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1 answer:
Answer:
41.04 meters
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. The initial position is given by A. The tree is denoted as C and the fence post is denoted as B. Since the use of sine rule will complicate the question, it will be easier to solve this question using the cosine rule. Therefore, cosine rule will be used to calculate the length of BC. The cosine rule is:
BC^2 = AB^2 + AC^2 - 2*AB*AC*cos(BAC).
The question specifies that AC = 70 meters, BAC = 25°, and AB = 35 meters. Plugging in the values:
BC^2 = 35^2 + 70^2 - 2(35)(70)*cos(25°).
Simplifying gives:
BC^2 = 1684.091844.
Taking square root on the both sides gives BC = 41.04 meters (rounded to two decimal places).
Therefore, the distance between the point on the tree to the point on the fence post is 41.04 meters!!!
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Answer:
Expected population in 2015: 19,152.58 or 19,000 people
Step-by-step explanation:
Given the decreasing rate of 2.5% per year, and a population of 28,000 in the year 2000:
We can solve for the rate of decrease by using the formula:
where:
A = population by year 2015
a = initial population (in year 2000) = 28,000
r = rate of change (decrease by 2.5% annually or 0.025)
t = time (in number of years) = 15
Plug in these given values into the formula:
A = 28,000(0.684)
A = 19,152.58 or about 19,000 people in 2015