As an artist, Ernest is doing a solo show titled CUBES. One of his pieces is shown below. Each layer of the piece is a cube. The bottom cube has a side
length of 3 m, the middle cube has a side length of 2 m, and the top cube has a
side length of 1 m. The top two layers are each centred on the layer below.
Ernest wishes to paint the piece. Since the piece will be suspended in the air, the
bottom will also be painted. Determine the total surface area of the piece,
including the bottom.

Geometry: determine whether segment mn is parallel to segment kl. justify your answer. jm 6 mk 3 jn 8 nl 4

Factor completely. 4p^2 + 36p + 81 express the answer in the form (ap + b)^2

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?