Solve 29<(m^2+9)/2<45
1 answer:
Answer:
-9 < m < -7 ∪ 7 < m < 9
Step-by-step explanation:
You can proceed in the usual way up to the point where you need to take the square root.
Multiply by 2:
58 < m^2 +9 < 90
Subtract 9:
49 < m^2 < 81
Take the square root:
7 < |m| < 9
This resolves to two sets of inequalities:
7 < -m < 9 ⇒ -9 < m < -7
7 < m < 9
The solution set is the union of these intervals: (-9, -7) ∪ (7, 9).
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Yes, it is possible
Step-by-step explanation:
In a triangle, the length of the longest side of the triangle cannot be larger than the sum of the lenghts of the two shortest sides.
In formula, this means that:
where
c is the length of the longest side
a, b are the lengths of the shortest side
In this problem, we want to build a triangle using 3 pieces of lumber, each of length:
a = 3 ft
b = 7 ft
c = 8 ft
We can verify that the length of the longest piece of lumber is less than the sum of the lengths of the other two sides, so:
Therefore, yes, it is possible to build a closed triangular pen.