reinout-g

Hey SpawnAngel,

I think you misread the question,

if I confess and my friend does not I will get 20 years and he will get 0.

The other way around I get 0 and he gets 20.

Also it's not a matter of confessing or not confessing.

The question is how big the odds of your friend confessing should be in order for you to choose to not confess or confess.

Have another look at it. It is not as difficult as it may seem, however it does require a little calculation 

Okay let me give you a hint;

Let p be the probability that your partner confesses

Choosing to confess gives a probability p of two confessions and a probability (1-p) that only you implicate your partner. If you don't confess, there is a probability p that he implicates you and a probability (1-p) that neither of you confess.

Furthermore, 1 year in jail gives you 2 suffering points and 1 year of your partner in jail gives you 1 suffering point. 

bump bump bump

bump bump bump

As long as your head jokes don't hurt the math, that's fine

Your question does not have an answer.

have a look at this;

$$\sqrt{p} = y$$

Now

if p=0 , y = 0

if p>0 , y >0

if p

Therefore if y

Hence, there exists no x for which $$\sqrt{x+6} = -8$$

There is a method involving non-real numbers which does solve your answer, but I don't assume you're a university student yet.

To make it more clear to you, let's say we work it out.

We square both sides (which is an operation where we need to check our answer)

$$x+6 = 64$$

$$x = 58$$

Now let's check the answer...

$$\sqrt{58+6} = \sqrt{64} = 8 \neq -8$$

And we find that there is no answer which suits our problem.

I guess most of them will still be here

But in the end, even that adds up to 42...

100% is denoted by 1 as a decimal and for example 105% as 1.05.

Therefore 8.3% can be denoted as 0.083

Does that solve your question?

Okay, so you can find the gravitational potential energy using ΔUg = mgh

where m is mass, g is gravitational force (usually threated as the constant 9.8N/kg ) and h is height

The marble gains all it's potential energy from the spring, therefore ΔUg = -ΔUs

 (Technically the spring transfers it's potential energy into kinetic energy after which it becomes potential energy) 

The formula for elastic potential energy is given by 

$$Pe = -\Delta Us = \frac{1}{2}kx^2$$

where k is the spring constant and x is the amount of compression

 edit: I think you can do the last one by yourself if you've finished these

You can see it when I write $$a^2 = a*a$$ and $$a^3 = a*a*a$$

$$a*2a^2*3a^3 = a * 2 * a * a * 3 * a * a * a = 2*3 * a * a * a * a * a * a = 6a^6$$