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Function can be used to represent a model in real-life situations.

Example:

One hundred meters of fencing is available to enclose a rectangular area next to a river (see figure). Give a function [tex]A[/tex] that can represent the area that can be enclosed, in terms of [tex]x[/tex].

Solution:

The area of the rectangular enclosure is [tex]A = xy[/tex]. We will write this as a function of [tex]x[/tex]. Since only 100 m of fencing is available, then [tex]x + 2y = 100[/tex] or [tex]y = \frac{100 - x}{2} = 50 - 0.5x[/tex]. Thus, [tex]A(x) = x(50 - 0.5x) = 50x - 0.5x^2[/tex].

Exercise:

Give a function [tex]C[/tex] that can represent the cost of buying [tex]x[/tex] meals, if one meal costs P40.

Sagot :

GinnyAnsweridn
To derive the function [tex]\( C \)[/tex] that represents the cost of buying [tex]\( x \)[/tex] meals, given that one meal costs 40 Pesos, follow these steps:

1. Understand the problem: You need to find the total cost of [tex]\( x \)[/tex] meals when one meal costs 40 Pesos.

2. Define the variables:
- [tex]\( x \)[/tex] represents the number of meals.
- The cost of one meal is 40 Pesos.

3. Determine the total cost:
- If one meal costs 40 Pesos, then [tex]\( x \)[/tex] meals would cost [tex]\( 40 \)[/tex] Pesos per meal times the number of meals [tex]\( x \)[/tex].

4. Formulate the function:
- The total cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] meals can be represented as:
[tex]\[ C(x) = 40 \times x \][/tex]

Therefore, the function [tex]\( C \)[/tex] that represents the cost of buying [tex]\( x \)[/tex] meals is:
[tex]\[ C(x) = 40x \][/tex]
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