Answer:
speaker64
--------
34x
Explanation:
64-34
x
speaker
4
2
4
788
- circuit
voltage
100000
x.34
Sorry but you have no picture shown
Answer:
31.1 N
Explanation:
m = mass attached to string = 0.50 kg
r = radius of the vertical circle = 2.0 m
v = speed of the mass at the highest point = 12 m/s
T = force of the string on the mass attached.
At the highest point, force equation is given as
![T + mg =\frac{mv^{2}}{r}](https://tex.z-dn.net/?f=T%20%2B%20mg%20%3D%5Cfrac%7Bmv%5E%7B2%7D%7D%7Br%7D)
Inserting the values
![T + (0.50)(9.8) =\frac{(0.50)(12)^{2}}{2}](https://tex.z-dn.net/?f=T%20%2B%20%280.50%29%289.8%29%20%3D%5Cfrac%7B%280.50%29%2812%29%5E%7B2%7D%7D%7B2%7D)
T = 31.1 N
Answer:
Thus the time taken is calculated as 387.69 years
Solution:
As per the question:
Half life of
= 28.5 yrs
Now,
To calculate the time, t in which the 99.99% of the release in the reactor:
By using the formula:
![\frac{N}{N_{o}} = (\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}](https://tex.z-dn.net/?f=%5Cfrac%7BN%7D%7BN_%7Bo%7D%7D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D)
where
N = No. of nuclei left after time t
= No. of nuclei initially started with
![\frac{N}{N_{o}} = 1\times 10^{- 4}](https://tex.z-dn.net/?f=%5Cfrac%7BN%7D%7BN_%7Bo%7D%7D%20%3D%201%5Ctimes%2010%5E%7B-%204%7D)
(Since, 100% - 99.99% = 0.01%)
Thus
![1\times 10^{- 4} = (\frac{1}{2})^{\frac{t}{28.5}}}](https://tex.z-dn.net/?f=1%5Ctimes%2010%5E%7B-%204%7D%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7Bt%7D%7B28.5%7D%7D%7D)
Taking log on both the sides:
![- 4 = \frac{t}{28.5}log\frac{1}{2}](https://tex.z-dn.net/?f=-%204%20%3D%20%5Cfrac%7Bt%7D%7B28.5%7Dlog%5Cfrac%7B1%7D%7B2%7D)
![t = \frac{-4\times 28.5}{log\frac{1}{2}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B-4%5Ctimes%2028.5%7D%7Blog%5Cfrac%7B1%7D%7B2%7D%7D)
t = 387.69 yrs
Answer:x=2 and x=3
Explanation:
Given
Potential Energy for a certain mass is
![U(x)=2x^3-15x^2+36x-23](https://tex.z-dn.net/?f=U%28x%29%3D2x%5E3-15x%5E2%2B36x-23)
and we know force is given by
![F=-\frac{\mathrm{d} U}{\mathrm{d} x}](https://tex.z-dn.net/?f=F%3D-%5Cfrac%7B%5Cmathrm%7Bd%7D%20U%7D%7B%5Cmathrm%7Bd%7D%20x%7D)
![F=-(2\times 3x^2-15\times 2x+36)](https://tex.z-dn.net/?f=F%3D-%282%5Ctimes%203x%5E2-15%5Ctimes%202x%2B36%29)
For Force to be zero F=0
![\Rightarrow 6x^2-30x+36=0](https://tex.z-dn.net/?f=%5CRightarrow%206x%5E2-30x%2B36%3D0)
![\Rightarrow x^2-5x+6=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2-5x%2B6%3D0)
![\Rightarrow x^2-2x-3x+6=0](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E2-2x-3x%2B6%3D0)
![\Rightarrow (x-2)(x-3)=0](https://tex.z-dn.net/?f=%5CRightarrow%20%28x-2%29%28x-3%29%3D0)
Therefore at x=2 and x=3 Force on particle is zero.