Answer:
Explanation:
We know that the volume V for a sphere of radius r is
![V(r) = \frac{4}{3} \ \pi \ r^3](https://tex.z-dn.net/?f=V%28r%29%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5C%20%5Cpi%20%5C%20r%5E3)
If we got an uncertainty
the formula for the uncertainty of V is:
![\Delta V(r) = \sqrt{ (\frac{dV}{dr} \Delta r)^2 }](https://tex.z-dn.net/?f=%5CDelta%20V%28r%29%20%3D%20%5Csqrt%7B%20%20%28%5Cfrac%7BdV%7D%7Bdr%7D%20%5CDelta%20r%29%5E2%20%20%7D)
We can calculate this uncertainty, first we obtain the derivative:
![\frac{dV}{dr} = 3 * \frac{4}{3} \ \pi \ r^2](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdr%7D%20%20%3D%203%20%2A%20%5Cfrac%7B4%7D%7B3%7D%20%5C%20%5Cpi%20%5C%20r%5E2)
![\frac{dV}{dr} = 4 \ \pi \ r^2](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdr%7D%20%20%3D%204%20%5C%20%5Cpi%20%5C%20r%5E2)
And using it in the formula:
![\Delta V(r) = \sqrt{ (4 \ \pi \ r^2\Delta r)^2 }](https://tex.z-dn.net/?f=%5CDelta%20V%28r%29%20%3D%20%5Csqrt%7B%20%20%284%20%5C%20%5Cpi%20%5C%20r%5E2%5CDelta%20r%29%5E2%20%20%7D)
![\Delta V(r) = \sqrt{ 4^2 \ \pi^2 \ r^4 \Delta r^2 }](https://tex.z-dn.net/?f=%5CDelta%20V%28r%29%20%3D%20%5Csqrt%7B%20%204%5E2%20%5C%20%5Cpi%5E2%20%5C%20r%5E4%20%5CDelta%20r%5E2%20%20%7D)
![\Delta V(r) = 4 \ \pi \ r^2 \Delta r](https://tex.z-dn.net/?f=%5CDelta%20V%28r%29%20%3D%20%204%20%5C%20%20%5Cpi%20%5C%20r%5E2%20%5CDelta%20r%20)
The relative uncertainty is:
![\frac{\Delta V(r)}{V(r)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20V%28r%29%7D%7BV%28r%29%7D)
![\frac{ 4 \ \pi \ r^2 \Delta r }{ \frac{4}{3} \ \pi \ r^3}](https://tex.z-dn.net/?f=%5Cfrac%7B%204%20%5C%20%20%5Cpi%20%5C%20r%5E2%20%5CDelta%20r%20%20%7D%7B%20%5Cfrac%7B4%7D%7B3%7D%20%5C%20%5Cpi%20%5C%20r%5E3%7D)
![\frac{ 3 \Delta r }{ r}](https://tex.z-dn.net/?f=%5Cfrac%7B%203%20%20%5CDelta%20r%20%20%7D%7B%20%20r%7D)
Using the values for the problem:
![\frac{ 3 * 0.09 m }{ 5.66 m} = 0.0477](https://tex.z-dn.net/?f=%5Cfrac%7B%203%20%2A%200.09%20m%20%20%7D%7B%20%205.66%20m%7D%20%3D%200.0477)
This is, a percent uncertainty of 4.77 %
The kinetic molecular theory of matter states that: ... Molecules in the solid phase have the least amount of energy, while gas particles have the greatest amount of energy. The temperature of a substance is a measure of the average kinetic energy of the particles.
Answer:
The magnitude of the flux of electric field through a square of surface area is zero.
Explanation:
![E=100 NC^{-1}\\\\A=2 m^2\\\\Electic\,\,flux\,\,flux\,\,is\,\,given\,\,as:\\\\\phi_E=E.A\,cos\,\theta](https://tex.z-dn.net/?f=E%3D100%20NC%5E%7B-1%7D%5C%5C%5C%5CA%3D2%20m%5E2%5C%5C%5C%5CElectic%5C%2C%5C%2Cflux%5C%2C%5C%2Cflux%5C%2C%5C%2Cis%5C%2C%5C%2Cgiven%5C%2C%5C%2Cas%3A%5C%5C%5C%5C%5Cphi_E%3DE.A%5C%2Ccos%5C%2C%5Ctheta)
It is given that square box is parallel to yz-plane which has normal vector perpendicular to plane in x-direction. Angle between normal vector of area and electric field is 90°. Substituting in (1)
![\phi_E=E.A\,cos\,(90^o)\\\\\phi_E=0](https://tex.z-dn.net/?f=%5Cphi_E%3DE.A%5C%2Ccos%5C%2C%2890%5Eo%29%5C%5C%5C%5C%5Cphi_E%3D0)
Answer:
40 meters. look for the dot above the 20 on the x-axis and follow it over to the left.
Explanation: