Expressing Area as a Function of Width

In summary, expressing area as a function of width means representing the area of a shape using the width as the independent variable in an equation. It is important because it allows us to understand the relationship between width and area and easily calculate area for different width values. The formula for expressing area as a function of width varies depending on the shape, and to graph it, you would plot width values on the x-axis and area values on the y-axis. An example of expressing area as a function of width is A = 10w, where w is the width, for a rectangle with a length of 10 cm.
  • #1
shoook
23
0
1. How should -2(125)^2 be calculated?

*The title is inaccurate, sorry i changed my question.*
 
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  • #2
What do you think? What are the rules of precedence?
 
  • #3


I would approach this question by first clarifying the intended meaning of "expressing area as a function of width." Area is typically calculated by multiplying two dimensions, such as length and width, so it is important to understand what specific formula or relationship is being referred to.

Assuming that the intended formula is for calculating the area of a rectangle, where the width is a variable and the length is fixed at -2(125)^2, the calculation would be as follows:

Area = length * width
Area = -2(125)^2 * width
Area = -2 * (125 * 125) * width
Area = -2 * 15625 * width
Area = -31250 * width

Therefore, the expression -2(125)^2 would be calculated by first squaring 125, then multiplying it by -2, and finally multiplying the result by the width. It is important to note that this calculation may not be the most accurate or appropriate depending on the context and intended use of the formula. It is always important to carefully consider the variables and equations being used in scientific calculations to ensure accuracy and relevance.
 

1. What does it mean to express area as a function of width?

Expressing area as a function of width means to represent the area of a two-dimensional shape (such as a rectangle or square) using the width as the independent variable in a mathematical equation. This allows us to calculate the area for any given width value.

2. Why is it important to express area as a function of width?

Expressing area as a function of width allows us to understand the relationship between the width and the area of a shape. It also allows us to easily calculate the area for different width values, making it useful in many real-life applications such as construction, landscaping, and manufacturing.

3. What is the formula for expressing area as a function of width?

The formula for expressing area as a function of width varies depending on the shape. For a rectangle, the formula is A = w * h, where w is the width and h is the height. For a square, the formula is A = w^2, where w is the length of one side.

4. How do you graph a function of area as a function of width?

To graph a function of area as a function of width, you would plot the width values on the x-axis and the corresponding area values on the y-axis. This would create a curve that represents the relationship between the width and area of the shape.

5. Can you give an example of expressing area as a function of width?

For a rectangle with a length of 10 cm, the area can be expressed as A = 10w, where w is the width. If the width is 5 cm, then the area would be 50 cm^2. This equation shows the relationship between the width and area of this rectangle.

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