Answer:
![A=42, B=-7](https://tex.z-dn.net/?f=A%3D42%2C%20B%3D-7)
Step-by-step explanation:
The current function of time is defined as follows:
![I(t)=\frac{dq(t)}{dt}](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7Bdq%28t%29%7D%7Bdt%7D)
where
is the charge function.
For the given charge function of time
we have the following current function:
![I(t)=\frac{d}{dt} \left(6\left( 1-e^{-7t}\right)\right)=42e^{-7t}](https://tex.z-dn.net/?f=I%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cleft%286%5Cleft%28%201-e%5E%7B-7t%7D%5Cright%29%5Cright%29%3D42e%5E%7B-7t%7D)
In the problem it is proposed that
.
Examining the expression of
we obtained by deriving
with the expression proposed by the problem and comparing term by term:
![I(t)=Be^{-At}=42e^{-7t}](https://tex.z-dn.net/?f=I%28t%29%3DBe%5E%7B-At%7D%3D42e%5E%7B-7t%7D)
We conclude that
and
.
Answer:
9.66666666667.... I guess
When you're talking about sums, that means you are adding. So, you do 8+7=15. The sum of it being doubled, you say? 15x2=30, or 15+15=30. Hope this helped :)
Answer:
The answer would be 7.
Step-by-step explanation:
Hope This Helps God Bless ;)
Answer:
![=\frac{8a+6}{\left(a-3\right)\left(a+3\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B8a%2B6%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D)
the third option is your answer
Step-by-step explanation:
![\frac{5}{a-3}+\frac{3}{a+3}\\\mathrm{Least\:Common\:Multiplier\:of\:}a-3,\:a+3:\quad \left(a-3\right)\left(a+3\right)\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\=\frac{5\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}+\frac{3\left(a-3\right)}{\left(a+3\right)\left(a-3\right)}\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{5\left(a+3\right)+3\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7Ba-3%7D%2B%5Cfrac%7B3%7D%7Ba%2B3%7D%5C%5C%5Cmathrm%7BLeast%5C%3ACommon%5C%3AMultiplier%5C%3Aof%5C%3A%7Da-3%2C%5C%3Aa%2B3%3A%5Cquad%20%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%5C%5C%5Cmathrm%7BAdjust%5C%3AFractions%5C%3Abased%5C%3Aon%5C%3Athe%5C%3ALCM%7D%5C%5C%3D%5Cfrac%7B5%5Cleft%28a%2B3%5Cright%29%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D%2B%5Cfrac%7B3%5Cleft%28a-3%5Cright%29%7D%7B%5Cleft%28a%2B3%5Cright%29%5Cleft%28a-3%5Cright%29%7D%5C%5C%5Cmathrm%7BSince%5C%3Athe%5C%3Adenominators%5C%3Aare%5C%3Aequal%2C%5C%3Acombine%5C%3Athe%5C%3Afractions%7D%3A%5Cquad%20%5Cfrac%7Ba%7D%7Bc%7D%5Cpm%20%5Cfrac%7Bb%7D%7Bc%7D%3D%5Cfrac%7Ba%5Cpm%20%5C%3Ab%7D%7Bc%7D%5C%5C%3D%5Cfrac%7B5%5Cleft%28a%2B3%5Cright%29%2B3%5Cleft%28a-3%5Cright%29%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D)
![\mathrm{Expand}\:5\left(a+3\right)+3\left(a-3\right):\quad 8a+6\\=\frac{8a+6}{\left(a-3\right)\left(a+3\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BExpand%7D%5C%3A5%5Cleft%28a%2B3%5Cright%29%2B3%5Cleft%28a-3%5Cright%29%3A%5Cquad%208a%2B6%5C%5C%3D%5Cfrac%7B8a%2B6%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D)