Answer:
B
Step-by-step explanation:
The wording in the problem statement is ...
... "less than 3 years"
... "at least 3. but less than 6 years"
so we expect the inequality symbols to look like ...
... 0 ≤ x < 3
... 3 ≤ x < 6
These match <em>the second piecewise function</em>.
Answer: see below
<u>Step-by-step explanation:</u>
C(x) = 39 when 0 < x ≤ 1.0
C(x) = 63 when 1.0 < x ≤ 2.0
C(x) = 87 when 2.0 < x ≤ 3.0
C(x) = 111 when 3.0 < x ≤ 4.0
C(x) = 135 when 4.0 < x ≤ 5.0
C(x) = 159 when 5.0 < x ≤ 6.0
Based on the information I provided above, the answers are:
a) x= 0.6, C(x) = 1.0
x = 1.0, C(x) = 39
x = 1.1, C(x) = 63
x = 2.5, C(x) = 87
x = 3.0, C(x) = 87
x = 4.8, C(x) = 135
x = 5.0, C(x) = 135
x = 5.3, C(x) = 159
b) If C(x) = 87, then 2.0 < x ≤ 3.0
c) Domain (all possible x-values): 0 < x ≤ 6.0
d) Range (all possible y-values): {39, 63, 87, 111, 135, 159}
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:
The correct answer is C if the answers are the same as the picture attached.
