class 051024

If y is proportional to x^(-2) and y = 12 when x = 30, then

If y is proportional to x^(-2) then

Plugging in y = 12 and x = 30 this gives us

The mass of a 4-inch sphere of concrete is 1.7 kg.

It takes 1200 small tiles to tile a certain bathtub, which is 6 feet long.  How many identical tiles will it take to tile a geometrically similar bathtub which is 8 feet long?

We're scaling up little squares.  The scale increases by a factor of 8/6 = 4/3.

Tiles cover area, and area is related to length dimension by

area = k * length^2.

If area is number of tiles, then we have

number of tiles = k * length^2 so

1200 = k * 6^2 and

k = 1200 / 6^2 = 33.3...

Thus when length = 8 ft we have

# of tiles = 33.3 * length^2 = 33.3 * 8^2 = 2133.