# We have a circle with an inscribed square with an inscribed circle with an inscribed equilateral triangle. The diameter of the outer circle is 8 feet. The triangle material cost $104.95 a square foot. What is the cost of the triangular center?

The cost of a triangular center is $1090.67

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To find the cost of the triangular center, we first need to determine the side length of the equilateral triangle inscribed within the circle.

The diameter of the outer circle is 8 feet, so the radius of the outer circle is ( \frac{8}{2} = 4 ) feet.

The side length of the equilateral triangle inscribed in the circle is equal to twice the radius of the outer circle, which is ( 2 \times 4 = 8 ) feet.

To find the area of an equilateral triangle, we use the formula ( A = \frac{\sqrt{3}}{4} \times \text{side length}^2 ).

Substituting the side length ( 8 ) feet into the formula, we get:

[ A = \frac{\sqrt{3}}{4} \times 8^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3} , \text{square feet} ]

The cost of the triangular center is the area of the triangle multiplied by the cost per square foot:

[ \text{Cost} = 16\sqrt{3} \times $104.95 = $1679.20 ]

So, the cost of the triangular center is $1679.20.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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