```python
# https://socratic.org/questions/a-fence-8-ft-tall-runs-parallel-to-a-tall-building-at-a-distance-of-4-ft-from-th-1
from IPython.display import Image
from IPython.core.display import HTML 
from sympy import *; x,h,y,n,t,d,c,A,r   = symbols("x h y n t d c A r"); C, D = symbols("C D", real=True)
Image(url= "https://i.imgur.com/XYvZXIq.png")
```









```python
Image(url= "https://i.imgur.com/2DeA9ZT.png")
# change 4 to 5
```









```python
Image(url= "https://i.imgur.com/um3ZnlW.png")
```









```python
h = factor(8*(5+x))/x
h
```




$\displaystyle \frac{8 \left(x + 5\right)}{x}$




```python
L = h**2+(x+5)**2
Eq(symbols("L")**2,L)
```




$\displaystyle L^{2} = \left(x + 5\right)^{2} + \frac{64 \left(x + 5\right)^{2}}{x^{2}}$




```python
diff(L)
```




$\displaystyle 2 x + 10 + \frac{64 \left(2 x + 10\right)}{x^{2}} - \frac{128 \left(x + 5\right)^{2}}{x^{3}}$




```python
solve(diff(L),x)
```




    [-5,
     4*5**(1/3),
     -2*5**(1/3) - 2*sqrt(3)*5**(1/3)*I,
     -2*5**(1/3) + 2*sqrt(3)*5**(1/3)*I]




```python
L.subs(x, 4*5**(1/3))
```




$\displaystyle 331.951408234819$




```python
sqrt(L.subs(x, 4*5**(1/3)))
```




$\displaystyle 18.2195336997087$




```python
Image(url= "https://i.imgur.com/yafiIYG.png")
```








390d432c583a83772d5e6237fbc7c685f8678c01
ipynb
Jupyter Notebook
Calculus_Homework/WWB14.6.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Calculus_Homework/WWB14.6.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Calculus_Homework/WWB14.6.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Qwen/Qwen-72B
1. YES
2. YES