360=LW
<span>W=5/8 L </span>
<span>360=L*5/8 L=5/8 L^2 </span>
<span>L^2=8*360/5=8*72 </span>
<span>L=sqrt(4*144)=24
The length is 24</span>
<u>Answer:</u>
<h2>(4, 6)</h2>
<u>Explanation:</u>
x = -4 + (12 - (-4))/2
x = -4 + (12+4)/2
x = -4 + 16/2
x = -4 + 8
x = 4
y = 2 + (10 - 2)/2
y = 2 + 8/2
y = 2 + 4
y = 6
the coordinates of the center of the circle: (4, 6)
Step-by-step explanation:
y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1
dy/dx = 12√x
Arc length is:
s = ∫ ds
s = ∫₀¹ √(1 + (dy/dx)²) dx
s = ∫₀¹ √(1 + (12√x)²) dx
s = ∫₀¹ √(1 + 144x) dx
If u = 1 + 144x, then du = 144 dx.
s = 1/144 ∫ √u du
s = 1/144 (⅔ u^(³/₂))
s = 1/216 u^(³/₂)
Substitute back:
s = 1/216 (1 + 144x)^(³/₂)
Evaluate between x=0 and x=1.
s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]
s = 1/216 (145)^(³/₂) − 1/216
s = (145√145 − 1) / 216
