Answer:
The initial population size is of 58.
The population size of the specie after t years is given by:
![P(t) = \frac{520}{1 + 8e^{-0.3t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20%5Cfrac%7B520%7D%7B1%20%2B%208e%5E%7B-0.3t%7D)
Step-by-step explanation:
Population size of the specie:
The population size of the specie after t years is given by:
![P(t) = \frac{520}{1 + 8e^{-0.3t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20%5Cfrac%7B520%7D%7B1%20%2B%208e%5E%7B-0.3t%7D)
Initial population size
This is P when
, that is,
. So
![P(0) = \frac{520}{1 + 8e^{-0.3*0} = \frac{520}{1+8} = \frac{520}{9} = 57.7](https://tex.z-dn.net/?f=P%280%29%20%3D%20%5Cfrac%7B520%7D%7B1%20%2B%208e%5E%7B-0.3%2A0%7D%20%3D%20%5Cfrac%7B520%7D%7B1%2B8%7D%20%3D%20%5Cfrac%7B520%7D%7B9%7D%20%3D%2057.7)
Rounding to the nearest number, 58
The initial population size is of 58.
I think I got it. Correct me if I am wrong.
Parallelogram diagram I believe down below. We must find the height and then the area using Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.
A^2 + B^2 = C^2
A^2 + 3^2 = 6^2
A^2 + 9 = 36
A^2 = 27
A = 3√3
Therefore the height is 3√3
Now calculate the area using A = bh
A = bh
= (12)(3√3)
= 36√3
So the area is 36√3 square units.
I cannot be sure of this answer because you did not provide a diagram.
Answer:
Base angle = 72
Vertex angle = 18
Step-by-step explanation:
Measure of the base angle = x. But there are two of them. (Definition of isosceles). Keep that in mind.
The vertex angle is 1/4 of one of the base angles. That means that the vertex is 1/4 x
All three angles = 180 degrees.
So we have x + x + x/4 = 180 degrees.
change 1/4x to 0.25x x since 1/4 = 0.25
Equation
x + x + 0.25 = 180
2.5x = 180
Solution
2.5x = 180 Divide by 2.5 on both sides
2.5x/2.5 = 180/2.5
x = 72
Answer
That means that each base angle = 72 degrees
The Vertex Angle = 72/4 = 18
Answer:
54
Step-by-step explanation: