Reference no: EM13203716

Let us consider the price of a cube shaped stone of edge length L inches. The cost of the raw stone is proportional to its weight which is proportional to cube of its length, i.e. L*L*L or L^3 (read "L cubed") . Assuming that it cost $1000 for one cubic inch of raw stone, we can write the cost of one raw stone as 1000L^3. Let cost of polishing a square inch of the surface area of the rock is $100. Noting that the surface area of rock is proportional to the square of length, i.e. L^2 (read "L squared") we have the cost of polishing the stone as 600L^2 (note there are 6 faces to a cube). *

In the previous topic we didn't consider the premium associated with the size of the stone. e.g. stones bigger than a certain size (say 1/8th inch edge length) are more expensive than small pieces having equivalent size when put together. Let this premium be $1.00 for sizes upto 1/6th inch. Consider the case of a locket with three X inch (X greater than 1/8 and less than 1/6th inch) stone in the center surrounded by ten Y inch (Y < 1/8) stones.

1. Write an expression for the cost of one big stone in the locket (take into account the premium)
2. Write an expression for the cost of the 3 big stones in the locket.
3. Write an expression for the cost of the 10 small stones in the locket
4. Write an expression for the cost of all the stones in the locket.

consider the following - the small stones (of length Y) are half the size of the big stones (of length X). i.e. Y = X/2;

5.Use this information to rewrite the expression for cost of all stones in the locket, in terms of X.

6. Can we use the distributive property here to simplify terms in the final expression? Show how.

6. What operations are associated with coefficient?

7. what are the different coefficients and what operations did we use on them?

8. What operations are associated with exponent?

9. Were there any exponents involved in the expressions in the previous questions?