The answer is 1/4 because all you have to really do is simplify
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
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You can work out the integral for area as a function of t. When you do, you will find it gives this same result.
<span>f(x) = x-2/3 and g(x) = 2-3x</span>
The answer to this question is 32
Ok, so increasing a recipe originally for 16 to 24, you need to figure out how many times larger you need the recipe, so divide 24 by 16, and you get 1.5 (one and a half times larger)
You then just need to take each ingredient amount and multiply it by 1.5
2 cans chopped clams x 1.5 = 3 cans
4 cups broth x 1.5 = 6 cups
6 cups milk x 1.5 = 9 cups
4 cups cubed potatoes x 1.5 = 6 cups
Does this make sense?
