Solve these recurrence relations together with the initial conditions given. an = an−1 + 6an−2 for n ≥ 2, a0 = 3, a1 = 6
1 answer:
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Answer:
The value of given expression i.e Ф is 90° and - 30°
Step-by-step explanation:
Given as :
4 cos²Ф + 2 sinФ = 2
∵ sin²Ф + cos²Ф = 1 , so , cos²Ф = 1 - sin²Ф
Or, 4 ( 1 - sin²Ф ) + 2 sinФ = 2
Or, 4 - 4 sin²Ф + 2 sinФ = 2
or, 4 sin²Ф - 2 sinФ - 4 + 2 = 0
or, 4 sin²Ф - 2 sinФ - 2 = 0
or, 2 sin²Ф - sinФ - 1 = 0
or, 2 sin²Ф - 2 sinФ + sinФ - 1 = 0
Or, 2 sinФ ( sinФ - 1 ) + 1 ( sinФ - 1 ) = 0
∴ ( sinФ - 1 ) ( 2 sinФ + 1 ) = 0
i.e ( sinФ - 1 ) = 0 And ( 2 sinФ + 1 ) = 0
since ( sinФ - 1 ) = 0
So, sinФ = 1
Or, Ф = = 90°
And ( 2 sinФ + 1 ) = 0
Or, 2 sinФ = - 1
Or, sinФ = -
Or, Ф = = - 30°
Hence the value of given expression i.e Ф is 90° and - 30° Answer
ANSWER
The correct answers are option B and D.
EXPLANATION
The given expression is
We need to simplify the above expression in order to determine the option that is equivalent to it.
The least common denominator for the last two fractions is 3.
This implies that,
We simplify to obtain,
This further simplifies to give us,
This is option B.
When we further factor -4, we get,
This is option D.
The correct answers are option B and D.
EXPLANATION
The given expression is
We need to simplify the above expression in order to determine the option that is equivalent to it.
The least common denominator for the last two fractions is 3.
This implies that,
We simplify to obtain,
This further simplifies to give us,
This is option B.
When we further factor -4, we get,
This is option D.
For this case we have:
We identify the points of the graph following the form (x, y).
Where:
- x: Represents the coordinate of the horizontal axis
- y: Represents the vertical axis coordinate
In the graph, each box has a value of 2 units.
When observing the points from left to right we find:
So, the correct option is the b
Answer:
Option B