Sorry i needed points but i hope u find the answer u needed
Answer:
2A/r + 2r
Step-by-step explanation:
A sector is made of an arc and two radii. As such, the perimeter of the sector is the sum of the length of an arc and the two radii. Given that the radius is r and the area is A, the area of a sector A
= Ф°/360° * πr²
The length L of an arc of the sector
= Ф°/360° * 2πr
Hence,
A/L = r/2
L = 2A/r
The perimeter of the sector
= L + 2r
= 2A/r + 2r
Answer:
- north and south sides are 38 8/9 ft long
- east and west sides are 17.5 ft long
Step-by-step explanation:
<u>Short answer</u>: area is maximized when half the cost is spent in each of the orthogonal directions. This means the east and west sides will total $350 at $20 per foot, so will be 17.5 feet. The north and south sides will total $350 at $9 per foot, so will be 38 8/9 feet.
The dimensions that maximize the area are 17.5 ft in the north-south direction by 38 8/9 ft in the east-west direction.
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<u>Long answer</u>: If x represents the length of the north and south sides, and y represents the length of the east and west sides, then the total cost is ...
10y +10y +2x +7x = 700
9x +20y = 700
y = (700 -9x)/20
We want to maximize the area:
A = xy = x(700 -9x)/20
We can do this by differentiating and setting the derivative to zero:
dA/dx = 700/20 -9x/10 = 0
350 -9x = 0 . . . . multiply by 10
x = 350/9 = 38 8/9
y = (700 -9(350/9))/20 = 350/20 = 17.5
The north and south sides are 38 8/9 ft long; the east and west sides are 17.5 ft long to maximize the area for the given cost.
56 reduced as a fraction is 56/100 or 14/25
