The number of rows in the arena is 26
<h3>How to determine the number of rows?</h3>
The hockey arena illustrates an arithmetic sequence, and it has the following parameters:
- First term, a = 220
- Sum of terms, Sn = 10920
- Common difference, d = 16
The number of rows (i.e. the number of terms) is calculated using:
So,we have:
Evaluate the terms and factors
Evaluate the like terms
21840 = n(424+ 16n)
Expand
21840 = 424n + 16n^2
Rewrite as:
16n^2 + 424n - 21840 = 0
Using a graphical tool, we have:
n = 26
Hence, the number of rows in the arena is 26
Read more about arithmetic sequence at:
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Answer:64
Step-by-step explanation:
Answer: I hope that this is right this calculator was being difficult lol.
Step-by-step explanation: it would cross at (-1,2) is what i got
Answer:
The lateral area of the figure = 480 m²
The surface area = 720 m²
Step-by-step explanation:
By definition, we have;
The lateral area is the area of the vertically facing sides of or the area of the triangular faces of a pyramid
The surface area is the area of the entire surface = Lateral area + The other surface areas of the object
For a pyramid, the surface area = Lateral area + Area of base
The figure in the question is a pentagon based pyramid with five triangles on the sides
The lateral area of the figure = 5 × area of the 5 triangles = 5 × Base × Height
The lateral area of the figure = 5 × 12 × 8 = 480 m²
The lateral area of the figure = 480 m²
The surface area = Area of the base + Lateral surface area
Area of the regular pentagon base = 1/2 × Perimeter of the pentagon × Apothem
Perimeter of the pentagon = 5 × 12 = 60 m
Apothem = Perpendicular distance from the pentagon's side to the center = 8.3 m
∴ Area of the regular pentagon base = 1/2 × 60 × 8 = 240 m²
∴ The surface area = 240 +480 =720 m²
The surface area = 720 m²
Answer:
In order to maximize profit, the company should sell each widget at $22.68.
Step-by-step explanation:
The amount of profit <em>y</em> made by the company for selling widgets at <em>x</em> price is given by the equation:
And we want to find to price for which the company should sell in order to maximize the profit.
Since our equation is a quadratic with a negative leading coefficient, its maximum will occur at the vertex point.
The vertex of a quadratic is given by the formulas:
In this case, <em>a</em> = -34, <em>b</em> = 1542, and <em>c </em>= -10037.
Find the <em>x-</em>coordinate of the vertex:
So, in order to maximize profit, the company should sell each widget at $22.68.
Extra Notes:
In order to find the maximum profit, substitute the price back into the equation:
