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3 years ago

How many runners ran fewer than 4 km?

Mathematics

2 answers:

Vinvika [58]3 years ago

4 0

10 runners ran fewer than 4 km

ICE Princess25 [194]3 years ago

3 0

10(ten) runners ran less than 4 meters.

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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

3 years ago

Read 2 more answers

HELP ASAP, ILL GIVE BRAINLIET BUT PLEASE BE RIGHT

aniked [119]

Answer:

(1,4) and (9,9)

Step-by-step explanation:

they form a straight line -- you can check with a ruler when going through these points.

6 0

3 years ago

Which amount is bigger

erastova [34]

What the two or more numbers or amounts? Something needs to be compared

8 0

3 years ago

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No clue how to do this

andreev551 [17]

B is your awnser! sorry if im wrong my calc shows its without a - symbol

7 0

3 years ago

Help me pleaseeee ???

Leokris [45]

There's only one solution...the one you get when you divide both sides by 22 to solve for x. 902/22 = 41. That exponent on the x, the one you don't see, is a "1" which tells us that there is only 1 solution to this problem. If your x is squared, then you have 2 solutions; if it's cubed, you have 3, etc.

7 0

3 years ago