We divide the thin rectangular sheet in small parts of height b and length dr. All these sheets are parallel to b. The infinitesimal moment of inertia of one of these small parts is
![dI =r^2*dm](https://tex.z-dn.net/?f=dI%20%3Dr%5E2%2Adm)
where
![dm =M(b*dr)/(ab)](https://tex.z-dn.net/?f=dm%20%3DM%28b%2Adr%29%2F%28ab%29)
Now we find the moment of inertia by integrating from
![-a/2](https://tex.z-dn.net/?f=-a%2F2)
to
![a/2](https://tex.z-dn.net/?f=a%2F2)
The moment of inertia is
![I= \int\limits^{-a/2}_{a/2} {r^2*dm} = M \int\limits^{-a/2}_{a/2} r^2(b*dr)/(ab)=(M/a)(r^3/3)](https://tex.z-dn.net/?f=I%3D%20%5Cint%5Climits%5E%7B-a%2F2%7D_%7Ba%2F2%7D%20%7Br%5E2%2Adm%7D%20%3D%20M%20%5Cint%5Climits%5E%7B-a%2F2%7D_%7Ba%2F2%7D%20r%5E2%28b%2Adr%29%2F%28ab%29%3D%28M%2Fa%29%28r%5E3%2F3%29)
(from (-a/2) to
![I=(M/3a)(a^3/8 +a^3/8)=(Ma^2)/12](https://tex.z-dn.net/?f=I%3D%28M%2F3a%29%28a%5E3%2F8%20%2Ba%5E3%2F8%29%3D%28Ma%5E2%29%2F12)
(a/2))
The independent variable is the different amount of repellent each person is given. This is because it does not depend on any variable. The dependent variable is what they are measuring, which would be the number of bites on each volunteer.
I hope this helps! :)
As they evolved and adapted, those of the fittest survived to reproduce. Those that did not adapt, died.
Answer:
Explanation:
a) Linear density is greater on the left side because the velocity of wave in a string is inversely proportional to the linear mass density of the string
b) We should start pulse from the left hand side so the reflected wave does not get inverted because the wave traveling from the denser to lighter medium gets reflected in the same phase.