The force exerted is:
\[ F = \frac{\Delta P}{\Delta t}. \]
Here:
\[ \Delta P = m \cdot v - 0 = 150 \times 10^{-3} \cdot 20 \, \text{kg m/s}, \]
\[ F = \frac{150 \times 10^{-3} \cdot 20}{0.1}. \]
\[ F = 30 \, \text{N}. \]
Final Answer: 30 N.
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to: