Respuesta :
Answer:
Area of square=[tex]a\times a=a^2units^2[/tex]
Perimeter of square=a+a+a+a=4a units
Step-by-step explanation:
We have to give the formula for the area and perimeter of square where the side length is the independent variable and the area and perimeter is the dependent variable.
Let the side of square be a units which is independent variable.
As square is also a rectangle whose area is [tex]length\times breadth[/tex]
Area of square=[tex]a\times a=a^2units^2[/tex]
Perimeter of square=a+a+a+a=4a units
Here, each two area and perimeter depend on the side of square implies area and square are dependent variable and side is independent.
Answer:
See explanation.
( Conditions of a function )
Step-by-step explanation:
Declaring Variables:
- The side length of the square = x.
- The area of square = A
- The perimeter of square = P
Solution:
- The area of the square A in terms of side length x is given by:
A(x) = x^2
Where, Area A is dependent on x side length which is independent.
However, the definition of a function does not imply that it should be a straight line , in fact, the function A(x) is not a straight line but a quadratic curve.
According to definition of function i.e the function should be differentiable over all real values of x or its derivative should exist over the entire domain. Hence,
A'(x) = 2*x
- From that we see that A'(x) has real values over the entire domain of x e [ 0 , +inf). Hence, A(x) is a function of x.
- Similarly, The Perimeter of the square P in terms of side length x is given by:
P(x) = 4*x
Where, Perimeter P is dependent on x side length which is independent.
- The function P(x) is a straight line.
- Also, according to definition of function i.e the function should be differentiable over all real values of x or its derivative should exist over the entire domain. Hence,
P'(x) = 4
- From that we see that P'(x) has real values over the entire domain of x e [ 0 , +inf). Hence, P(x) is a function of x.
