How to write (0,8] as an inequality

1 answer:

3 0

Answer: $0 \ \textless \ x \le 8$

What is given to you is interval notation. We have the interval start at 0 and end at 8. The value 0 is not included in the interval as indicated by the parenthesis. So we go with a "less than" sign (instead of a "less than or equal to" sign)

The value 8 is included since a square bracket is used here. The use of "or equal to" is needed to make sure the endpoint 8 is included.

So x can be any number between 0 and 8. It can't be 0 but it can be 8.

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HELP EXPLAIN STEP BY STEP In a circle whose radius is 8, the length of an arc of the circle is 2π. In radians, what is the measu

Travka [436]

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What is the value of angle x°?

erastova [34]

Answer:

$64^\circ$

Step-by-step explanation:

Please refer to the attached figure for the labeling and construction in the given figure:

Given that minor angle of arc AB is $116^\circ$ .

Or in other words, we can say that angle subtended on the center O by the arc is $116^\circ$ .

Now, PA and PB are the tangents so, if we join the center of circle O with A and B, the angles formed are right angles.

i.e.

$\angle PAO = 90^\circ\\\angle PBO = 90^\circ$

Now, we know that sum of internal angles of a quadrilateral is equal to $360^\circ$ .

Here, we have the quadrilateral AOPB.

$\therefore \angle PAO +\angle PBO+\angle AOB +\angle APB=360^\circ\\\Rightarrow 90+90+116+x=360^\circ\\\Rightarrow x = 360 - 180 - 116\\\Rightarrow x = 64^\circ$