Answer:
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Step-by-step explanation:
Arc length of a parametric curve is:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
x = t + cos t, dx/dt = 1 − sin t
y = t − sin t, dy/dt = 1 − cos t
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Or, if you wish to simplify:
L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt
L = ∫₀²ᵖⁱ √(3 − 2 sin t − 2 cos t) dt
Answer:
(4, 8) where =(x, y)
Step-by-step explanation:
x + 4(-x + 12) = 36
x -4x + 48 = 36
-3x = -12
x = 4
4 + 4y = 36
4y = 32
y = 8
For the last part, you have to find where 
attains its maximum over 
. We have
so that
with critical points at 
such that
So either
or
where 
is any integer. We get 8 solutions over the given interval with 
from the first set of solutions, 
from the set of solutions where 
, and 
from the set of solutions where 
. They are approximately
Answer:
question 8 : it is equal to 0
Question 9 : 4+5
Step-by-step explanation:
= 
Answer:
3 /5
Step-by-step explanation:
Given that:
Ratio of red to green to tiles = 2:3
Red = 2
Green = 3
Total sum of each part (red + green) = (2 + 3) = 5
Fraction of green tiles :
Green / total sum
3 / 5
