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Write an inequality that describes the region where the grass has been planted

Yazan975

Member
Sep 14, 2018
30
Screen Shot 2019-05-05 at 10.26.36 AM.png

I do not know how to start thinking about part a and then got even more confused when I saw the answer be:
P<x^2-5x.

I ask for your guidance please.
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
643
The problem is rather misleading since the perimeter upper edge follows the path of the parabolic curve $P = 5x-x^2$ for values $0 \le x \le 5$. The sketch shown looks more like a semicircle (why, I don't know). See the attached graph for a better depiction.

Since grass is planted below the edge defined by that parabola, then the planted region, $R$, is located under the curve that defines the upper edge and above the x-axis ... that is $0 \le R \le P = 5x-x^2$. So I do not agree with the inequality you stated, $P < x^2-5x$.

Are you able to answer the remaining questions?