The area of a rectangular athletic field is represented by the expression -15x^5+75y^3-30xy square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution.
area= -15x^5+75y^3-10xy
area= 15(-x^5+5y^3-2/3 xy)
l= 15, w=(above)
To represent the dimensions (length times width) of the athletic field using an algebraic expression, we can factor out the common variables from the given expression.
The given expression for the area of the athletic field is:
A = -15x^5 + 75y^3 - 30xy square meters
To find the dimensions (length times width), we need to identify the factors of the given expression.
The terms -15x^5, 75y^3, and -30xy can be factored as:
-15x^5 = -5x * 3x^4
75y^3 = 5y * 15y^2
-30xy = -10x * 3y
Now, we can write the expression representing the dimensions of the athletic field:
Dimensions = (-5x * 3x^4) * (5y * 15y^2) * (-10x * 3y)
This can be simplified further:
Dimensions = (-5 * 3 * 5 * 15 * -10) * (x * x^4 * y * y^2 * x * y)
Simplifying:
Dimensions = 22500 * x^6 * y^4
So, one possible set of dimensions for the athletic field is:
Length = 22500x^6 meters
Width = y^4 meters