The polygon in the diagram is a regular octagon with center A. Find the area of the octagon to the nearest tenth of a foot. A) 2
2.6 ft2 B) 45.3 ft2 C) 90.5 ft2 D) 121.8 ft2
btw the radius is 4 feet.
https://www.usatestprep.com/modules/gallery/files/25/2560/2560.png
here is the picture link
btw the radius is 4 feet.
https://www.usatestprep.com/modules/gallery/files/25/2560/2560.png
here is the picture link
1 answer:
Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.
Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:
Area = 2√2 × r²
where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25
Rounded to the nearest tenth:
Area = 45.3 ft²
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Answer:
The total revenue is .
The marginal revenue is .
The fixed cost is $900.
The marginal cost function is .
Step-by-step explanation:
The Total Revenue () received from the sale of
goods at price
is given by
The Marginal Revenue () is the derivative of total revenue with respect to demand and is given by
From the information given we know that the price they can sell cakes is given by the function , where
is the number of cakes sold per day.
So, the total revenue is
And the marginal revenue is
The Fixed Cost () is the amount of money you have to spend regardless of how many items you produce.
The Marginal Cost () function is the derivative of the cost function and is given by
We know that the total cost function of the company is given by , which it is equal to
From the total cost function and applying the definition of fixed cost, the fixed cost is $900.
And the marginal cost function is