Answer:
14
Step-by-step explanation:
The least common multiple is a number that both numbers can multiply something to get to, and the smallest possible common one.
Let's try listing out the multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
And the multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70
Notice that both have the number 14 in common, and it is the first number that they do so. There are lots of other multiples that they have in common too, but 14 is the least.
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}](https://tex.z-dn.net/?f=%5Cfrac%7Bdm%7D%7Bdt%7D%20%3D%20-%5Cfrac%7Bt%7D%7B%5Ctau%7D)
Where:
- Current mass of the isotope, measured in kilograms.
- Time, measured in days.
- Time constant, measured in days.
The solution of the differential equation is:
![m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }](https://tex.z-dn.net/?f=m%28t%29%20%3D%20m_%7Bo%7D%5Ccdot%20e%5E%7B-%5Cfrac%7Bt%7D%7B%5Ctau%7D%20%7D)
Where
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}](https://tex.z-dn.net/?f=%5Cln%20%5Cfrac%7Bm%28t%29%7D%7Bm_%7Bo%7D%7D%20%3D%20-%5Cfrac%7Bt%7D%7B%5Ctau%7D)
![\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }](https://tex.z-dn.net/?f=%5Ctau%20%3D%20-%5Cfrac%7Bt%7D%7B%5Cln%20%5Cfrac%7Bm%28t%29%7D%7Bm_%7Bo%7D%7D%20%7D)
The half-life of a isotope (
) as a function of time constant is:
![t_{1/2} = \tau \cdot \ln2](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%20%3D%20%5Ctau%20%5Ccdot%20%5Cln2)
![t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%20%3D%20-%5Cleft%28%5Cfrac%7Bt%7D%7B%5Cln%5Cfrac%7Bm%28t%29%7D%7Bm_%7Bo%7D%7D%20%7D%5Cright%29%20%5Ccdot%20%5Cln%202)
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|](https://tex.z-dn.net/?f=%5CDelta%20t_%7B1%2F2%7D%20%3D%20%5Cleft%7C%20-%5Cleft%28%5Cfrac%7Bt_%7BA%7D%7D%7B%5Cln%20%5Cfrac%7Bm_%7BA%7D%28t%29%7D%7Bm_%7Bo%2CA%7D%7D%20%7D%20%5Cright%29%5Ccdot%20%5Cln%202%2B%5Cleft%28%5Cfrac%7Bt_%7BB%7D%7D%7B%5Cln%20%5Cfrac%7Bm_%7BB%7D%28t%29%7D%7Bm_%7Bo%2CB%7D%7D%20%7D%20%5Cright%29%5Ccdot%20%5Cln%202%5Cright%7C)
If
,
and
, 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|](https://tex.z-dn.net/?f=%5CDelta%20t_%7B1%2F2%7D%20%3D%20%5Cleft%7C-%5Cleft%28%5Cfrac%7B33%5C%2Cdays%7D%7B%5Cln%200.90%7D%20%5Cright%29%5Ccdot%20%5Cln%202%20%2B%20%5Cleft%28%5Cfrac%7B43%5C%2Cdays%7D%7B%5Cln%200.90%7D%20%5Cright%29%5Ccdot%20%5Cln%202%5Cright%7C)
![\Delta t_{1/2} \approx 65.788\,days](https://tex.z-dn.net/?f=%5CDelta%20t_%7B1%2F2%7D%20%5Capprox%2065.788%5C%2Cdays)
The approximate difference in the half-lives of the isotopes is 66 days.
Answer:
28980
Step-by-step explanation:
Also "<em>nice</em>"
Answer:
x = 4
y = 11
Step-by-step explanation:
Set your formula as follow:
2x+3=3x-1 -> 2x+3-3x=-1 -> -x+3 = -1 -> -x=-4 -> x=4
now substitute x for 4 in the following
y-2=2(4)+1 -> y-2=8+1 ->y-2 = 9y -> y=11
Answer:
B. 4t=27
Step-by-step explanation:
let t be the price of one ticket,
since there are 4 people buying tickets in total, the price of 4 tickets would be 4t.
so
.