What number comes next?

Oh boy, well looking in perspective 47.50 per ton
there are 2.5 tons. Lets break this down:
2 and half tons
2 x 47.50= N
Noted after using our trusty calculator you'll get 95
2 x 47.50= 95
then you have that half
which would look like this : 2/47.50
Divide 47.50 by 2 (Because a half is .5 or 1/2 of the whole number in this case 47.50)
2/47.50 =23.75
Next add up your two new answers 23.75 + 95 = ?
Hope this helps.

7 0

3 years ago

A radioactive isotope has a half life of 1 min. The amount of material, A(t), at t = 0 is 10 kg.

Stella [2.4K]

The particular solution to the ordinary differential equation that describes the one-step disintegration of the isotope is equal to the function $A(t) = 10\cdot e^{-\frac{t}{1.443} }$ .

<h3>How to derive the equation of a radioactive decay </h3>

In this question we have a case of simple disintegration of an isotope, that is, that the radioactive isotope has only one stage of disintegration. This process is represented by the following ordinary differential equation:

$\frac{dA}{dt} = -\frac{t}{\tau}$ (1)

Where:

A - Amount of material, in kilograms
t - Time, in minutes
τ - Time constant, in minutes

The solution of this differential equation is:

$A(t) = A_{o}\cdot e^{-\frac{t}{\tau} }$ (2)

The time constant can be calculated from the half-life:

$\tau = \frac{t_{1/2}}{\ln 2}$ (3)

If we know that $t_{1/2} = 1\,min$ and $A_{o} = 10\,kg$ , then the particular solution of the differential equation is:

τ = (1 min)/ln 2

τ = 1.443 min

$A(t) = 10\cdot e^{-\frac{t}{1.443} }$

The particular solution to the ordinary differential equation that describes the one-step disintegration of the isotope is equal to the function $A(t) = 10\cdot e^{-\frac{t}{1.443} }$ .

To learn more on isotopes: brainly.com/question/12955625

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4 0

2 years ago