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:
16.07 milligrams
Step-by-step explanation:
From the question,
Using the formula of radioactive decay,
R/R' = 2ᵃ/ᵇ..................... Equation 1
Where R = Original mass of the polonium-210, R' = Final mass of polonium-210 after decaying, a = Total disintegration time, b = half life of polonium-210.
Make R' the subject of the equation
R' = R/(2ᵃ/ᵇ)................ Equation 2
Given: R = 100 milligrams, a = 1 years = 365 days, b = 138.39 days
Substitute these values into equation 2
R' = 100/(2³⁶⁵⁰⁰/¹³⁸³⁹)
R' = 100/(6.222)
R' = 16.07 milligrams of plonium-210
Answer:
the answer is the First option.
Its the last choice there. Converting that to degrees you get the interval of 90<O<120, which is the only angle that lies in the quadrant in which cosine is negative, which is the second quadrant. Cosine is also negative in the third quadrant, but you don't have choices for the third quadrant.
Answer:
(4,-2)
Step-by-step explanation:
y - 3x < - 4
-2-3(4) < -4
-2-12 <-4
-14 < - 4
