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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) = (x-s)q(x) + r(x), where deg(r) < deg(x-s) = 1, which would mean that r(x) is a constant, say r0, so p(x) = (x-s)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.

Hint: cos(w) = sin(90-w)

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 well-defined 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 10-²7 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...."
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