Which numbers are divisible by 9? 119 702 432 641 372
2 answers:
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9514 1404 393
Answer:
obtuse
Step-by-step explanation:
The law of cosines tells you ...
b² = a² +c² -2ac·cos(B)
Substituting for a²+c² using the given equation, we have ...
b² = b²·cos(B)² -2ac·cos(B)
We can subtract b² to get a quadratic in standard form for cos(B).
b²·cos(B)² -2ac·cos(B) -b² = 0
Solving this using the quadratic formula gives ...
The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...
The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.
The graph is shown below. I used GeoGebra to create the graph. The graph is restricted on the domain meaning that everything to the left of x = 0 is not drawn, and the same for everything to the right of x = 2.
A table of values is included as well. Each row in the table represents an ordered pair point (x,y) that is on the blue cosine graph.
