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

• MHB
• Yazan975
In summary, the conversation discusses a confusing problem involving a parabolic curve and a semicircle. The expert points out that the sketch shown looks more like a semicircle and clarifies that the planted region is located under the curve defined by the upper edge and above the x-axis. The expert disagrees with the inequality provided and asks if there are any remaining questions.
Yazan975
View attachment 8955

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.

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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?

## What is an inequality?

An inequality is a mathematical statement that compares two values or expressions using symbols such as <, >, ≤, or ≥ to show which value is larger or smaller.

## How can an inequality describe a region?

An inequality can describe a region by setting boundaries or limitations on the values that can be included in that region. In the case of the grass being planted, the inequality would set boundaries for the area where the grass has been planted.

## What are the variables in the inequality for the planted grass region?

The variables in the inequality would depend on the specific situation, but they could include the coordinates of the boundaries of the planted grass region or the amount of grass planted in a certain area.

## What are the symbols used in an inequality?

The symbols used in an inequality are <, >, ≤, and ≥. These symbols represent less than, greater than, less than or equal to, and greater than or equal to, respectively.

## How can I graph an inequality for the planted grass region?

To graph an inequality for the planted grass region, you would first need to determine the boundaries of the region. Then, you would plot those boundaries on a graph and shade in the area between the boundaries to represent the region where the grass has been planted.

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