Answer:
![t'_{1\2} = 6.6 sec](https://tex.z-dn.net/?f=t%27_%7B1%5C2%7D%20%3D%206.6%20sec)
Explanation:
the half life of the given circuit is given by
![t_{1\2} =\tau ln2](https://tex.z-dn.net/?f=t_%7B1%5C2%7D%20%3D%5Ctau%20ln2)
where [/tex]\tau = RC[/tex]
![t_{1\2} = RCln2](https://tex.z-dn.net/?f=t_%7B1%5C2%7D%20%3D%20RCln2)
Given ![t_{1\2} = 3 sec](https://tex.z-dn.net/?f=t_%7B1%5C2%7D%20%3D%203%20sec)
resistance in the circuit is 40 ohm and to extend the half cycle we added new resister of 48 ohm. the net resitance is 40+48 = 88 ohms
now the new half life is
![t'_{1\2} =R'Cln2](https://tex.z-dn.net/?f=t%27_%7B1%5C2%7D%20%3DR%27Cln2)
Divide equation 2 by 1
![\frac{t'_{1\2}}{t_{1\2}} = \frac{R'Cln2}{RCln2} = \frac{R'}{R}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%27_%7B1%5C2%7D%7D%7Bt_%7B1%5C2%7D%7D%20%3D%20%5Cfrac%7BR%27Cln2%7D%7BRCln2%7D%20%3D%20%5Cfrac%7BR%27%7D%7BR%7D)
![t'_{1\2} = t'_{1\2}\frac{R'}{R}](https://tex.z-dn.net/?f=t%27_%7B1%5C2%7D%20%3D%20t%27_%7B1%5C2%7D%5Cfrac%7BR%27%7D%7BR%7D)
putting all value we get new half life
![t'_{1\2} = 3 * \frac{88}{40} = 6.6 sec](https://tex.z-dn.net/?f=t%27_%7B1%5C2%7D%20%3D%203%20%2A%20%5Cfrac%7B88%7D%7B40%7D%20%20%3D%206.6%20sec)
![t'_{1\2} = 6.6 sec](https://tex.z-dn.net/?f=t%27_%7B1%5C2%7D%20%3D%206.6%20sec)
Answer:
f(x)=23x−2
Explanation:
still trying to figure that out
Answer:
The pressure reduces to 2.588 bars.
Explanation:
According to Bernoulli's theorem for ideal flow we have
![\frac{P}{\gamma _{w}}+\frac{V^{2}}{2g}+z=constant](https://tex.z-dn.net/?f=%5Cfrac%7BP%7D%7B%5Cgamma%20_%7Bw%7D%7D%2B%5Cfrac%7BV%5E%7B2%7D%7D%7B2g%7D%2Bz%3Dconstant)
Since the losses are neglected thus applying this theorm between upper and lower porion we have
![\frac{P_{u}}{\gamma _{w}}+\frac{V-{u}^{2}}{2g}+z_{u}=\frac{P_{L}}{\gamma _{w}}+\frac{V{L}^{2}}{2g}+z_{L}](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7Bu%7D%7D%7B%5Cgamma%20_%7Bw%7D%7D%2B%5Cfrac%7BV-%7Bu%7D%5E%7B2%7D%7D%7B2g%7D%2Bz_%7Bu%7D%3D%5Cfrac%7BP_%7BL%7D%7D%7B%5Cgamma%20_%7Bw%7D%7D%2B%5Cfrac%7BV%7BL%7D%5E%7B2%7D%7D%7B2g%7D%2Bz_%7BL%7D)
Now by continuity equation we have
![A_{u}v_{u}=A_{L}v_{L}\\\\\therefore v_{L}=\frac{A_{u}}{A_{L}}\times v_{u}\\\\v_{L}=\frac{d^{2}_{u}}{d^{2}_{L}}\times v_{u}\\\\\therefore v_{L}=\frac{2500}{900}\times 3.5\\\\\therefore v_{L}=9.72m/s](https://tex.z-dn.net/?f=A_%7Bu%7Dv_%7Bu%7D%3DA_%7BL%7Dv_%7BL%7D%5C%5C%5C%5C%5Ctherefore%20v_%7BL%7D%3D%5Cfrac%7BA_%7Bu%7D%7D%7BA_%7BL%7D%7D%5Ctimes%20v_%7Bu%7D%5C%5C%5C%5Cv_%7BL%7D%3D%5Cfrac%7Bd%5E%7B2%7D_%7Bu%7D%7D%7Bd%5E%7B2%7D_%7BL%7D%7D%5Ctimes%20v_%7Bu%7D%5C%5C%5C%5C%5Ctherefore%20v_%7BL%7D%3D%5Cfrac%7B2500%7D%7B900%7D%5Ctimes%203.5%5C%5C%5C%5C%5Ctherefore%20v_%7BL%7D%3D9.72m%2Fs)
Applying the values in the Bernoulli's equation we get
![\frac{P_{L}}{\gamma _{w}}=\frac{300000}{\gamma _{w}}+\frac{3.5^{2}}{2g}-\frac{9.72^{2}}{2g}(\because z_{L}=z_{u})\\\\\frac{P_{L}}{\gamma _{w}}=26.38m\\\\\therefore P_{L}=258885.8Pa\\\\\therefore P_{L}=2.588bars](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7BL%7D%7D%7B%5Cgamma%20_%7Bw%7D%7D%3D%5Cfrac%7B300000%7D%7B%5Cgamma%20_%7Bw%7D%7D%2B%5Cfrac%7B3.5%5E%7B2%7D%7D%7B2g%7D-%5Cfrac%7B9.72%5E%7B2%7D%7D%7B2g%7D%28%5Cbecause%20z_%7BL%7D%3Dz_%7Bu%7D%29%5C%5C%5C%5C%5Cfrac%7BP_%7BL%7D%7D%7B%5Cgamma%20_%7Bw%7D%7D%3D26.38m%5C%5C%5C%5C%5Ctherefore%20P_%7BL%7D%3D258885.8Pa%5C%5C%5C%5C%5Ctherefore%20P_%7BL%7D%3D2.588bars)
Answer:
System integration can be defined as the progressive linking and testing of system components to merge their functional and technical characteristics into a comprehensive interoperable system.
Explanation:
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