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.
8/12 and 9/12. Respectively.
<h2>
Answer: <em>x = 7.5</em></h2>
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Step-by-step explanation:
Use the Pythagorean Theorem ( 
)
The longest side is <em>c = the hypotenuse</em>, and <em>a and b = the other sides</em> of the triangle.
a = 4 First: 
b = x Second: 
c = 8.5 Third: 
Fourth: 
Fifth: x = 7.5
First, x intercepts are (-1,0) and (-3,0). y intercept is(0,2)
second, left side is a function because there are no x-values paired with two different y-values. right side is not a function because the x-value 3 is paired with two different y-values values
third, slope is ride over run, or the difference in y values divided by difference in x values. slope is 1/2. intercept is at (0,2). the equation is then y=1/2*x + 2
The Pythagorean Theorem formula is listed below. It can only be applied to right triangles.
(side1)^2 + (side2)^2 = (hypotenuse)^2
Since we are given that the base is 8cm, we know that the side of one triangle is 4cm. We are also given that the hypotenuse is 8cm. The height of the cone will be one of the short sides. If we plug these numbers into the formula, we get the following...
4^2 + height^2 = 8^2
If we solve for height, we get the following...
height = sqrt(8^2 - 4^2) = sqrt(64 - 16) = sqrt(48)
Since we are only asked for what is inside the square root, our answer is 48.
