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.
with1) Comparing those fractions we can note the following, after some simplifying.
We can compare them by their decimal value or its integer value obtained by dividing the numerator by the denominator
a) 6/12 = 1/2 = 0.5 < 4/6 =2/3 = 0.67
b) 4/3 =1.33 > 7/6 =1.16
c) 8/5 = 1.6 < 400/100 = 4
d) 12/10=6/5= 1.2 < 35/5=7
e) 11/4 = 2.75 < 17/8= 2.125
f) 7/12 =0.583 < 4/3 =1.33
Answer:
x + z = 180
x = 180 - z
y + z +10 = 180
y = 170 - z
w + z - 13 = 180
w = 193 - z
x + y + w = 180⁰
180 - z + 170 - z + 193 - z = 180
-3z = -363
z = 121⁰
Apnswer:
p = 1
q = -2
Step-by-step explanation:
5p - 2q = 9 eqn 1
3p + 2q = 7 eqn 2
subtract equation 2 from 1
2p = 2
p = 1
Substitute for p in equation 1
5(1) - 2q = 9
5 - 2q = 9
-2q = 4
q = -2