Answer:
An “international employee” is defined as an employee of Stanford University whose work site is located.
Explanation:
Answer:
The component form will be;
In the x-axis = 121.73 due west
In the y-axis = 690.35 due south
Explanation:
An image of the calculation has been attached
Answer:
![T_1=T_3=\dfrac{2\pi}{21}](https://tex.z-dn.net/?f=T_1%3DT_3%3D%5Cdfrac%7B2%5Cpi%7D%7B21%7D)
![T_2=T_4=\dfrac{2\pi}{42}](https://tex.z-dn.net/?f=T_2%3DT_4%3D%5Cdfrac%7B2%5Cpi%7D%7B42%7D)
Explanation:
Wave 1, ![y_1=0.12\ cos(3x-21t)](https://tex.z-dn.net/?f=y_1%3D0.12%5C%20cos%283x-21t%29)
Wave 2, ![y_2=0.15\ sin(6x+42t)](https://tex.z-dn.net/?f=y_2%3D0.15%5C%20sin%286x%2B42t%29)
Wave 3, ![y_3=0.13\ cos(6x+21t)](https://tex.z-dn.net/?f=y_3%3D0.13%5C%20cos%286x%2B21t%29)
Wave 4, ![y_4=-0.27\ sin(3x-42t)](https://tex.z-dn.net/?f=y_4%3D-0.27%5C%20sin%283x-42t%29)
The general equation of travelling wave is given by :
![y=A\ cos(kx\pm \omega t)](https://tex.z-dn.net/?f=y%3DA%5C%20cos%28kx%5Cpm%20%5Comega%20t%29)
The value of
will remain the same if we take phase difference into account.
For first wave,
![\omega_1=21](https://tex.z-dn.net/?f=%5Comega_1%3D21)
![\dfrac{2\pi }{T_1}=21](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Cpi%20%7D%7BT_1%7D%3D21)
![T_1=\dfrac{2\pi}{21}](https://tex.z-dn.net/?f=T_1%3D%5Cdfrac%7B2%5Cpi%7D%7B21%7D)
For second wave,
![\omega_2=42](https://tex.z-dn.net/?f=%5Comega_2%3D42)
![\dfrac{2\pi }{T_2}=42](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Cpi%20%7D%7BT_2%7D%3D42)
![T_2=\dfrac{2\pi}{42}](https://tex.z-dn.net/?f=T_2%3D%5Cdfrac%7B2%5Cpi%7D%7B42%7D)
For the third wave,
![\omega_3=21](https://tex.z-dn.net/?f=%5Comega_3%3D21)
![\dfrac{2\pi }{T_3}=21](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Cpi%20%7D%7BT_3%7D%3D21)
![T_3=\dfrac{2\pi}{21}](https://tex.z-dn.net/?f=T_3%3D%5Cdfrac%7B2%5Cpi%7D%7B21%7D)
For the fourth wave,
![\omega_4=42](https://tex.z-dn.net/?f=%5Comega_4%3D42)
![\dfrac{2\pi }{T_4}=42](https://tex.z-dn.net/?f=%5Cdfrac%7B2%5Cpi%20%7D%7BT_4%7D%3D42)
![T_4=\dfrac{2\pi}{42}](https://tex.z-dn.net/?f=T_4%3D%5Cdfrac%7B2%5Cpi%7D%7B42%7D)
It is clear from above calculations that waves 1 and 3 have same time period. Also, wave 2 and 4 have same time period. Hence, this is the required solution.
Answer:
![\vec{E}=(-15.78\hat{i}+63.81\hat{j})\frac{N}{C}](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%3D%28-15.78%5Chat%7Bi%7D%2B63.81%5Chat%7Bj%7D%29%5Cfrac%7BN%7D%7BC%7D)
Explanation:
In this case we have to work with vectors. Firs of all we have to compute the angles between x axis and the r vector (which points the charges):
![\theta_1=tan^{-1}(\frac{0.6m}{0m})=90\° \\\\\theta_2=tan^{-1}(\frac{0.4m}{1.3m})=17.10\°](https://tex.z-dn.net/?f=%5Ctheta_1%3Dtan%5E%7B-1%7D%28%5Cfrac%7B0.6m%7D%7B0m%7D%29%3D90%5C%C2%B0%20%5C%5C%5C%5C%5Ctheta_2%3Dtan%5E%7B-1%7D%28%5Cfrac%7B0.4m%7D%7B1.3m%7D%29%3D17.10%5C%C2%B0)
the electric field has two components Ex and Ey. By considering the sign of the charges we obtain that:
![\vec{E} = E_x \hat{i}+E_y\hat{j}\\\\\vec{E}=(E_1cos\theta_1-E_2cos\theta_2)\hat{i}+(E_1sin\theta_1-E_2sin\theta_2)\hat{j}\\\\E_1=k\frac{q}{r_1^2}=(8.99*10^{9}\frac{N}{m^2C^2})\frac{2.75*10^{-9}C}{(0.6m)^2}=68.67\frac{N}{C}\\\\E_2=k\frac{q}{r_2^2}=(8.99*10^{9}\frac{N}{m^2C^2})\frac{3.40*10^{-9}C}{((1.3m)^2+(0.4m)^2)}=16.52\frac{N}{C}](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%20%3D%20E_x%20%5Chat%7Bi%7D%2BE_y%5Chat%7Bj%7D%5C%5C%5C%5C%5Cvec%7BE%7D%3D%28E_1cos%5Ctheta_1-E_2cos%5Ctheta_2%29%5Chat%7Bi%7D%2B%28E_1sin%5Ctheta_1-E_2sin%5Ctheta_2%29%5Chat%7Bj%7D%5C%5C%5C%5CE_1%3Dk%5Cfrac%7Bq%7D%7Br_1%5E2%7D%3D%288.99%2A10%5E%7B9%7D%5Cfrac%7BN%7D%7Bm%5E2C%5E2%7D%29%5Cfrac%7B2.75%2A10%5E%7B-9%7DC%7D%7B%280.6m%29%5E2%7D%3D68.67%5Cfrac%7BN%7D%7BC%7D%5C%5C%5C%5CE_2%3Dk%5Cfrac%7Bq%7D%7Br_2%5E2%7D%3D%288.99%2A10%5E%7B9%7D%5Cfrac%7BN%7D%7Bm%5E2C%5E2%7D%29%5Cfrac%7B3.40%2A10%5E%7B-9%7DC%7D%7B%28%281.3m%29%5E2%2B%280.4m%29%5E2%29%7D%3D16.52%5Cfrac%7BN%7D%7BC%7D)
Hence, by replacing E1 and E2 we obtain:
![\vec{E}=[(68.67N/C)cos(90\°)-(16.52N/C)cos(17.10\°)]\hat{i}+[(68.67N/C)sin(90\°)-(16.52N/C)sin(17.10\°)]\hat{j}\\\\\vec{E}=(-15.78\hat{i}+63.81\hat{j})\frac{N}{C}](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%3D%5B%2868.67N%2FC%29cos%2890%5C%C2%B0%29-%2816.52N%2FC%29cos%2817.10%5C%C2%B0%29%5D%5Chat%7Bi%7D%2B%5B%2868.67N%2FC%29sin%2890%5C%C2%B0%29-%2816.52N%2FC%29sin%2817.10%5C%C2%B0%29%5D%5Chat%7Bj%7D%5C%5C%5C%5C%5Cvec%7BE%7D%3D%28-15.78%5Chat%7Bi%7D%2B63.81%5Chat%7Bj%7D%29%5Cfrac%7BN%7D%7BC%7D)
hope this helps!!
Mercury is used as thermometeric liquid because it is a good conductor of heat colorful, expansion rate is uniform and it doesn't wet the wall of capillary