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

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The discussion centers on determining the correct inequality for the region where grass is planted, which is below the parabolic curve defined by P = 5x - x^2 for 0 ≤ x ≤ 5. The initial confusion arises from an incorrect inequality, P < x^2 - 5x, which does not accurately represent the planted area. Instead, the correct representation is that the region R is located under the curve and above the x-axis, leading to the inequality 0 ≤ R ≤ P. Clarification is sought on how to approach the remaining questions related to this problem. The conversation highlights the importance of accurately interpreting the geometric representation of the problem.
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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.
 

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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?
 

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