First note the domain of the expressions on either side of the equation,
√<em>x</em> is defined only for <em>x</em> ≥ 0, so we need to have
and
but <em>x</em> ² ≥ 0 for all real <em>x</em>, so both conditions will always be satisfied.
Back to the equation - take the square of both sides and solve for <em>x</em> :
<u>Given</u>:
Given that the perimeter of a regular decagon is 150 inches.
The apothem of a regular decagon is 23.1 inches.
We need to determine the area of the polygon.
<u>Area of the regular decagon:</u>
The area of the regular decagon can be determined using the formula,
where a is the apothem and p is the perimeter of the polygon.
Substituting the values, we get;
Multiplying, we get;
Dividing, we get;
Thus, the area of the regular decagon is 1732.5 square inches.
Answer:
60ft
Step-by-step explanation:
Let's x, y be the width and length of the surrounding rectangle. Since the area is 450 sq feet, this means xy = 450 or y = 450/x
The perimeter of this rectangle is (since there are 3 sides only)
f(x,y) = 2x + y
This is something we need to minimize. We can start by substituting y = 450/x
f(x) = 2x + 450/x
Let's take the first derivative of this function and set it to 0
y = 450 / 15 = 30ft
so the minimum perimeter that needs taping over is
f(x,y) = 2x + y = 2*15 + 30 = 60ft