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Mamont248 [21]
3 years ago
9

The current in a circuit element is i(t) = 3(1 - e-2t) A when t ≥ 0 and i(t) = 0 when t < 0. The total charge that has entere

d the circuit element for t ≥ 0 can be represented as q left-parenthesis t right-parenthesis equals Upper A ⁢ plus Upper B t plus Upper C e Superscript negative a t coulomb, where A, B, C and a are real constants. Determine the values of A, B, C and a.
Mathematics
1 answer:
lesantik [10]3 years ago
4 0

Answer:

A=-3/2

B=3

c=3/2

a=-2

Step-by-step explanation:

Knowing that for t>0 i(t)=2\left(1-e^{-2t}\right) A, i(t)=0 when t<0 and using the definition of charge

q(t)=\int_{-\infty}^0i(t')dt'+\int_0^t i(t')dt'=0+\int_0^t i(t')dt'

The first term corresponds to q(0), the charge accumulated before t=0, in this case it luckily gives zero so we don't have to worry about it.

Let's proceed and integrate i(t) then when t>0

i(t)=3\int_0^t \left[ \int_0^tdt'-\inte_0^t e^{-2t'}dt' \right]dt'=3\left[ t+\frac{1}{2}\left( e^{-2t}-1 \right) \right]=3t+\frac{3}{2}e^{-2t}-\frac{3}{2}\,\, C

It is clear that:

A=-3/2

B=3

c=3/2

a=-2

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36

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Data provided in the question:

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Now,

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4 years ago
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vitfil [10]
1.
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2.
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5 0
4 years ago
In the final quarter of 2011, a company received 32% of the total profit for all mobile phone manufacturers. If the total profit
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The total profit received for all mobile phone manufacturers for all carriers was 1.54 billion

Step-by-step explanation:

Given,

Profit received = 32%

Total profit received = $4.8 billion

Amount of profit received for mobiles = 32% of total profit

Amount received = \frac{32}{100}*4.8

Amount received = \frac{153.6}{100}

Amount received = 1.536 billion

Rounding off

Amount received = 1.54 billion

The total profit received for all mobile phone manufacturers for all carriers was 1.54 billion

Keywords: percentage, division

Learn more about percentage at:

  • brainly.com/question/10940255
  • brainly.com/question/10941043

#LearnwithBrainly

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4 years ago
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