Anita

If z is one of the fifth roots of unity, not 1, show that:

a) 1 + z + z^2 + z^3 + z^4 = 0

b) z - z^2 + z^3 - z^4 = 2(sin(2pi/5)-sin(pi/5))i

Thanks in advance for any help :)

Each fare-paying passenger on a domestic airline is allowed free carriage of one piece of baggage of weight not exceeding 30kg with maximum linear dimensions (ie. length + width + depth) up to 140cm.

- Diagram of a rectangular prism. length = x, width = x, height = h-

a) If the dimensions of the square base are each x cm, express the height, h, in terms of x

b) Construct a function that defines the volume, V, stating its domain

c) The maximum volume occurs when x lies between 40 and 50. With the aid of a calculator, show that this value of x is approximately 47

An excess of nitric acid is added to 2.374g of metallic tin and heated. After the reaction is completed, the sample is dried to give a solid containing only tin and oxygen. If the mass of this solid is 3.014g, what is the empirical formula of the compound?

Don't get this at all ): solution with working would be much appreciated :)