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
Answer:
D
Step-by-step explanation:
Answer:
9.
Step-by-step explanation:
334÷38=8.79, rounded up to 9.
To determine the perimeter of the triangle given the vertices, calculate the distances between pair of points. For the first pair (-5,1) and (1,1), the distance is 6. For the next pair, (1,1) and (1, -7), the distance is 8. Lastly, for the pair of points (-5,1) and (1, -7), the distance is 10. Adding all the distance will give the perimeter of the triangle. Thus, the perimeter is 24.
