3 years ago

What are the steps to find (2+2i)(5+3i)?

Mathematics

1 answer:

Scilla [17]3 years ago

4 0

Answer:

Step-by-step explanation:

(2+2i)(5+3i)

(2)5+(2)3i=10+6i

(2i)5+(2i)3i=10i+6i^2

10+6i+10i+6i^2

6i^2+6i+10i+10

6i^2+16i+10

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Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve the following. The half-life of a certai

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Answer:

It will take 7 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

$A=A_0 e^{kt}$

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$A_0$ = Initial amount of the substance,

If the half life of the substance is 19 years,

Then if t = 19, amount of the substance = $\frac{A_0}{2}$ ,

i.e.

$\frac{A_0}{2}=A_0 e^{19k}$

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$0.5 = e^{19k}$

Taking ln both sides,

$\ln(0.5) = \ln(e^{19k})$

$\ln(0.5) = 19k$

$\implies k = \frac{\ln(0.5)}{19}\approx -0.03648$

Now, if the substance to decay to 78% of its original amount,

Then $A=78\% \text{ of }A_0 =\frac{78A_0}{100}=0.78 A_0$

$0.78 A_0=A_0 e^{-0.03648t}$

$0.78 = e^{-0.03648t}$

Again taking ln both sides,

$\ln(0.78) = -0.03648t$

$-0.24846=-0.03648t$

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Hence, approximately the substance would be 78% of its initial value after 7 years.

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