In scientific notation", that number would be written as
6.81 x 10⁻⁴ .
Answer:
![T_b=107.3784\ ^{\circ}C](https://tex.z-dn.net/?f=T_b%3D107.3784%5C%20%5E%7B%5Ccirc%7DC)
Explanation:
Given:
- thickness of the base of the kettle,
![dx=0.52\ cm=5.2\times 10^{-3}\ m](https://tex.z-dn.net/?f=dx%3D0.52%5C%20cm%3D5.2%5Ctimes%2010%5E%7B-3%7D%5C%20m)
- radius of the base of the kettle,
![r=0.12\ m](https://tex.z-dn.net/?f=r%3D0.12%5C%20m)
- temperature of the top surface of the kettle base,
![T_t=100^{\circ}C](https://tex.z-dn.net/?f=T_t%3D100%5E%7B%5Ccirc%7DC)
- rate of heat transfer through the kettle to boil water,
![\dot Q=0.409\ kg.min^{-1}](https://tex.z-dn.net/?f=%5Cdot%20Q%3D0.409%5C%20kg.min%5E%7B-1%7D)
- We have the latent heat vaporization of water,
![L=2260\times 10^3\ J.kg^{-1}](https://tex.z-dn.net/?f=L%3D2260%5Ctimes%2010%5E3%5C%20J.kg%5E%7B-1%7D)
- and thermal conductivity of aluminium,
![k=240\ W.m^{-1}.K^{-1}](https://tex.z-dn.net/?f=k%3D240%5C%20W.m%5E%7B-1%7D.K%5E%7B-1%7D)
<u>So, the heat rate:</u>
![\dot Q=\frac{0.409\times 2260000}{60}](https://tex.z-dn.net/?f=%5Cdot%20Q%3D%5Cfrac%7B0.409%5Ctimes%202260000%7D%7B60%7D)
![\dot Q=15405.67\ W](https://tex.z-dn.net/?f=%5Cdot%20Q%3D15405.67%5C%20W)
<u>From the Fourier's law of conduction we have:</u>
![\dot Q=k.A.\frac{dT}{dx}](https://tex.z-dn.net/?f=%5Cdot%20Q%3Dk.A.%5Cfrac%7BdT%7D%7Bdx%7D)
![\dot Q=k\times \pi.r^2\times \frac{T_b-T_t}{5.2\times 10^{-3}}](https://tex.z-dn.net/?f=%5Cdot%20Q%3Dk%5Ctimes%20%5Cpi.r%5E2%5Ctimes%20%5Cfrac%7BT_b-T_t%7D%7B5.2%5Ctimes%2010%5E%7B-3%7D%7D)
where:
area of the surface through which conduction occurs
temperature of the bottom surface
![15405.67=240\times \pi\times 0.12^2\times \frac{T_b-100}{5.2\times 10^{-3}}](https://tex.z-dn.net/?f=15405.67%3D240%5Ctimes%20%5Cpi%5Ctimes%200.12%5E2%5Ctimes%20%5Cfrac%7BT_b-100%7D%7B5.2%5Ctimes%2010%5E%7B-3%7D%7D)
is the temperature of the bottom of the base surface of the kettle.
Series circuits split the voltage of resistors, so if you see several diodes connected <em>in series </em>or all next to each other, just a complete loop, it will be in series.
Parallel circuits split the current of resistors, so if you see several diodes connected along different branches or pathways, it will be in parallel.
The velocity when function p(t)=11 is 8 .
According to the question
The position of a car at time t represented by function :
Now,
When function p(t) = 11 , t will be
11 = t²+2t-4
0 = t² + 2t - 15
or
t² +2t-15 = 0
t² +(5-3)t-15 = 0
t² +5t-3t-15 = 0
t(t+5)-3(t+5) = 0
(t-3)(t+5) = 0
t = 3 , -5
as t cannot be -ve as given ( t≥0)
so,
t = 3
Now,
the velocity when p(t)=11
As we know velocity =
therefore to get the value of velocity from function p(t)
we have to differentiate the function with respect to time
v(t) = 2t + 2
where v(t) = velocity at that time
as t = 3 for p(t)=11
so ,
v(t) = 2t + 2
v(t) = 2*3 + 2
v(t) = 8
Hence, the velocity when function p(t)=11 is 8 .
To know more about function here:
brainly.com/question/12431044
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