Abstract Algebra

Boolean Algebra is the study of the algebra of logic whilst Mathematical logic is a way of applying Boolean algebra. Other applications include set theory, digital logic and probability.

There is no simple formula for population growth.

Some of the factors that you need to take account of are:

Emigration rates

Immigration rates

Demographics

Age-specific fertility rates

Death rates

Both matrix and determinants are the part of business mathematics. Both are useful for solving business problem. Both are helpful for calculation of each other. For calculation of inverse of matrix, we need to calculate the determinant. For calculating the value of 3X3 matrix or more matrix, we need to divide determinants in sub-matrix. but there are many differences between matrix and determinants which we can explain in following points.

1. Matrix is the set of numbers which are covered by two brackets. Determinants is also set of numbers but it is covered by two bars.

2. It is not necessary that number of rows will be equal to the number of columns in matrix. But it is necessary that number of rows will be equal to the number of columns in determinant.

3. Matrix can be used for adding, subtracting and multiplying the coefficients. Determinant can be used for calculating the value of x, y and z with Cramer's Rule.

By Er. Hafijullah

Equations are an algebraic way of writing down a maths problem in shorthand.

Two or more simultaneous equations may be used to describe the same problem.

Matrices can be used to solve these simultaneous linear equations (that is equations with two or more unknown variables) and obtain the answer to those unknowns which satisfies both.

Equations are therefore generally solved to get values of unknown variables.......

Variable values are calculated (or assumed) to know all working or constant parameters of a system...

e.g. for a chemical reaction; generally pressure, temperature, concentration of reactant etc., may be combinations of unknown variables.

i.e. If these parameters are varied resultant yield get affected.........

We never know all properties at start, we first found relations between variables by doing practicals & form equations.........

Then these equations can be solved by many methods.......

Out of these many methods matrices is one......

So which ever system can be represented by equations, matrices have application there........

e.g. engineering problems, weather forecasting, aerospace design, financial calculations, chemical processes, construction calculations etc...........

And.....they were used by Albert Einstein to come up with his theories for General and Special Relativity.

The formula for population growth is based on the formula for interest. The formula is Final Population is equal to Initial Population multiplied by e raised to the power of the product of the rate of growth multiplied by the time of growth, or P(f) = P(o) * e ^ (rt).

The form of the piecewise functions can be arbitrarily complex, but higher degrees of specification require considerably more user input.

This is a very nice shotgun with the woodstoc quite nicely refinished, natural and steel-wool finished with a polyuerathane finish

The coin is very common, coins showing heavy to moderate wear are valued for the silver only, about $3.25 higher circulated grade are less than $4.00

Consider 2 convex functions g(x) and f(x).

Using property of second derivative test we have:

g(x)'' > 0 and f(x)'' > 0.

We are interested in showing that y(x) = g(x) + f(x) is also convex.

y(x)'' = c*g(x)'' + k*f(x)'', where c and k are positive numbers (where is no convex function those coeficients after diferentiation will give you negative numbers).

Because c, g(x)'', k, f(x)'' are > 0 , we get y(x)'' also >0, hence y(x) is a convex function.

this rifle is going for $430.00 new. a rifle in used but good condition should fetch $380-400.

Many of the boats are valued in price close to $4,200 each. The amount will vary depending upon its condition and any upgrades that it has on it.

None of the dual-date 1776-1976 Bicentennial Quarters regardless of mintmark struck for general circulation have more than face value. Only proof and uncirculated collectors coins sold from the Mint have premiums

Depending on the rifle, the maker and overall condition anywhere from 50-1500 USD.

Less than $100 - possibly much less, depending on condition

7-10-11>>> Assuming the coin is circulated and has no mintmark, the 1911 Barber dime is a comm date of the series. For an accurate assessment of value the coin needs to be seen and graded. Most coins of this type have seen heavy use and show a lot of wear. In general, the retail value of average circulated grade coins is $3.00-$8.00. Values are a market average and only for coins in collectible condition, coins that are bent, corroded, scratched, used as jewelry or have been cleaned have far less value if any to a collector or dealer.

You can download papers with answers on google just type in Jumior Maths Olympiad Papers

In Good Condition, September 25, 2007 = $310.00

Depending on condition, $50 (poor) to $250 (excellent). Since these were inexpensive boys' rifles they are seldom found in higher grades.

Need more information. A 1976 what? Cent, nickel, foreign coin ...

its around $15-$20. There is no such thing as an M8A1 bayonet. The M8A1 is the designation of the scabbard that holds the M-4, M-5 (series), M-6, and M-7 bayonet.