Answer:
<em>The shortest side of the fence can have a maximum length of 80 feet</em>
Step-by-step explanation:
<u>Inequalities</u>
To solve the problem, we use the following variables:
x=length of the longer side
y=length of the sorter side
The perimeter of a rectangle is calculated as:
P = 2x + 2y
The perimeter of the fence must be no larger than 500 feet. This condition can be written as:

The second condition states the longer side of the fence must be 10 feet more than twice the length of the shorter side.
This can be expressed as:
x = 10 + 2y
Substituting into the inequality:

This is the inequality needed to determine the maximum length of the shorter side of the fence.
Operating:

Simplifying:

Subtracting 20:


Solving:


The shortest side of the fence can have a maximum length of 80 feet
Here, we are required to find the vertical and horizontal intercepts for r⁴ + s² − r s = 16.
The vertical and horizontal intercepts are s = ±4 and r = ±2 respectively.
According to the question;
- the r-axis is the horizontal axis.
- the s-axis is the vertical axis.
Therefore, to get the horizontal intercepts, r we set the vertical axis, s to zero(0).
- i.e s = 0
- the equation r⁴ + s² − r s = 16, then becomes;
- r⁴ = 16
- Therefore, r = ±2.
Also, to to get the vertical intercepts, s we set the horizontal axis, r to zero(0).
- i.e r = 0.
- the equation r⁴ + s² − r s = 16, then becomes;
- s² = 16.
- Therefore, s = ±4.
Therefore, the vertical and horizontal intercepts are s = ±4 and r = ±2 respectively.
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