Johnny D

My friend is a recovering heroin addict. She says she was raped recently and she is asking me for money to buy weed as she is feeling the urge to shoot up and smoking helps ease that urge. She told me that she was going to shoot up if she doesn't get weed but I still told her no. She doesn't have a job right now and I am of the belief that if you are going to smoke weed you should be able to bear the financial burden. I know if she gives in to her urges she will trade sex for heroin/money. I don't want to lose her to heroin but I don't want to enable an unhealthy lifestyle either. Not sure if I'm making the right decision by cutting her off financially. What do you think?

In school, on the street even in the workplace I hear Americans making disgusting remarks about other people and when they're confronted about these remarks they justify them by talking about this "freedom of speech" their constitution guarantees them. So I ask you this Americans, does freedom of speech mean you can be as verbally inconsiderate as you want?

Why is a dot usually used for hydrates such as CrCl3∙6H2O instead of enclosing the complex ion in brackets? I know the dot was used before a lot was known about coordination compounds but now that we know the structure of these compounds why use the dot? To me it would make more sense to use brackets to emphasize the structure of the compound. Is there an advantage to using a dot other than its simplicity?

What does [Cr(H2O)4Cl2]Cl∙2H2O mean? Not the name, I'm asking what does the 2H2O outside of the brackets mean? Are those H2O molecules outside the brackets chemically bonded to anything?

Find the equations of all the lines that are tangent to both the graph of f(x)=x² and f(x)=-x²+6x-5.

I need to know how to solve this type of problem in a timely and efficient manner without a calculator or any graphical aid.

http://www.amazingrust.com/Experiments/background_...

What does that color look like to you? Wikipedia says it's blue-green but what does that really mean, teal, turquoise, cyan etc?

Take a look and tell me what color it is.

Solid Copper(II) chloride is dissolved in water. Solid aluminum is then added to the aqueous solution of Copper(II) chloride. A student observes the entire process from start to finish, explain what the student sees making sure to note things such as color changes, etc and explain why the student sees this in terms of what is happening chemically/physically.

Find a sequence An where n is the number of sides of the regular polygon that gives the perimeter of any regular polygon inscribed in unit circle with at least one side of the polygon perpendicular to the positive x-axis.

So far I've figured out the perimeter for a triangle, square and I think I found the perimeter for a pentagon but I can't figure out a way to generalize it in terms of the number of sides.

Show that sin^4(θ)=(3/8)-(1/2)cos(2θ) + (1/8)cos(4θ)

If you calculate e^(πi), e^(i)^(π) or e^(π*i) on a Ti-83 plus graphing calculator it gives the answer as -1. However if you calculate e^(π)^(i) it gives the answer, -1+1x10^-13i.

A friend pointed this out to me and I asked him to prove it mathematically but he said he tried to prove it but couldn't so I was wondering if this is a calculator error or is it actually provable. I've never learned about raising real numbers to imaginary/complex numbers so I have no idea how to go about this but I'm hoping someone can explain this in clear and comprehensible manner. Use any mathematical method.