I’d help but the image isn’t working its all blurry on my end fam sorry
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.
The line which rises to the left has slope of -1/3 and y intercept of 2 so we have
y = -1/3x + 2
3y = -x + 6
x + 3y = 6
Shading is below and the line is solid so the inequality is
x + 3y ≤ 6
The other line has equation
y = 3x - 1
and inequality is
y ≥ 3x - 1
The answer is B
Answer:
Step-by-step explanation:
what question?
The answer is 18.975 but you might want to round that to 18.98
