Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

A liquid contains 7 litres of water and 18 litres of acid. More acid is added to it. The relation between the amount of acid added and the change in the percentage of acid in the liquid.

Consider all rectangles that can be made with a 1 metre long rope. Take one of its sides as x centimetres and the area enclosed as a(x) square centimetres.

i) Write the relation between a(x) and x as an equation.

ii) Why are the numbers a(10) and a(40) equal?

iii) To get the same numbers as a(x), for two different numbers as x, what must be the relation between the numbers?

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

An 1 metre wide path goes around a square ground. The relation between the length of a side of the ground and the area of the path.

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

Two poles of heights 3 metres and 4 metres are erected upright on the ground, 5 metres apart. A rope is to be stretched from the top of one pole to some point on the ground and from there to the top of the other pole:

The relation between the distance of the point on the ground from the foot of a pole and the total length of the rope.

Write each of the operations below as an algebraic expression, find out which are polynomials and explain why.

i) Sum of a number and its reciprocal.

ii) Sum of a number and its square root.

iii)Product of the sum of difference of a number and its square root.