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Natural numbers are closed under division: false.
A set is closed under a certain operation if the results of that operation are always inside that set.
So, if natural numbers were closed under division, the division of two natural numbers would always be a natural number.
You have plenty of counterexamples, to pick one you may divide any odd number by 2: 5/2 is not a natural number.
Negative numbers are closed under addition: true.
Let be two positive numbers. So,
are two negative numbers. Their sum is
And since is positive, we deduce that
is negative, so the sum of two negative numbers is still negative.
Prime numbers are closed under subtraction: false.
This would mean that the subtraction of two primes is also a prime. Again, there are many counterexamples: 7 is prime and so is 3, but their difference 7-3 is 4, which is not prime.
Answer:
The vertical distance from the ground to the bird's eyes is 47.67 m
Step-by-step explanation:
* Lets explain the situation of the problem
- There is a bird on the top of a tree
- The bird looks down on a field mouse at an angle of depression of 50°
- The field mouse is 40 meters from the base of the tree
* Consider that the vertical distance from the ground to the bird's eyes,
the distance from the field mouse to the base of the tree distance
from the bird eyes to the field mouse formed a right triangle
- The hypotenuse is the distance from the bird eyes to the field mouse
- The horizontal side is the distance from the field mouse to the base
of the tree
- The angle between the hypotenuse and the horizontal side is the
angle of depression which = 50°
- The opposite side to the angle of measure 50° is the vertical distance
from the ground to the bird's eyes
* Lets use trigonometry functions to find the vertical distance
∵ The length of the adjacent side to the angle of measure 50° is 40 m
∵ The length of the opposite side to the angle of measure 50° is h m
∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф
∵ Ф = 50°
∴ tan 50° = h/40 ⇒ by using cross multiplication
∴ 40 tan 50° = h
∴ h = 47.67 m
* The vertical distance from the ground to the bird's eyes is 47.67 m
