Answer:
100 residents/
Step-by-step explanation:
In order to find the population density, we have to calculate the area of the township first.
We know that:
L = length = 5 km
W = width = 4 km
So the area of the township is
Now we can find the population density by using
where N is the number of residents, and A is the area.
Substituting N = 2000, we find:
so, 100 residents per kilometer squared.
The value of cos 4x from the given identity is 0.999
<h3>Trigonometry identity</h3>
Given the cosine identity
cos8x = 13/36
Determine the value of x
8x = arccos(13/36)
8x = 0.36111
x = 0.36111/8
x = 0.04514
Determine the value of cos4x
cos4x = cos4(0.04514)
cos4(0.04514) = 0.999
Hence the value of cos 4x from the given identity is 0.999
Learn more trig identity here; brainly.com/question/7331447
Record the data on the line plot. <---------------------> 1,3,1,1,2,2,3,3,4,5,4,3,1,2
igomit [66]
1 3
1 2 3
1 2 3 4
<---- 1 2 3 4 5---->
something like this.. where you put the numbers on top of one another in order creating a line plot of your data, with the numbers above the line
1.029 is greater than 1.0275
1. Rewrite the expression in terms of logarithms:
Then differentiate with the chain rule (I'll use prime notation to save space; that is, the derivative of <em>y</em> is denoted <em>y' </em>)
2. Chain rule:
Since , we can cancel one factor of sine:
3. Chain rule:
4. If you're like me and don't remember the rule for differentiating logarithms of bases not equal to <em>e</em>, you can use the change-of-base formula first:
Then
So we have
and we can use the double angle identity and logarithm properties to condense this result:
5. Differentiate both sides:
6. Same as with (5):
7. Looks like
Compute the second derivative:
Set this equal to 0 and solve for <em>x</em> :