = 2sin * 1/cos x = 2tan Where does the x^2 come from and where does the y come from?

Homework Statement Given r = 2tan(theta)sec(theta) Find cos(theta) then use inverse key to find sec(theta) The answer given in the solution guide is y = 1/2 x^2 Attempt at solution Since tan = sin/cos and sec = 1/cos We have r = 2sin/cos * 1/cos So rcos^2 = 2sin rcos^2 is defined...