Exercise about the concept of functions

[Nich6ls]

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! =)

 

[topsquark]

\(\displaystyle A = x^2\) and \(\displaystyle P = 4x\). So solve for x and put it into A.

Now do the same for \(\displaystyle A = \pi r^2\) and \(\displaystyle C = 2 \pi r\).

-Dan

 

[Nich6ls]

\(\displaystyle A = x^2\) and \(\displaystyle P = 4x\). So solve for x and put it into A.

Now do the same for \(\displaystyle A = \pi r^2\) and \(\displaystyle C = 2 \pi r\).

-Dan

Those are the answers the book gives, how did you get to them? An explanation I need.

 

[topsquark]

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 \(\displaystyle A = x^2\). 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: \(\displaystyle A = x^2\), \(\displaystyle P = 4x\).

Circle: \(\displaystyle A = \pi r^2\), \(\displaystyle C = 2 \pi r\).

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

 

[Nich6ls]

Are you asking about the area formulas? What's the area of a square with a side x? It's defined as \(\displaystyle A = x^2\). 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: \(\displaystyle A = x^2\), \(\displaystyle P = 4x\).

Circle: \(\displaystyle A = \pi r^2\), \(\displaystyle C = 2 \pi r\).

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.