Answer:
Florence is often named as the birthplace of the Renaissance. The early writers and artists of the period sprung from this city in the northern hills of Italy. As a center for the European wool trade, the political power of the city rested primarily in the hands of the wealthy merchants who dominated the industry
Explanation:
Answer:
1)
, 2) ![K = \frac{1}{10}\cdot m \cdot (b^{2}+c^{2})](https://tex.z-dn.net/?f=K%20%3D%20%5Cfrac%7B1%7D%7B10%7D%5Ccdot%20m%20%5Ccdot%20%28b%5E%7B2%7D%2Bc%5E%7B2%7D%29)
Explanation:
1) The kinetic energy due to the rotation is:
![K = \frac{1}{2}\cdot I\cdot \omega^{2}](https://tex.z-dn.net/?f=K%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20I%5Ccdot%20%5Comega%5E%7B2%7D)
Where
and
are the moment of inertia and angular speed, respectively. The moment of inertia of the circular cone is:
![I = \frac{3}{10}\cdot m\cdot r^{2}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B3%7D%7B10%7D%5Ccdot%20m%5Ccdot%20r%5E%7B2%7D)
The kinetic energy is:
![K = \frac{3}{20}\cdot m\cdot r^{2}\cdot \omega^{2}](https://tex.z-dn.net/?f=K%20%3D%20%5Cfrac%7B3%7D%7B20%7D%5Ccdot%20m%5Ccdot%20r%5E%7B2%7D%5Ccdot%20%5Comega%5E%7B2%7D)
2) The moment of inertia of the ellipsoid is (where a is the major semiaxis):
![I = \frac{1}{5}\cdot m \cdot (b^{2}+c^{2})](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5Ccdot%20m%20%5Ccdot%20%28b%5E%7B2%7D%2Bc%5E%7B2%7D%29)
The kinetic energy is:
![K = \frac{1}{10}\cdot m \cdot (b^{2}+c^{2})](https://tex.z-dn.net/?f=K%20%3D%20%5Cfrac%7B1%7D%7B10%7D%5Ccdot%20m%20%5Ccdot%20%28b%5E%7B2%7D%2Bc%5E%7B2%7D%29)
A. A medium of exchange ....
Hope am right !!!
Answer:
The value of the power is ![P_c = 38.55 \ W](https://tex.z-dn.net/?f=P_c%20%20%3D%20%2038.55%20%5C%20%20W%20)
Explanation:
From the question we are told that
The power rating ![P_{1000} =P_b= 52 \ W](https://tex.z-dn.net/?f=P_%7B1000%7D%20%3DP_b%3D%20%2052%20%5C%20%20W)
The frequency is ![f = 1000 \ Hz](https://tex.z-dn.net/?f=f%20%3D%201000%20%5C%20%20Hz)
The frequency at which the sound intensity decreases ![f_k = 20 \ Hz](https://tex.z-dn.net/?f=f_k%20%20%3D%20%2020%20%5C%20%20Hz)
The decrease in intensity is by ![\beta = 1.3 dB](https://tex.z-dn.net/?f=%5Cbeta%20%20%3D%20%201.3%20dB)
Generally the initial intensity of the speaker is mathematically represented as
![\beta_1 = 10 log_{10} [\frac{P_b}{P_a} ]](https://tex.z-dn.net/?f=%5Cbeta_1%20%3D%20%2010%20log_%7B10%7D%20%5B%5Cfrac%7BP_b%7D%7BP_a%7D%20%5D)
Generally the intensity of the speaker after it has been decreased is
![\beta_2 = 10 log_{10} [\frac{P_c}{P_a} ]](https://tex.z-dn.net/?f=%5Cbeta_2%20%3D%20%2010%20log_%7B10%7D%20%5B%5Cfrac%7BP_c%7D%7BP_a%7D%20%5D)
So
![\beta_1-\beta_2 = 10 log_{10} [\frac{P_c}{P_a} ]- 10 log_{10} [\frac{P_b}{P_a} ]](https://tex.z-dn.net/?f=%5Cbeta_1-%5Cbeta_2%20%3D%20%2010%20log_%7B10%7D%20%5B%5Cfrac%7BP_c%7D%7BP_a%7D%20%5D-%2010%20log_%7B10%7D%20%5B%5Cfrac%7BP_b%7D%7BP_a%7D%20%5D)
=> ![\beta = 10 log_{10} [\frac{P_c}{P_a} ]- 10 log_{10} [\frac{P_b}{P_a} ]= 1.3](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20%2010%20log_%7B10%7D%20%5B%5Cfrac%7BP_c%7D%7BP_a%7D%20%5D-%2010%20log_%7B10%7D%20%5B%5Cfrac%7BP_b%7D%7BP_a%7D%20%5D%3D%201.3)
=> ![\beta =10log_{10} [\frac{\frac{P_b}{P_a}}{\frac{P_c}{P_a}} ] = 1.3](https://tex.z-dn.net/?f=%5Cbeta%20%3D10log_%7B10%7D%20%5B%5Cfrac%7B%5Cfrac%7BP_b%7D%7BP_a%7D%7D%7B%5Cfrac%7BP_c%7D%7BP_a%7D%7D%20%5D%20%3D%201.3)
=> ![\beta =10log_{10} [\frac{P_b}{P_c} ] = 1.3](https://tex.z-dn.net/?f=%5Cbeta%20%3D10log_%7B10%7D%20%5B%5Cfrac%7BP_b%7D%7BP_c%7D%20%5D%20%3D%201.3)
=> ![10log_{10} [\frac{P_b}{P_c} ] = 1.3](https://tex.z-dn.net/?f=10log_%7B10%7D%20%5B%5Cfrac%7BP_b%7D%7BP_c%7D%20%5D%20%3D%201.3)
=> ![log_{10} [\frac{P_b}{P_c} ] = 0.13](https://tex.z-dn.net/?f=log_%7B10%7D%20%5B%5Cfrac%7BP_b%7D%7BP_c%7D%20%5D%20%3D%200.13)
taking atilog of both sides
=>
=> ![P_c = \frac{52}{1.34896}](https://tex.z-dn.net/?f=P_c%20%20%3D%20%20%5Cfrac%7B52%7D%7B1.34896%7D)
=> ![P_c = 38.55 \ W](https://tex.z-dn.net/?f=P_c%20%20%3D%20%2038.55%20%5C%20%20W%20)