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Think Conservation of angular momentum. Compute the moment of inertia of the system before and after the student walked toward the center.

Draw the Cartesian plane and paint every point ( x, y) for which 2x + 3y = 0, say, blue.

There is a unique 4th degree polynomial P such that P(1) = 1, P(2) = 5, and P(n) would be the nth term of the sequence. Maybe that's it.

I finally found the answer to this question after some extensive research. The song came out in 1984. The artist is:
Emile den Tex, and they are from the Netherlands.
I guess I stumped everyone,...

Hint: Say p(x) = (xs)q(x) + r(x), where deg(r) < deg(xs) = 1, which would mean that r(x) is a constant, say r0, so p(x) = (xs)q(x) + r0.
Then, p(s) = 0*q(s) + r0 = r0, is the remainder.

ln(x^x) = x ln x, so x^x = e^(x ln x). Now, ln (x^(x^x)) = (x^x) ln x
= (ln x)(e^(x ln x)). Thus, x^(x^x) = e^((ln x)(e^(x ln x))).
Thus, dy/dx = e^((ln x)(e^(x ln x)))*d/dx((ln x)(e^(x ln x)))...

E(X) = mX'(0). Hint: Differentiate the Taylor series expansion of
mX(t) at t=0.


Differentiate v with respect to t. (a = dv/dt)

To show that angle KPA = angle KQA = 90  angle PAQ, note that PK is perpendicular to AQ and intersects AQ at, say, R. Similarly, QK is perpendicular to AP and intersects AP at, say, S. Triangles...

I think that they want you to prove that f(x,y) is differentiable on U, as it is not welldefined on all of R2. For example, what is f(3,4)?

In this case, lambda = 0 is not an eigenvalue, as the only solution that corresponds to it is the trivial solution. The only real eigenvalue in this case is lambda = (ln(2+sqrt(3)))^2. A...

Hint: The water in tank alpha is wa(t) = 48  (16/5)t
t/
The water in tank bravo is wb(t) = 48 +  ((t/3) 1) dt.
...

In an inelastic collision, the total kinetic energy after is less than the total kinetic energy before the collision. My bad. Hope this helps.
CWH :)

Hint: Use the law of conservation of momentum.
m1v*1 + m2v*2 before = m1v*1 + m2v*2 after.
Here, v* denotes the velocity vector, and v denotes the speed.
In an elastic collision, kinetic...

Hint: Adding any amount of a stronger concentration of HCl will lower the pH.

You must have a typographical error in the problem, because the boundary conditions that were given allow y(x)=x to be an eigenfunction corresponding to lambda = 0, and y(x) = sin (2Pi x) to be an...

To show that the above boundary value problem is not a Sturm  Liouville problem, observe that the general solution to y'' + hy = 0 is:
y = A cos x sqrt(h) + B sin x sqrt(h). As y(0) = 0, ...

1.75 g Zn x (1 mole Zn/65.38 g Zn) x (1 mole Zn/ 1 mole ZnS) =
0.02677 moles ZnS will be produced, which is
0.02677 moles ZnS x (97.44 g ZnS/ 1 mole ZnS) =
2.608 g ZnS will be...

True. The angle of the brush is not known. Call it a. Then,
F = 12N / (cos a  0.2 sin a) provided tan a < 5. Otherwise, he cannot push the brush up.
P. S. a is the angle of the brush...

E = hv where h= Planck's constant = 6.626 x 10²7 erg sec, and v is the frequency.
So the energy is (6.626 * 10^27 erg sec)(5 * 10^12 sec^1) = 3.313*10^14 erg.

He pushes it up with a force of 12N, to cancel the force of gravity.

Correction 1033.6 cm H2O. I hate typing on this phone!
CWH :)

Correction 103.36 cm H2O.

The water column that will give the same pressure would be:
76 cm Hg x 13.6 g/cc Hg / 1.0 g/cc H2O = 1035.2 cm H2O.

This pop song came out between 1981 & 1984. It's called "Face to Face". The lyrics start like this: "Face to face. Every day. Face to face. Eye to eye. Face to face. Young dog's in love...."
...
