Algebra Answers

How to write the converse of the statement:
If p and q are the only roots of a polynomial f over C, then deg f = 2 .

A prefilled bag of infusion fluid contains a concentration of 0.5% of the medication and you are asked to administer 50mgs.How many mls do you administer to give the required dose?

For a₁,....,aₙ∈R, a₁<a₂<....<aₙ, show that :
n/a₁-a₀+n-1/a₂-a₁+....+
1/aₙ-aₙ₋₁≥∑^n_k=1(k²/a_k)

To give a direct proof, as well as a proof by contradiction, of the following statement:
'A∩B is contained in A∪B for any two sets A and B.'

Apply Cardano's method for finding the roots of 2x³+3x²-8x-12=0

Prove that (A∪B)\(A∩B)=(A\B)∪(B\A) for any two sets A and B in a universal set U.

Let A={x∈Z|x is a multiple of 5} and B= {x∈Z|x is a divisor of 20}.
Represent A,B and Aᶜ∩B by the listing method and in a venn diagram.

Use DeMoivre's theorem to show that cos3θ=4cos³θ-3cosθ

For a₁,....,aₙ ∈ R, a₁<a₂< .... <aₙ, show that
n/(a₁-a₀)+(n-1)/(a₂-a₁)+....+1/(aₙ-aₙ₋₁)≥∑ⁿᵤ₌₁u²/aᵤ

A water tank has 8 feet of water in it. At the end of each hour the water level falls to 75% of the previous level. Identify the graph of the sequence and the correct description of its pattern. Then identify the what the water level will be after 6 hours.