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Genrish500 [490]
3 years ago
15

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b obtuse. What must be true?​

Mathematics
2 answers:
kotykmax [81]3 years ago
8 0

Answer:

C

Step-by-step explanation:

If the angle opposite b is the obtuse angle then the answer is a² + c² < b² because in an obtuse triangle, the sum of the squares of the shortest sides must be less than the square of the longest side. In this case, the longest side is the one opposite the largest angle, which is b.

zheka24 [161]3 years ago
5 0

Answer:

C.

Step-by-step explanation:

In triangles, the largest angle is always opposite from the longest side.

In other words, since the angle opposite to side b is obtuse and there are only 180 degrees in a triangle, then side b must be the longest side.

In an obtuse triangle, the longest side squared will always be greater than the squared values of the two shorter sides.

The correct answer is C.

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The population of rabbits on an island is growing exponentially. In the year 1994, the population of rabbits was 9600, and by 20
drek231 [11]

Answer:

49243

Step-by-step explanation:

Given that the population of rabbits on an island is growing exponentially.

Let the population, P=P_0e^{bt}

where, P_0 and b are constants, t=(Current year -1994) is the time in years from 1994.

In 1994, t=0, the population of rabbit, P=9600, so

9600=P_0e^{b\times 0}

So, P_0=9600

and in 2000, t=2000-1994=6 years and population of the rabbit, P=18400

18400=9600 \times e^{b\times 6} \\\\\frac{18400}{9600}=e^{b\times 6} \\\\

\ln(23/12}=6b \\\\

b = \frac{\ln{1.92}}{6} \\\\

b=0.109

On putting the value of P_0 and b, the population of the rabbit after t years from 1994 is

P=9600 \times e^{0.109\times t}

In 2009, t= 2009-1994=15 years,

So, the population of the rabbit in 2009

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Hence, the population of the rabbit in 2009 is 49243.

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