SOLUTION: Suppose the population density in the Wichita, Kansas, area is related to the distance from the center of the city. This is modeled by D = 4500x/x^2+32 where D is the population

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Suppose the population density in the Wichita, Kansas, area is related to the distance from the center of the city. This is modeled by D = 4500x/x^2+32 where D is the population      Log On


   

Question 1094521: Suppose the population density in the Wichita, Kansas, area is related to the distance from the center of the city.
This is modeled by D = 4500x/x^2+32 where D is the population density (in people per square mile) and x is the distance (in miles) from the center of the city.
Find the distance(s) where the population density is 375 people per square mile.
Hi! Thank you so much in advance. Also, I want to ask a question. Is it possible to be good in Math even if you've grown up being so not good in it? I've been trying so hard because I want to maintain my good grades but Math's just dragging my grades down. :( I want to have scholarship this year. What are the ways to be good in it? Also, solving word problems is harder for me. :( Thank you so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'm assuming the equation is D+=+%284500x%29%2F%28x%5E2%2B32%29. If so, then we replace D with 375 and solve for x.

D+=+%284500x%29%2F%28x%5E2%2B32%29

375+=+%284500x%29%2F%28x%5E2%2B32%29

375%28x%5E2%2B32%29+=+4500x

375%28x%5E2%29%2B375%2832%29+=+4500x

375x%5E2%2B12000+=+4500x

375x%5E2%2B12000-4500x+=+0

375%28x%5E2-12x%2B32%29+=+0

x%5E2-12x%2B32+=+0

%28x-8%29%28x-4%29+=+0 Note: -8 and -4 add to -12 and multiply to 32

x-8=0 or x-4+=+0

x+=+8 or x+=+4

So if you're at a distance of 4 miles or 8 miles from the city center, then the population density will be 375 people per square mile.

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