An isosceles trapezoid has base angles of 45° and bases of lengths 8 and 14. The area of the trapezoid is
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Given:
The measure of three sides of a triangle are 8, 7 and 14.
To find:
The measure of the angle opposite the side of length 8.
Solution:
According to the Law of Cosine:
Let a=8, b=7 and c=14, then by using Law of Cosine, we get
Taking cos inverse on both sides.
Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.
Answer:
(-∞, -2), (-2, -0.618), and (1.618, 3)
Step-by-step explanation:
The red plus (+) signs indicate the regions in which the function is concave up, and the red negative (-) signs indicate the regions in which the function is concave down.
Note that the sign of the concavity changes at an inflection point.
Let's examine the intervals given.
(-∞, -2): Yes, concave up.
(-∞, -1.17): No. Concave up in (-∞, -2) but concave down in (-2, -1.17).
(-2, 0): No. Concave down in (-2, -1.17) but increasing in (-1.17, 0.0).
(-1.17, 0.689): Yes. Concave up.
(-0.618, 1.618): No. Concave up in (-0.618, 0.689) but concave down in (0.689, 1.618).
(0, 3): No. Concave up in (0, 0.689), concave down in (0.689, 2.481), and concave up in (2.481, 3).
(2.481, ∞): Yes. Concave up.
The three intervals that are concave up are (-∞, -2), (-1.17, -0.689), and (2.481, ∞).
