Sorry, it's late, and I'm a bad explainer.
The error is adding (2x-12) with x and 30. This is wrong because you are adding the angles inside the triangle and you are assuming that (2x - 12) is the unlabeled angle INSIDE the triangle, when it is the exterior angle/outside of the triangle.
A straight line is also 180°.
(2x - 12) + ? = 180
30 + x + ? = 180
If you look at the equations, and put parentheses around 30 + x, (30 + x) and (2x - 12) should be the SAME NUMBER. So you could set them equal to each other to find x. (or you could also look at the picture and see that they both need/are missing the same angle)
2x - 12 = 30 + x
x = 42
Now you plug 42 into the exterior angle equation
2(42) - 12 = 84 - 12 = 72°
vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.
Givens
vi = 160 ft/s
vf = 0 (the rocket stops at the maximum height.)
a = - 9.81 m/s
t = ????
Remark
YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.
Equation
a = (vf - vi)/t
Solve
- 32 = (0 - 160)/t Multiply both sides by t
-32 * t = - 160 Divide by -32
t = - 160/-32
t = 5
You will also need to solve for the height to answer part B
t = 5
vi = 160 m/s
a = - 32
d = ???
d = vi*t + 1/2 a t^2
d = 160*5 + 1/2 * - 32 * 5^2
d = 800 - 400
d = 400 feet
Part B
You are at the maximum height. vi is 0 this time because you are starting to descend.
vi = 0
a = 32 m/s^2
d = 400 feet
t = ??
formula
d = vi*t + 1/2 a t^2
400 = 0 + 1/2 * 32 * t^2
400 = 16 * t^2
400/16 = t^2
t^2 = 25
t = 5 sec
The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.
Answer:
The second term of the sequence is 8 False ⇒ B
The third term of the sequence is 3 True ⇒ A
The fourth term of the sequence is -3 True ⇒ A
Step-by-step explanation:
The form of the recursive rule is:
f(1) = first term; f(n) = f(n - 1) + d, where
- f(n - 1) is the term before the nth term
- d is the common difference
∵ f(1) = 15, f(n) = f(n - 1) - 6 for n ≥ 2
∴ The first term = 15
∴ d = -6
let us find the 2nd, 3rd, and 4th terms
∵ n = 2
∴ f(2) = f(1) - 6
∵ f(1) = 15
∴ f(2) = 15 - 6 = 9
∴ The second term is 9
∴ The second term of the sequence is 8 False
∵ n = 3
∴ f(3) = f(2) - 6
∵ f(2) = 9
∴ f(3) = 9 - 6 = 3
∴ The third term is 3
∴ The third term of the sequence is 3 True
∵ n = 4
∴ f(4) = f(3) - 6
∵ f(3) = 3
∴ f(4) = 3 - 6 = -3
∴ The fourth term is -3
∴ The fourth term of the sequence is -3 True
Trapezoid because it’s the only shape that has only one pair of parallel lines
Answer:
4
Step-by-step explanation:
