<span>a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.
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a) This part is already complete I think..
b) This is a cuboid and lateral surface area of cuboid is: 2(lb +bh + hl)
= 2( 10 × 3 + 3 × 7 + 7 × 10)
= 2(30 + 21 + 70)
= 2 × 121 = 242 cm²
Now, the area of top & bottom: lb
= 2 × 10 × 3
= 60 cm²
Neglecting the top & bottom surface area of cuboid:
= 242 - 60
= 180 cm²
c) The total surface area us 242.. I have already done that part above...
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If i have done something wrong.. please lemme know :)
We can compare the two units or object performances by that.... even in the case of magnitude lower than zero....
Answer:
Step-by-step explanation:
We can write 
as follows:
![\frac{11s}{s^2-12s+52}\\=11\left [ \frac{s}{s^2-12s+52} \right ]\\=11\left [ \frac{s}{(s-6)^2+16} \right ]\\=11\left [ \frac{s-6+6}{(s-6)^2+16} \right ]\\=11\left [ \frac{s-6}{(s-6)^2+16} \right ]+\frac{66}{(s-6)^2+16}](https://tex.z-dn.net/?f=%5Cfrac%7B11s%7D%7Bs%5E2-12s%2B52%7D%5C%5C%3D11%5Cleft%20%5B%20%5Cfrac%7Bs%7D%7Bs%5E2-12s%2B52%7D%20%5Cright%20%5D%5C%5C%3D11%5Cleft%20%5B%20%5Cfrac%7Bs%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D%5C%5C%3D11%5Cleft%20%5B%20%5Cfrac%7Bs-6%2B6%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D%5C%5C%3D11%5Cleft%20%5B%20%5Cfrac%7Bs-6%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D%2B%5Cfrac%7B66%7D%7B%28s-6%29%5E2%2B16%7D)
To find:
![L^{-1}\left [ \frac{11s}{s^2-12s+52 \right ]}\\=L^{-1}\left [ 11\left [ \frac{s-6}{(s-6)^2+16} \right ]+\frac{66}{(s-6)^2+16} \right ]](https://tex.z-dn.net/?f=L%5E%7B-1%7D%5Cleft%20%5B%20%5Cfrac%7B11s%7D%7Bs%5E2-12s%2B52%20%5Cright%20%5D%7D%5C%5C%3DL%5E%7B-1%7D%5Cleft%20%5B%2011%5Cleft%20%5B%20%5Cfrac%7Bs-6%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D%2B%5Cfrac%7B66%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D)
We will use formulae:
we get solution as :
![L^{-1}\left [ 11\left [ \frac{s-6}{(s-6)^2+16} \right ]+\frac{66}{(s-6)^2+16} \right ]\\=L^{-1}\left [ 11\left [ \frac{s-6}{(s-6)^2+4^2} \right ]+\frac{66}{4}\left [ \frac{4}{(s-6)^2+4^2} \right ] \right ]\\=11e^{6t}\cos 4t+\frac{33}{2}e^{6t}\sin 4t](https://tex.z-dn.net/?f=L%5E%7B-1%7D%5Cleft%20%5B%2011%5Cleft%20%5B%20%5Cfrac%7Bs-6%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D%2B%5Cfrac%7B66%7D%7B%28s-6%29%5E2%2B16%7D%20%5Cright%20%5D%5C%5C%3DL%5E%7B-1%7D%5Cleft%20%5B%2011%5Cleft%20%5B%20%5Cfrac%7Bs-6%7D%7B%28s-6%29%5E2%2B4%5E2%7D%20%5Cright%20%5D%2B%5Cfrac%7B66%7D%7B4%7D%5Cleft%20%5B%20%5Cfrac%7B4%7D%7B%28s-6%29%5E2%2B4%5E2%7D%20%5Cright%20%5D%20%5Cright%20%5D%5C%5C%3D11e%5E%7B6t%7D%5Ccos%204t%2B%5Cfrac%7B33%7D%7B2%7De%5E%7B6t%7D%5Csin%204t)
