Alan

Depends which direction y is acting!  Assuming you mean y is acting along the slope, then it must equal the component of the weight of the particle that acts down the slope:   y = mg*sin(theta) where theta is the angle of the slope to the horizontal.

As below:

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Here's one way:

As below:

Well, when n = 6, the number of dots will be 17 + 3 = 20

when n = 7, the number of dots will be 20 + 3 = 23

... you could continue this way until you reach 32.

Alternatively, you could notice that the n'th term is given by 2 + n*3.  where n starts at 0.  Set this equal to 32 and solve for n.

That is     2 + n*3 = 32   so what must n be?

Again, look at the difference between each of the numbers of dots in the second row of the table. 

1. You are right Melody, the graph would have been really boring!  

2. Here are a couple of graphs to illustrate the solution when n = 2 (so f(x) = x⁵ + 7) 

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Guest is correct: the temperatures need to be absolute, so should be in °K not °C.

Turn the depth from km into m (to get 2000m) then multiply this depth by the given area (in square metres).  The result will be in cubic metres.

Alternatively, turn the surface area into square km (divide by 10^6) and multiply by the given depth (in km).  The result will be in cubic km.

I thought this was interesting too.  I'd like to make it both simpler (1. below) and more complicated (2. below)!

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