1) The half-life is the time required for a substance to reduce to half its initial value. In formulas:
![\frac{m(t)}{m_0} = ( \frac{1}{2} )^{t/t_{1/2}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bm%28t%29%7D%7Bm_0%7D%20%20%3D%20%28%20%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7Bt%2Ft_%7B1%2F2%7D%7D)
(1)
where
m(t) is the amount of substance left at time t
m0 is the initial mass
![t_{1/2}](https://tex.z-dn.net/?f=t_%7B1%2F2%7D)
is the half-life
In this problem, the half-life of the substance is 20 years:
![t_{1/2} = 20 y](https://tex.z-dn.net/?f=t_%7B1%2F2%7D%20%3D%2020%20y)
therefore, the fraction of sample left after t=40 years will be
![\frac{m(t)}{m_0}=( \frac{1}{2})^ \frac{40 y}{20 y} = ( \frac{1}{2})^2 = \frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bm%28t%29%7D%7Bm_0%7D%3D%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E%20%5Cfrac%7B40%20y%7D%7B20%20y%7D%20%20%3D%20%28%20%5Cfrac%7B1%7D%7B2%7D%29%5E2%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%20)
So, only 1/4 of the original sample will be left, which corresponds to 25%.
2) We can use again formula (1), by re-arranging it:
![m_0 = \frac{m(t)} {( \frac{1}{2} )^{ \frac{t}{t_{1/2} }}}](https://tex.z-dn.net/?f=m_0%20%3D%20%20%5Cfrac%7Bm%28t%29%7D%20%7B%28%20%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7B%20%5Cfrac%7Bt%7D%7Bt_%7B1%2F2%7D%20%7D%7D%7D)
If we use m(t)=10 g (mass of uranium left at time t), and
![t=4 t_{1/2}](https://tex.z-dn.net/?f=t%3D4%20t_%7B1%2F2%7D)
(the time is equal to 4 half lifes), we get
![m_0 = \frac{10 g}{ (\frac{1}{2})^4 } =16 \cdot 10 g = 160 g](https://tex.z-dn.net/?f=m_0%20%3D%20%20%5Cfrac%7B10%20g%7D%7B%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E4%20%7D%20%3D16%20%5Ccdot%2010%20g%20%3D%20160%20g)
So, the initial sample of uranium was 160 g.
Answer:
Distance between motorists equals 10440 feet
Explanation:
In the figure shown below we have
![x=\frac{H}{tan(37)}\\\\Similarly\\\\y=\frac{H}{tan(55)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7BH%7D%7Btan%2837%29%7D%5C%5C%5C%5CSimilarly%5C%5C%5C%5Cy%3D%5Cfrac%7BH%7D%7Btan%2855%29%7D)
Thus the distance between the motorists is ![x+y](https://tex.z-dn.net/?f=x%2By)
Distance=![\frac{5150}{tan(37)}+\frac{5150}{tan(55)}](https://tex.z-dn.net/?f=%5Cfrac%7B5150%7D%7Btan%2837%29%7D%2B%5Cfrac%7B5150%7D%7Btan%2855%29%7D)
distance = 10440 feet
Paint is immiscible because the layer that forms on top of settled paint is a substance which cannot dissolve with the rest of the paint. Stirring the paint is only temporarily in effort to form an even and thoroughly mixed solution by physically mixing the separate molecules of the solution. However, for it to be miscible, it the solution has to be evenly distributed (chemically) on a molecular level as to not separate when left for a lengthy period of time.
Answer:
The strength of the gravitational force between two objects depends on two factors, mass and distance. the force of gravity the masses exert on each other. If one of the masses is doubled, the force of gravity between the objects is doubled. increases, the force of gravity decreases.
Answer:
From far away, Saturn looks like it has seven large rings. Each large ring is named for a letter of the alphabet. The rings were named in the order they were discovered.