Answer:
n = 0 or n = -5/2
Step-by-step explanation:
We'd like to solve this equation for n: .
Cross-multiply and distribute:
(2 - n) * n = (n + 4) * 3n
2n - n² = 3n² + 12n
Move everything to one side:
3n² + n² + 12n - 2n = 0
4n² + 10n = 0
Factor our 2n:
2n * (2n + 5) = 0
By the Zero Property of Multiplication, either 2n = 0 or 2n + 5 = 0 to make this equation true:
2n = 0 OR 2n + 5 = 0
n = 0/2 = 0 OR 2n = -5 ⇒ n = -5/2
Thus, n = 0 or n = -5/2.
<em>~ an aesthetics lover</em>
Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
