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
To determine the median, we need to set up our numbers from least to greatest, and then place T in later to figure out what T is.
8, 9, 9, 9, 10, 11, 12, 15. Cross out the smallest number with the largest number.
9, 9, 9, 10, 11, 12.
9, 9, 10, 11.
9, 10.
9.5 is our median currently.
Since we need to get a number after 10 to make 10 the median, let's use 12.
8, 9, 9, 9, 10, 11, 12, 12, 15.
9, 9, 9, 10, 11, 12 ,12.
9, 9, 10, 11, 12.
9, 10, 11.
10 is now our median since we inserted 12 into our list.
Your answer is 12.
I hope this helps!
Answer:
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = - 6
Answer:
Only the first pair can be so mapped
Step-by-step explanation:
Reflection across AB and translation will leave the segment corresponding to AB having the same "north-south" (vertical) orientation. The reflection will reverse the clockwise ordering of corresponding vertices.
- selection 2: segment AY is not vertical
- selection 3: the ordering of the vertices is unchanged, not reversed
- selection 4: segment XY is not vertical
