Answer:
<em>Terry had £780 initially and Faye had £1300</em>
Step-by-step explanation:
<u>System of Equations</u>
We'll call the following variables:
x = Terry's balance in his bank account
y = Faye's balance in her bank account
The initial relation between them is:
Cross-multiplying:
5x = 3y [1]
If Terry put £220 in his account he had x+220 and if Faye withdrew £300 from her account, she had y-300. Both quantities are equal, thus
x + 220 = y - 300
Subtracting 220:
x = y - 520 [2]
Substituting in [1]
5(y - 520) = 3y
Multiplying:
5y - 2600 = 3y
Adding 2600 and subtracting 3y:
2y = 2600
Dividing by 2:
y = 1300
From [2]:
x = 1300 - 520
x = 780
Terry had £780 initially and Faye had £1300
Assignment: 
<><><><><><><>
Answer: 
<><><><><><><>
Explanation: 
<><><><><><><>
[ Step One ] Subtract 12 From Both Sides
[ Step Two ] Simplify
[ Step Three ] Subtract 8x From Both Sides
[ Step Four ] Simplify
[ Step Five ] Divide Both Sides By 3
[ Step Six ] Simplify
<><><><><><><>
Answer:
<h2>n = -19</h2>
Step-by-step explanation:
X = 4(cosθ - cos²θ) = 4cosθ - 4cos²<span>θ
</span>dx/dθ = -4sinθ + 8sinθcosθ = -4sinθ(1 - 2cos<span>θ)
dy/d</span>θ = 4(cosθ - cos²θ + sin²θ) = 4(cos<span>θ - 1)
</span>∴dy/dx = 4(cosθ - 1)/-4sinθ(1 - 2cosθ) = 1-cosθ/(sinθ - 2sinθcosθ<span>)
Now, we're finding a horizontal tangent, which is when dy/dx = 0 (horizontal tangent).
1-cos</span>θ/(sinθ - 2sinθcosθ) = 0
1-cosθ = 0
cosθ = 1
θ = 0, 360 in the interval [0, 360].
At θ = 0, x = 0, y = 0
Only points in the open interval [-2π, 2π] are at (0, 0), unless I made a mistake somewhere.
