2(x + delta x) = 2x + 2 delta x
so on top you have 2x + 2 delta x - 2x
which is 2 delta x
the delta x cancels out and you are left with just 2
so the limit is 2
4sin²(x) = 5 - 4cos(x)
4{¹/₂[1 - cos(2x)]} = 5 - 4cos(x)
4{¹/₂[1] - ¹/₂[cos(2x)]} = 5 - 4cos(x)
4[¹/₂ - ¹/₂cos(2x)] = 5 - 4cos(x)
4[¹/₂] - 4[¹/₂cos(2x)] = 5 - 4cos(x)
2 - 2cos(2x) = 5 - 4cos(x)
- 2 - 2
-2cos(2x) = 3 - 4cos(x)
-2[2cos²(x) - 1] = 3 - 4cos(x)
-4cos²(x) + 2 = 3 - 4cos(x)
- 2 - 2
-4cos²(x) = 1 - 4cos(x)
-4cos²(x) + 4cos(x) - 1 = 0
4cos²(x) - 4cos(x) + 1 = 0
[2cos(x) - 1]² = 0
2cos(x) - 1 = 0
+ 1 + 1
2cos(x) = 1
2 2
cos(x) = ¹/₂
cos⁻¹[cos(x)] = cos⁻¹(¹/₂)
x = 60, 300
x = π/3, 5π/3
[0, 2π) = 0 ≤ x < 2π
[0, 2π) = 0 ≤ π/3 ≤ 2π or 0 ≤ 5pi/3 < 2π
Answer:
$295
Step-by-step explanation:
Let d represent the amount Danny contributed. Then Beth contributed (d+80) and Katie contributed ((d+80)-20) = (d+60). The total from the three friends is ...
d + (d+80) +(d+60) = $1025
3d = 885 . . . . . . . . . . . . . . . . . . . subtract 140
d = 295 . . . . . . . . . . . . . . . . . . . . divide by 3; Danny's contribution
Danny contributed $295.
1. Distribute the 6 to the 2x and the -11
12x-22+15=3x+12
2. Combine like terms
12x-7=3x+12
9x=+19
x=19/9
Part B x=19/9
Answer:
Vertical Stretch & horizontal translation
Step-by-step explanation:
the vertical stretch makes the line bigger
Horizontal translation will move the shape 2 left of the x axis
