I don't think googling math word problems will help in google search. We have to be more specific for the type of the problem. For example; if we google fractions division word problems it google shows some good sites having grade 6 or higher word problems in math.
So the key is to more specific...
Definitely expanding. It is same true as the Sun is hot. Spots on the expanding balloon just is an analogy not a theory; as said by DaveC.
I think the red shift is enough proof to simulate the moving away stars to spots on the balloon.
I don't think so, at least not in forseeable future. Sun is super duper hot, huge gravity, huge pressur. I think right now the topic is to colonize the Mars (we can think of it...)
As you know that sin^2 x + cos^2 x = 1 hence the Left Hand Side is Sin^2 x as the denominator is 1.
Now Prove Right Hand Side equal to sin^2 x too.
The right side is tan^2 x / 1 + tan^2 x convert everything into sin and cos as shown below;
(sin^2 x/cos^2 x)/(1 + sin^2 x/cos^2 x)
=...