User:TanyaJacob

Hi! This is Tanya. I'm originally from India but I have been living in Singapore for the past 7 years. I'm in first year Sauder :)

The Pythagorean Theorem

The Pythagorean theorem is a concept in geometry which shows the relation of the sides of a right angle triangle. It can be used to figure out any of the unknown sides of the right angle triangle. This theorem is named after the mathematician Pythagoras. The equation of the theorem is:

c^2= a^2 + b^2

where c is the hypotenuse of the triangle and a and b are the other two sides of the triangle.

This theorem can be proven through similar triangles. By equating the sides of the similar triangles regardless of the size, the Pythagoras theorem can be derived. There are various other proofs for this theorem such as subtraction proof, Algebraic proof etc. Lastly even Pythagoras triples exist which are sizes of the sides which always remain the same due to the fact these numbers are only divisible by 1. For example: 3,4,5.

CALULUS IN ECONOMICS

Economics is a social science and it's about the distribution, production and consumption of goods and services in an economy. In economics, there is a term called elasticity. Elasticity is the responsiveness of z when there is a slight change in the Y.

Elasticity = (percentage change in Z) / (percentage change in Y)

Using basic calculus, we can figure out the elasticity:

(percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)

Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)

Using calculus to calculate the elasticity of demand:

Elasticity of demand is the responsiveness of demand from the consumers when there is a slight change in the price of the goods and services provided to the economy.

Price elasticity of demand: = (dQ / dP)*(P/Q)

Example:

If the demand equation for a product is Q = 110 - 4P After differentiation, the answer will be dQ/dP = -4

Substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation: Price elasticity of demand: = (dQ / dP)*(P/Q) = (-4)*(P/(110-4P) = -4P/(110-4P)

At price=5:

Price elasticity of demand: = -4P/(110-4P) = -20/90 = -2/9

As the value is less than 1, it is said the good or service is price inelastic. This means any small change in price of a product does not have a huge impact on the demand of the product.