MHB Exercise about the concept of functions

AI Thread Summary
The discussion revolves around understanding functions through geometric formulas for area and perimeter. The area of a square is expressed as A = x^2, with the perimeter as P = 4x, while the area of a circle is A = πr^2, related to its circumference C = 2πr. Participants clarify that these formulas are foundational definitions in geometry, and the relationship between area and perimeter/circumference can be expressed by substituting variables. The original poster seeks further clarification on how these concepts relate to functions, indicating a need for a deeper understanding of dependency in mathematical terms. Overall, the thread emphasizes the importance of grasping these basic geometric relationships to comprehend functions better.
Nich6ls
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Hi everyone! =) . I'm having some issues with this exercises, It's about functions. I remember the basic geometrics formulas and how to get the area and perimeter of a square or a circle but I don't get it. I need an explanation.

1. Express the area A of a square as a function of (a) the length of one side x; (b) the perimeter p.
2.Express the area A of a circle as a function of its circumference c.

Answers:

1.
(a) \[ A= x^2 \] (b)\[ A= P^2/16 \]
2.
\[ A= c^2/4π \]

Thank you, stay safe! =)
 
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[math]A = x^2[/math] and [math]P = 4x[/math]. So solve for x and put it into A.

Now do the same for [math]A = \pi r^2[/math] and [math] C = 2 \pi r[/math].

-Dan
 
topsquark said:
[math]A = x^2[/math] and [math]P = 4x[/math]. So solve for x and put it into A.

Now do the same for [math]A = \pi r^2[/math] and [math] C = 2 \pi r[/math].

-Dan

Those are the answers the book gives, how did you get to them? An explanation I need.
 
Nich6ls said:
Those are the answers the book gives, how did you get to them? An explanation I need.
Are you asking about the area formulas? What's the area of a square with a side x? It's defined as [math]A = x^2[/math]. What's the perimeter? It's a "line" P = x + x + x + x = 4x long. For the area and circumference of a circle, the formulas are as I gave above. These are known formulas and if someone were to ask how to explain them you would either have to say they are definitions, or that you will have to wait until a "higher" Math level has been reached.
Square: [math]A = x^2[/math], [math]P = 4x[/math].

Circle: [math]A = \pi r^2[/math], [math]C = 2 \pi r[/math].

Take these formulas as givens. For the square solve the perimeter equation for x in terms of P and sub into the area equation. For the circle solve the circumference equation for r in terms of C and sub into the area equation.

-Dan
 
topsquark said:
Are you asking about the area formulas? What's the area of a square with a side x? It's defined as [math]A = x^2[/math]. What's the perimeter? It's a "line" P = x + x + x + x = 4x long. For the area and circumference of a circle, the formulas are as I gave above. These are known formulas and if someone were to ask how to explain them you would either have to say they are definitions, or that you will have to wait until a "higher" Math level has been reached.
Square: [math]A = x^2[/math], [math]P = 4x[/math].

Circle: [math]A = \pi r^2[/math], [math]C = 2 \pi r[/math].

Take these formulas as givens. For the square solve the perimeter equation for x in terms of P and sub into the area equation. For the circle solve the circumference equation for r in terms of C and sub into the area equation.

-Dan

Thank you Dan, what I don't understand is how these exercises are related to functions. I understand that it's something that depends on something else, but I'm not sure, sorry I just started with this today.
 
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