If a function f is additive, and function f is proportional to function g, is function g also additive?
Function f is additive: f(a) + f(b) f(a+b) Function f is proportional to function g: g(a) k f(a) g(b) k f(b) g(a+b) k f(a+b) g(a) + g(b) k f(a) + k f(b) . k (f(a) + f(b)) . k (f(a+b)) . g(a+b) YES, g is also additive
Yes, fairly simply: f is additive: f(x+y) f(x) + f(y) g is proportional to f: g(x) af(x), where a is a constant. So test g for additivity: g(x+y) af(x+y) a(f(x) + f(y)) af(x) + af(y) g(x) + g(y) QED
You can paint them. Spray them with Zinc first to provide a sacrificial anode. It is silver coloured but not shiny. You can leave it like that. If you want colour then paint over them in a latex paint - two coats.
Very simple to make silver Use a damp sponge and solder the pipe wipe the hot solder all over the pipe Call a plumber to do it if you are not comfortable with solder on pipes helps to have the water OFF while you do it
