Answer:
a)
, b)
,
, c)
, d) ![x = -6](https://tex.z-dn.net/?f=x%20%3D%20-6)
Step-by-step explanation:
a) Let derive the function:
![f'(x) = \frac{10\cdot x \cdot (x+3)-5\cdot x^{2}}{25\cdot (x+3)^{2}}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B10%5Ccdot%20x%20%5Ccdot%20%28x%2B3%29-5%5Ccdot%20x%5E%7B2%7D%7D%7B25%5Ccdot%20%28x%2B3%29%5E%7B2%7D%7D)
is undefined when denominator equates to zero. The critical point is:
![x = -3](https://tex.z-dn.net/?f=x%20%3D%20-3)
b)
when numerator equates to zero. That is:
![10\cdot x \cdot (x+3) - 5\cdot x^{2} = 0](https://tex.z-dn.net/?f=10%5Ccdot%20x%20%5Ccdot%20%28x%2B3%29%20-%205%5Ccdot%20x%5E%7B2%7D%20%3D%200)
![10\cdot x^{2}+30\cdot x -5\cdot x^{2} = 0](https://tex.z-dn.net/?f=10%5Ccdot%20x%5E%7B2%7D%2B30%5Ccdot%20x%20-5%5Ccdot%20x%5E%7B2%7D%20%3D%200)
![5\cdot x^{2} + 30\cdot x = 0](https://tex.z-dn.net/?f=5%5Ccdot%20x%5E%7B2%7D%20%2B%2030%5Ccdot%20x%20%3D%200)
![5\cdot x \cdot (x+6) = 0](https://tex.z-dn.net/?f=5%5Ccdot%20x%20%5Ccdot%20%28x%2B6%29%20%3D%200)
This equation shows two critical points:
, ![x = -6](https://tex.z-dn.net/?f=x%20%3D%20-6)
c) The critical points found in point b) and the existence of a discontinuity in point a) lead to the conclusion of the existence local minima and maxima. By plotting the function, it is evident that
corresponds to a local maximum. (See Attachment)
d) By plotting the function, it is evident that
corresponds to a local minimum. (See Attachment)
An ecosystem is a geographic area where plants, animals, and other organisms, as well as weather and landscape, work together to form a bubble of life.
Answer:
-3(4c-2) -2c = -14c+6
Step-by-step explanation:
We need to find the equivalent expression for -3(4c-2) -2c.
First we open the brackets as follows :
-3(4c-2) -2c
= -12c+6-2c
=-12c-2c+6
=-14c+6
So, the equivalent expression is -14c+6.
The answer is 145 divided by tan 65 degrees.
Since the equation for tangent is opposite/adjacent, you can just plug the numbers in.
tan(65)=145/x (x being the height that you are trying to find)
tan(65) * x = 145
Then divide tan(65) to isolate the x and you get:
145/tan(65)
Hope this helps!