Answer:

Step-by-step explanation:
Taking into account that the growth rate of the number of species on the island is proportional to the density of species (number of species between area of the island), a model based on a differential equation is proposed:

This differential equation can be solved by the method of separable variables like this:
with what you get:

. Taking exponentials on both sides of the equation:


how do you have to
, then

Since absolute value is just taking the positive value of whatever you put in the function, it is 7.8 as well. Also, absolute value can be described as the distance from 0 on the number line. 7.8 is 7.8 "units" away from 0, thus meaning it is equal to 7.8.
Answer:
106.1 ft/s
Step-by-step explanation:
You know the diagonal of a square is √2 times the length of one side, so the distance from 3rd to 1st is 90√2 feet ≈ 127.2792 ft.
The speed is the ratio of distance to time:
speed = distance/time = 127.2972 ft/(1.2 s) ≈ 106.1 ft/s.
_____
In case you have never figured or seen the computation of the diagonal of a square (the hypotenuse of an isosceles right triangle), consider the square with side lengths 1. The diagonal will cut the square into halves that are isosceles right triangles with leg lengths 1. Then the Pythagorean theorem can be used to find the diagonal length d:
d² = 1² + 1²
d² = 2
d = √2
Since this is the diagonal for a side length of 1, any other side length will serve as a scale factor for this value. A square with a side length of 90 ft will have a diagonal measuring 90√2 ft.
Answer:
a) f(-1/2) = -2 is NOT TRUE.
b) f(0) =3/2 is TRUE.
c) f(1) = -1 is NOT TRUE.
d) f(2) = 1 is NOT TRUE.
e) f(4) = 7/2 is TRUE.
Step-by-step explanation:
Here, the given function is 
Now, checking for each values for the given function:
a) Putting x = (-1/2):

and (5/4) ≠ -2
Hence, f(-1/2) = -2 is NOT TRUE.
b)Putting x = 0 :

Hence, f(0) =3/2 is TRUE.
c) Putting x = 1:

Hence, f(1) = -1 is NOT TRUE.
d)Putting x = 2:

and (5/2) ≠ 1
Hence, f(2) = 1 is NOT TRUE.
e)Putting x = 4:

Hence, f(4) = 7/2 is TRUE.