How many integers $n$ satisfy the inequality $3n^2 - 4 \le 44$?
2 answers:
Answer:
7 integers
Step-by-step explanation:
The inequality to solve is
We can do algebra and solve this:
If we solve , we will get the intercepts. So:
<em>Since, the inequality is less than, the solution set is all numbers between -4 and 4. So</em>
<em>-4 < n < 4</em>
<em />
<em>*note: -4 and 4 is NOT included, so the integers in the range are:</em>
<em>-3, -2, -1, 0, 1 , 2, 3</em>
<em>Which is </em><em>7 integers.</em>
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The arc length of AB is 8 m (app.)
Explanation:
Given that the radius of the circle is 8 m.
The central angle is 60°
We need to determine the arc length of AB
The arc length of AB can be determined using the formula,
Substituting central angle = 60° and circumference = 2πr in the above formula, we get,
Simplifying the terms, we get,
Dividing, we get,
Hence, the arc length is approximately equal to 8.
Therefore, the arc length of AB is 8 m