Mathematics: Fine two consecutive even integers such that twice the smaller is 26 more than the larger.

Fine two consecutive even integers such that twice

Ответ:

y0gurlk

11.03.2022

Mathematics

n, n + 2 - two consecutive even integers

twice the smaller is 26 more than the larger

2n = (n + 2) + 26

2n = n + 2 + 26

2n = n + 28 subtract n from both sides

n = 28

n + 2 = 28 + 2 = 30

28, 30.

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Ответ:

lindsaynielsen13

02.10.2021

Mathematics

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

$P(t) = P(0)e^{-kt}$

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that P(300) = 0.694P(0) . We use this to find k.

$P(t) = P(0)e^{-kt}$

$0.694 = P(0)e^{-300k}$

$e^{-300k} = 0.694$

$\ln{e^{-300k}} = \ln{0.694}$

$-300k = \ln{0.694}$

$k = -\frac{\ln{0.694}}{300}$

k = 0.0012

$P(t) = P(0)e^{-0.0012t}$

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

$0.5P(0) = P(0)e^{-0.0012t}$

$e^{-0.0012t} = 0.5$

$\ln{e^{-0.0012t}} = \ln{0.5}$

$-0.0012t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0012}$

t = 569.27

The half-life of this substance is of 569.27 days.

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Fine two consecutive even integers such that twice the smaller is 26 more than the larger.

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