Let x = the length of the rectangle
Let w= the width
Two sections are required, hence 2w of fence required
2x+3w=500
this can be written as:
3w=1500-2x
w=(1500-2x)/3
Area=x*w
replacing w with our expression:
A=x(1500-2x)/3
A=(500x-2x^2)/3
This is a quadratic equation, if we find the axis of symmetry we will know what value of x gives maximum area:
Axis of symmetry: x=-b/2a
From our equation we get:
a=-2/3; b=1500/3
thus
x=(1500/3)/(-(-2/3))
x=750
thus the maximum area will be given by length of 750
Let the variable of the equation be x.
I'm gonna go backwards of the factorization process.
Given,
x = 11 or 3
(x - 11)(x - 3) = 0
x² -3x -11x + 33 = 0
x² -14x + 33 = 0
Hence, f(x) = x² - 14x + 33.
The Pythagorean Proposition can help you explain this:
S5=10 means the 5th number is 10.
So the arithmetic sequence is s1, s2,s3, s4, 10