<h3>Given</h3>
A regular polygon with area 500 ft² and apothem 10 ft
Cost of fence is $7.95 per ft
<h3>Find</h3>
Part III The cost of fence around an area scaled to 60 times the size
<h3>Solution</h3>
You don't want to think too much about this, because if you do, you find the regular polygon has 3.087 sides. The closest approximation, an equilateral triangle, will have an area of 519.6 ft² for an apothem of 10 ft.
For similar shapes of scale factor "s", the larger shape will have an area of s² times that of the smaller one. Here, it appears the area scale factor s² is 60, so the linear scale factor is
... s² = 60
... s = √60 ≈ 7.7460
The perimeter fence of the 500 ft² area is presumed to be 100 ft long (twice the area of the polygon divided by the apothem—found in Part I), so the perimeter fence of the industrial farm is ...
... (100 ft)×7.7460 = 774.60 ft
and the cost to construct it is
... ($7.95/ft)×(774.60 ft) ≈ $6158
Answer:
The integer is 1 or 9.
Step-by-step explanation:
Let the integer be x, then:
x^2 + 7 = 10x - 2
x^2 - 10x + 9 = 0
(x - 9)(x - 1) = 0
x = 1, 9.
Verifying
9^2 + 7 = 88
10*9 - 2 = 88 So 9 is correct.
1^2 + 7 = 8
10*1 - 2 = 8 So 1 is also correct.
In a triangle, the three interior angles always add to 180°
x + 3x + 5x = 180
9x = 180
x = 180/9
x = 20
<span>the smallest angle = x = 20</span>°
X would equal 1 in this problem since 1+2=3 and the absolute value(s) in this equation would be -1+(-2)=3 since, a negative plus a negative equals a positive.
I hope this helped you!
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