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2 years ago

Please help this is urgent

Mathematics

1 answer:

Mars2501 [29]2 years ago

6 0

Answer:

Step-by-step explanation:

-2(-3)+5

6+5 = 11

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Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

Andrews [41]

Answer:

The approximate difference in the half-lives of the isotopes is 66 days.

Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

$\frac{dm}{dt} = -\frac{t}{\tau}$

Where:

$m$ - Current mass of the isotope, measured in kilograms.

$t$ - Time, measured in days.

$\tau$ - Time constant, measured in days.

The solution of the differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $m_{o}$ is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

$\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}$

$\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }$

The half-life of a isotope ( $t_{1/2}$ ) as a function of time constant is:

$t_{1/2} = \tau \cdot \ln2$

$t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2$

The half-life difference between isotope B and isotope A is:

$\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|$

If $\frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9$ , $t_{A} = 33\,days$ and $t_{B} = 43\,days$ , the difference in the half-lives of the isotopes is:

$\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|$

$\Delta t_{1/2} \approx 65.788\,days$

The approximate difference in the half-lives of the isotopes is 66 days.

4 0

2 years ago

Read 2 more answers

10 plus 10 divided and rounded to next 20

BartSMP [9]

10.5 I looked it up OKAY

7 0

2 years ago

The Philadelphia Cream Cheese Company produces 42 pounds of cream cheese in each batch. A batch is split up into small portions,

alexandr402 [8]

Answer:

336

Step-by-step explanation:

1/8 pound * by 8 would get you to 1 pound

you have 42 pounds.

8 * 42 = 336

8 0

3 years ago

Read 2 more answers

Find the value of x. Round to

wlad13 [49]

The answer would be 13.7

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2 years ago

Filled in the box. The solution should be infinitely many solution

hichkok12 [17]

Any real number meaning a number that doesnt have a decimal point behind it would be the correct answer in this cause due to the final answer being 7x=0

4 0

2 years ago