Algebra Answers

1. The third and the six term of a G.P are 108 and -32 respectively find the sum of first seven term.
2. The first and last term of a G.P are 2048 respectively the sum of the series is 2730. Find the number of terms and common ratio.

Express sin^5 x as a linear combination of sin kx and coskx, k belongs to Z

A farmer has 200 acres of land suitable for growing rice, wheat and maize. The cost of growing maize, wheat and rice is Rs.40/-, Rs.60/- and Rs.80/- per acre, respectively.
The farmer has Rs.12,600/- available. To grow maize she requires 20 hours of labour per acre, for wheat 25 hours of labour per acre and for rice 40 hours of labour per acre.
She has a maximum of 5950 hours of labour available. If she wants to use all her cultivable land, all the budget and all the labour available, how many acres of each crop should she plant?

Express sin^5 x
as a linear combination of sin kx and coskx, k belongs to Z.

Prove that if a complex number z is an nth root of a real number a , then so
is z bar.

Let C ,A be subsets of a set. Prove that ,B A ∩ B ⊆ C iff A ⊆ B complement ∪ C.

6+t=20

Determine the square root of 1296

Five less than six times a number is 61

Determine the rule for the sequence:6;-4;6;1;6;6;6;11;6