Answer:
![x= -\frac{ln [\frac{5P}{8000-P}]}{0.002}](https://tex.z-dn.net/?f=%20x%3D%20-%5Cfrac%7Bln%20%5B%5Cfrac%7B5P%7D%7B8000-P%7D%5D%7D%7B0.002%7D)
a) ![x= -\frac{ln [\frac{5*200}{8000-200}]}{0.002} =1027.062 \approx 1027](https://tex.z-dn.net/?f=%20x%3D%20-%5Cfrac%7Bln%20%5B%5Cfrac%7B5%2A200%7D%7B8000-200%7D%5D%7D%7B0.002%7D%20%3D1027.062%20%5Capprox%201027)
b) ![x= -\frac{ln [\frac{5*800}{8000-800}]}{0.002} =293.893 \approx 294](https://tex.z-dn.net/?f=%20x%3D%20-%5Cfrac%7Bln%20%5B%5Cfrac%7B5%2A800%7D%7B8000-800%7D%5D%7D%7B0.002%7D%20%3D293.893%20%5Capprox%20294)
Step-by-step explanation:
For this case we have the following function:

We can solve for x like this. First we can reorder the expression like this:



Now we can apply natura log on both sids and we got:
![ln[\frac{40000}{8000-P} -5] = ln e^{-0.002x}](https://tex.z-dn.net/?f=%20ln%5B%5Cfrac%7B40000%7D%7B8000-P%7D%20-5%5D%20%3D%20ln%20e%5E%7B-0.002x%7D)
![ln [\frac{5P}{8000-P}] = -0.002x](https://tex.z-dn.net/?f=%20ln%20%5B%5Cfrac%7B5P%7D%7B8000-P%7D%5D%20%3D%20-0.002x%20)
And if we solve for x we got:
![x= -\frac{ln [\frac{5P}{8000-P}]}{0.002}](https://tex.z-dn.net/?f=%20x%3D%20-%5Cfrac%7Bln%20%5B%5Cfrac%7B5P%7D%7B8000-P%7D%5D%7D%7B0.002%7D)
Part a
For this case we can replace P = 200 and see what we got for x like this:
![x= -\frac{ln [\frac{5*200}{8000-200}]}{0.002} =1027.062 \approx 1027](https://tex.z-dn.net/?f=%20x%3D%20-%5Cfrac%7Bln%20%5B%5Cfrac%7B5%2A200%7D%7B8000-200%7D%5D%7D%7B0.002%7D%20%3D1027.062%20%5Capprox%201027)
Part b
For this case we can replace P = 800 and see what we got for x like this:
![x= -\frac{ln [\frac{5*800}{8000-800}]}{0.002} =293.893 \approx 294](https://tex.z-dn.net/?f=%20x%3D%20-%5Cfrac%7Bln%20%5B%5Cfrac%7B5%2A800%7D%7B8000-800%7D%5D%7D%7B0.002%7D%20%3D293.893%20%5Capprox%20294)
For a line to be parallel, the slope has to be the same(1/3) only its coordonate on the y axis (b) changes.
Therefore the new equation will be y=1/3x+b
To find be, tou have to isolate it after inputting the new coordinates (-9,4)
(4)=1/3(-9)+b
4=-3+b
7=b
Therefore, the new equation is
y=1/3x+7
1:5
2/2=1
10/2=5
Therefore, 2:10=1:5
There are several. Parallelograms are shapes were the opposite side is the same. Therefore, squares, rectangles, rhombuses, and trapezoids are all quadrilaterals that are parallelograms.