Parabola

The parabola y= x^2+9 has two tangents which pass through the point (0,-4). One is tangent to the parabola at (a, a^2+9) and the other at (-a, a^2+9) where a is a certain positive number. The question: a=?

Basic Algebraic Coding Theory : How do I figure out the addition and multiplication tables for: Z mod 2 [x] / (x^2) ?

How do I figure out the addition and multiplication tables for: Z mod 2 [x] / (x^2) ?

Coding Theory : How do I compute the addition and multiplication tables for Z mod 2 [x] / (1+x^2)?

How do I compute the addition and multiplication tables for: Z mod 2 [x] / (1+x^2)? z mod 2 [x] = 1 z mod 2 [x] = 0 z mod 2 [x] = 1+x z mod 2 [x] = 1+ x + x^2 I think that 1+ x^2 = 0 so x^2 = -1. Thats as far as I got.

Short Programming Assignment

I need help with writing a program that will generate message words (in 0's and 1's) and then compute the code words (in 0's and 1's). Ex: Generating Matrix for the (3,4) Parity check code: 100 1 010 1 001 1 derived from using the identity matrix and then solving for x,y,z in the 4th column Message words Code words 000 0000 001 0011 010 0101 011 0110 100 1001 101 1010 110 1100 111 1111

Applications of Linear Equations : A Quick Setting Grout

A quick setting grout made from a mixture of cement/sandwater and an additive is needed for a tunnelling project Two trial mixes have been made with the following combinations of grout and additive. 5 litres of sand/cement/water + 1 litre of additive =6 liter of grout mass=12.487kg 5 liters of sand/cement/water =1.5litre of additive=6.5liter of grout mass=12.98kg (a) from this information find the densities of the sand/cement/water mixture and the additive in kg/litre, giving your answers accurate to three decimal place. (b) using this information determine the quantities needed to make 5 litres of grout with a density of 2.000kg/litre