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miv72 [106K]
3 years ago
12

Using a number line, find both the intersection and the union of the following intervals: (−3, +∞) and (4, +∞)

Mathematics
1 answer:
sammy [17]3 years ago
3 0

Answer:

The intersection of the two intervals = 4, 5, 6,.......+∞ = (4, +∞)

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, +∞)

Step-by-step explanation:

The given intervals are;

First interval  = (-3, +∞)

Second interval  = (4, +∞)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

The second interval includes, 4, 5,.....,+∞

Which gives the intersection as 4, 5, 6,.......+∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

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The reason the above value is correct is as follows;

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By sine rule, we have

\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}

sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})

\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}

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A_{req} = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

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