SOLUTION: Hi, I need help solving this math word problem please. The average number of vehicles waiting in line to enter a sports arena parking lot is modeled by the function w(x)=x^2/2(1

Click here to see ALL problems on Functions

Question 914483: Hi, I need help solving this math word problem please.
The average number of vehicles waiting in line to enter a sports arena parking lot is modeled by the function w(x)=x^2/2(1-x), where x is a number between 0 and 1 and known as the traffic intensity. Find the average number of vehicles waiting if the traffic intensity is 0.63.
According to my professor, the answer is: 0.54 -average number of vehicles waiting (rounded to nearest hundreth)
Would you please show me the steps on how my professor got this answer please. Thank you.
Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
By w(x)=x^2/2(1-x), your professor must mean w(x)=x^2/[2(1-x)]= ,
where the 2 and the (1-x) are both in the denominator.
It is not be the same as w(x)=x^2/2*(1-x)=

Then, for ,

NOTES:
That long horizontal line/fraction bar in is a grouping symbol, just like the parentheses.

If I had to write that in one line, I would write
w(x)=x^2/[2(1-x)], or w(x)=x^2/2/(1-x), to make it perfectly clear that both, x and (1-x) are dividing .

You have to be careful about those "undercover grouping symbols" when entering calculations into a calculator.
Doing calculations one at a time as I showed above may be safer.
To enter into a calculator as one calculation I would enter
0.63 2 1 0.63
or
0.63 2 1 0.63