Answer:
x >= 20
Step-by-step explanation:
Solve for x:
Start to isolate x by subtracting the 6 from both sides.
Then multiply 10 from each side.
After that, you would get x >= 20
40 feet or 13 yards and 1 foot
using the conversion
1 yard = 3 feet then 1 yard 2 feet = 5 feet ← material for 1 pillow, hence
8 pillows require 8 × 5 = 40 feet
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.
M is the slope and b is the y-intercept in the form
.. y = mx +b
You have
.. y = -10x +1
Matching patterns, you see that
.. m = -10
.. b = 1
The slope is -10
The y-intercept is 1
