The equation you can use to solve the problem is;
50/30 = 300/x
Next Cross Multiply
50x = 9000
x = 9000/50
x = 180
The building's shadow is 180 feet tall
10m ----> 3 sec
x meters ----> 50 sec
50(10) = 3x
500 = 3x
devide both in 3
x = 166.66 m
Use the power rule for differentiation:

You can use this formula if you remember that a root is just a rational exponential:
![\sqrt[4]\ln(x) = (\ln(x))^{\frac{1}{4}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%5Cln%28x%29%20%3D%20%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20)
So, remembering that the derivative of the logarithm is 1/x, you have

Which you can rewrite as
![\dfrac{1}{4}(\ln(x))^{\frac{1}{4}-1}\dfrac{1}{x} =\dfrac{1}{4}(\ln(x))^{\frac{-3}{4}}\dfrac{1}{x} =\dfrac{1}{4}\dfrac{1}{\sqrt[4]{\ln(x))^3}}\dfrac{1}{x} = \dfrac{1}{4x\sqrt[4]{\ln(x))^3}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B1%7D%7B4%7D-1%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%5Cdfrac%7B1%7D%7B4%7D%28%5Cln%28x%29%29%5E%7B%5Cfrac%7B-3%7D%7B4%7D%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%5Cdfrac%7B1%7D%7B4%7D%5Cdfrac%7B1%7D%7B%5Csqrt%5B4%5D%7B%5Cln%28x%29%29%5E3%7D%7D%5Cdfrac%7B1%7D%7Bx%7D%20%3D%20%5Cdfrac%7B1%7D%7B4x%5Csqrt%5B4%5D%7B%5Cln%28x%29%29%5E3%7D%7D%20)
Answer:
14 cm
Step-by-step explanation:
Use the formula for the area of a square, a = s², where s is the side length of the square.
Plug in 196 as the area, then solve for s.
a = s²
196 = s²
14 = s
So, the length of the pathway is 14 cm