Solve 1/2cot(x)>=1/2 over 0<=x<=2pi
1 answer:
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Answer:
(0, π/4] ∪ (π, 5π/4]
Step-by-step explanation:
Multiplying by 2 gives ...
cot(x) ≥ 1
The cotangent function decreases from ∞ to 1 in the domain (0, π/4], and again in the domain (π, 5π/4]. The solution is the union of these two intervals.
x ∈ (0, π/4] ∪ (π, 5π/4]
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(a, b] is interval notation for a < x ≤ b
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Answer:
- x - 5y = -5; x -5y = 35
- there are no solutions, the lines are parallel so do not intersect
Step-by-step explanation:
<h3>1.</h3>We judge the x-intercept to be about 5 times as far from the origin as the y-intercept is. If we take the y-intercept of the blue line to be +1, then the equation of that line can be x -5y = -5. The y-intercept of the black line appears to be about 7 times as far from the origin as for the blue line, so the constant will be multiplied by -7: x -5y = 35.
The two equations in the system of equations could be ...
- x -5y = -5
- x -5y = 35
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<h3>2.</h3>We have assumed the two lines are parallel, so they will not intersect. A point of intersection would be a solution to the system. The system of equations will have no solutions.
