√50 lies between 7 and 8.
The parametric equations for x and y describe a circle of radius 10 m, so the length of the base of the fence is the length of the circumference of a circle of radius 10 m. The formula for that circumference (C) is ...
... C = 2πr
... C = 2π·(10 m) = 20π m
The height as a function of angle (t) is found by substituting for x and y.
... h(t) = h(x(t), y(t)) = 4 + 0.01·((10cos(t))²-)10sin(t))²) = 4+cos(2t)
The average value of this over the range 0 ≤ t ≤ 2π is 4, since the cosine function has two full cycles in that range, and its average value over a cycle is zero.
Thus, the area of one side of the fence is that of a rectangle 20π m long and 4 m wide. That will be
... (20π m)·(4 m) = 80π m²
The amount of paint required to cover both sides of the fence is
... 2×(80π m²)×(1 L)/(10 m²) = 16π L ≈ 50.3 L
_____
You can work out the integral for area as a function of t. When you do, you will find it gives this same result.
Answer:
3 1/3 gum balls per friend
Step-by-step explanation:
Packs of gum balls Pete has = 4
Each pack = 5 gum balls
Total gum balls Pete has = Number of packs of gum balls × Number of gum balls in each pack
= 4 × 5
= 20 gum balls
Pete gives the same number of gum balls to 6 friends.
Each friend gets = Total gum balls / number of friends
= 20 gum balls / 6 friends
= 3 2/6 gum balls per friend
= 3 1/3 gum balls per friend
