<span>Short-range forecasts are more accurate than longer range ones. Short term forecasts may use mathematical techniques such as moving averages and, exponential smoothing. Longer term forecasts not only use different methodologies, such as qualitative vs. quantitative, they also tend to consider different issues.</span>
The intensity of a light in a surface follows the inverse square law formula which can be mathematically expressed as,
I = k/d²
where I is intensity, d is distance, and k is the proportionality constant. For us to increase the intensity, we should lower the distance from the source to the surface.
The weight of the meterstick is:

and this weight is applied at the center of mass of the meterstick, so at x=0.50 m, therefore at a distance

from the pivot.
The torque generated by the weight of the meterstick around the pivot is:

To keep the system in equilibrium, the mass of 0.50 kg must generate an equal torque with opposite direction of rotation, so it must be located at a distance d2 somewhere between x=0 and x=0.40 m. The magnitude of the torque should be the same, 0.20 Nm, and so we have:

from which we find the value of d2:

So, the mass should be put at x=-0.04 m from the pivot, therefore at the x=36 cm mark.
Answer: m= 35.6 kg
Explanation:
For finding the mass of the stone we have the formula
v= 
Here, Tension= m*g = m*9.81
and linear mass density= 
Linear mass density= 
Linear mass density= 0.0127 kg/m
Velocity= 
Velocity= 2 * 
Velocity= 165.8 m/s
So putting all these values in equation we get
v= 
165.8= 
Solving we get
m= 35.58 kg
or m= 35.6 kg