CO2 Pollution

Sirius Ex. 3.75
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Look at the graph:
graph

The horizontal blue line marks the level at which the emission C = 200 g/km.

If you go vertically down at the points where that line intersects with your graph, you find the velocity-values v1 and v2 for which C(v1) and C(v2) = 200 g/km.

Here, v1 = 38 km/h and v2 = 112 km/h.

It's easier to calculate this directly, but you need to know how to do this.

The equation to solve is

             2
200 = 0.045 v  - 6.75 v + 393

This simplifies to

       2
0.045 v  - 6.75 v + 193 = 0

The solutions to this equation are

     6.75 - sqrt( -4*0.045*193 + 6.75^2 )
v1 = ------------------------------------ = 38.44
             	2*0.045
     6.75 + sqrt( -4*0.045*193 + 6.75^2 )
v2 = ------------------------------------ = 112.55
             	2*0.045

Rounded to km, we find again v1 = 38 km/h and v2 = 112 km/h.

Yet another question

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