(50 points) What is the value of x in the triangle?
1 answer:
Answer:
x = 23.78 cm to the nearest hundredth
Step-by-step explanation:
In a right-angled triangle:
The opposite "O" is the opposite side to the angle
The adjacent side "A" is adjacent side to the angle
The hypotenuse "H" is the long side that joins the 2 legs
For this triangle, we have:
angle = 18°
adjacent (A) = x
hypotensue (H) = 25
So we can use the trig formula:
Therefore,
Multiply both sides by 25: 25 cos(18) = x
Therefore, x = 23.77841291...
So x = 23.78 cm to the nearest hundredth
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Answer:
<em>C. 3.8 years</em>
Step-by-step explanation:
<u>Exponential Growth </u>
The natural growth of some magnitudes can be modeled by the equation:
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
The actual population of deer in a forest is Po=800 individuals. It's been predicted the population will grow at a rate of 20% per year (r=0.2).
We have enough information to write the exponential model:
It's required to find the number of years required for the population of deers to double, that is, P = 2*Po = 1600. We need to solve for t:
Dividing by 800:
Taking logarithms:
Dividing by log 1.2:
Calculating:
t = 3.8 years
Answer: C. 3.8 years