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?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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