Answer:
= 1.75
Step-by-step explanation:
7/6 divided by 6
= 7/36
7/36 = x/9
Cross multiply fractions:
36x = 63
Divide each side by 36:
x = 7/4 or 1.75
Answer:
Step-by-step explanation:
Foil the equation!
1. You see that is to the second power so it means this
2. Then you use the Foil method. First, Outside, Inside, and Last.
3. Combined like terms
4. Answer!
A tip you can use to avoid Foil is this mental math trick: (Keep in mind this only works if the polynomial is being squared.)
1. Multiply the first number by itself =
2. Add the first number by itself =
3. Multiply the last number by itself =
4. Combined to form your answer =
NOTE: This is the same thing as a foil but it uses mental math so it takes less time!
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.