Two researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. After how many years will the two populations be the same? The two populations will be the same after
years.

3 years

Step-by-step explanation:

Let y = number of orangutans, and let x = number of years.

For each study, the population, y, after x years is:

First study:

y = 784 - 25x

Second study:

y = 817 - 36x

We set the populations equal and solve for x, the number of years.

784 - 25x = 817 - 36x

Add 36x to both sides. Subtract 784 from both sides.

11x = 33

Divide both sides by 11.

x = 3

3 years

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west