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.
Answer:
11.6 foot
Step-by-step explanation:
Length of the Ladder=12 foot
Distance of the base of the Ladder from the House=3 foot
Since the ladder leans against the wall in a slant position, it is the hypotenuse.
From Pythagoras Theorem,
Hypotenuse ²= Opposite ²+ Adjacent ²
12²=3²+x²
x²= 12²-3²=144-9=135
x=√135=11.61895003862
The Ladder reaches up to a height of 11.6 foot (to the nearest tenth) on the house.
Probably D, I’m not sure if this helped but if it did, I’m glad that I helped
z = 106
y = 74
Since angle 74 and angle y are the same sizes, you can know for a fact they are the same measurments. Next, you would do 74(2) and that would get you 148. 360 - 148 is 212. 212/2 is 106. TADAAAAA. That's the answer.
Answer:
x^2 + y^2 = a
Step-by-step explanation:
a > or = 36
