Answer:
θ = π n + π/2 for n element Z
Step-by-step explanation:
Solve for θ:
1 + 2 cos(2 θ) + cos^2(2 θ) = 0
Write the left hand side as a square:
(cos(2 θ) + 1)^2 = 0
Take the square root of both sides:
cos(2 θ) + 1 = 0
Subtract 1 from both sides:
cos(2 θ) = -1
Take the inverse cosine of both sides:
2 θ = 2 π n + π for n element Z
Divide both sides by 2:
Answer: θ = π n + π/2 for n element Z
Answer:
The slope of the line that contains the points (-1, 2) and (4, 3) is:
Step-by-step explanation:
Given the points
Finding the slope between (-1, 2) and (4, 3)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [3 - 2] / [4 - (-1)]
= 1 / 5
Thus, the slope of the line that contains the points (-1, 2) and (4, 3) is:
The formula for infinite geometric series is equal to a1 / (1-r) where in this problem a1 is equal to 8 and r is equal to 4. In this case, r is not equal to less than 1. This means the sum should be infinity and cannot be determined definitely.
Answer:
B
Step-by-step explanation:
given the 2 equations
y - 4x = 12 → (1)
2 - y = 2(x + 2)² → (2)
rearrange (1) expressing y in terms of x
y = 12 + 4x
Simplify (2) by expanding factor and substituting y = 12 + 4x
2 - (12 + 4x) = 2(x² + 4x + 4)
2 - 12 - 4x = 2x² + 8x + 8
- 10 - 4x = 2x² + 8x + 8 ← rearrange into standard form
add 10 + 4x to both sides
2x² + 12x + 18 = 0 ← in standard form
divide through by 2
x² + 6x + 9 = 0
(x + 3)(x + 3) = 0 ⇒ (x + 3)² = 0 ⇒ x = - 3
Point of intersection = (- 3, 0 ) → B
Answer:
5
Step-by-step explanation:
