Answer:
y=2/5x+2
slope: 2/5
y=-1/4x+4
y-intercept: 4
Step-by-step explanation
The equation for slope-intercept form is y=mx+b.
m=the slope
b= the y-intercept
Angie buys 1 software package and 3 months of game play
Kenny buys 1 software package and 4 months of game play
price of each software package = $20
total cost = $117
cost of one month game play = ?
let y is the cost of one month play
Angie buys 3 months game play and paid $20 = 20 + 3y
Kenny buys 4 months game play and paid $20 = 20 + 4y
total cost of both is $117
So the equation becomes,
(20 + 3y) + (20 + 4y) = 117
7y + 40 = 117
7y = 117 - 40
7y = 77
dividing with 7 on both sides, we get
y = 11
so, $11 is the cost of one month game play
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.
