SOLUTION: Could you please help me with this problem? It looks like Greek to me. The numberof parts per million of nitric oxide emissions y from a certain car engine is approximated by th

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Question 13411: Could you please help me with this problem? It looks like Greek to me.
The numberof parts per million of nitric oxide emissions y from a certain car engine is approximated by the model y=-5.05x^3+3857x-38411.25 (13
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
WOW!! What an intimidating problem!
Let's try to simplify things a little bit. First of all, you are given an incredibly intimidating formula: y=+-5.05x%5E3+%2B3857x+-+38411.25, where y is 2400 and x is the unknown that you need to find: the air-fuel ratio.

Substitute the value of y:
2400+=+-5.05x%5E3+%2B+3857x+-+38411.25+

Subtract 2400 from each side:
0+=+-5.05x%5E3+%2B+3857x+-+38411.25+-2400+
+0+=+-5.05x%5E3+%2B+3857x+-+40811.25+

Now you have a really ugly equation to solve, and it looks like a real-life problem, probably one that is not going to come out even--it probably won't factor! So use a graphing calculator to solve it.

The problem is to graph y+=+-5.05x%5E3+%2B+3857x+-+40811.25+, and find the x intercept(s). That will be the solution. Also, in the problem, it says that we are looking for values of x that are between 13 and 18. The graph should look like this between x = 10 and x= 20 and y between -1000 and 1000:
graph+%28+300%2C+300%2C+10%2C+20%2C+-1000%2C+1000%2C+-5.05x%5E3+%2B+3857x+-+40811.25+%29

There appear to be two points where the graph crosses the x axis within this interval. With further calculation it seems that the first point is exact at x= 15. The second number looks like 17, but it turns out to be approximately 16.89.

Neat problem!! Where did you get it??

R^2 at SCC