The horizontal asymptote of the function is the minimum number of deer in the area.
- The equation of horizontal asymptote is:
![\mathbf{y = 40}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%2040%7D)
- The horizontal asymptote means that, the number of deer will never be less than 40
The equation is given as:
![\mathbf{f(x) = \frac{40 + 2x}{1 + 0.05x}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%20%5Cfrac%7B40%20%2B%202x%7D%7B1%20%2B%200.05x%7D%7D)
Expand the numerator
![\mathbf{f(x) = \frac{40(1 + 0.05x)}{1 + 0.05x}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%20%5Cfrac%7B40%281%20%2B%200.05x%29%7D%7B1%20%2B%200.05x%7D%7D)
Cancel out the common factor
![\mathbf{f(x) = 40}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%2040%7D)
Hence, the equation of horizontal asymptote is:
![\mathbf{y = 40}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%2040%7D)
The horizontal asymptote means that, the number of deer will never be less than 40
Read more about horizontal asymptotes at:
brainly.com/question/4084552
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Answers
4b+9=8
This is the required statement
Answer:
-sinx
Step-by-step explanation:
a trig identity that is crucial to solving this problem is: sin^2 + cos^2 = 1
with knowing that, you can manipulate that and turn it into 1 - sin^2x = cos^x
so 1-sin^2x/sinx - cscx becomes cos^2x/sinx - cscx
it is also important to know that cscx is the same thing as 1/sinx
knowing this information, cscx can be replaced with 1/sinx
(cos^2x)/(sinx - 1/sinx)
now sinx and 1/sinx do not have the same denominator, so we need to multiply top and bottom of sinx by sinx; it becomes....
cos^2x
---------------------
(sin^2x - 1)/sinx
notice how in the denominator it has sin^2x-1 which is equal to -cos^2x
so now it becomes:
cos^2x
--------------
-cos^2x/sinx
because we have a fraction over a fraction, we need to flip it
cos^2x sinx
---------- * ----------------
1 - cos^2x
because the cos^2x can cancel out, it becomes 1
now the answer is -sinx