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Which of the following shows a group of possible angles a triangle could have?
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Answer:
22.38 g of silicone-32 will be present in 300 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
where,
= quantity of the substance remaining
= initial quantity of the substance
= time elapsed
= half life of the substance
From the information given we know:
- The initial quantity of silicone-32 is 30 g.
- The time elapsed is 300 years.
- The half life of silicone-32 is 710 years.
So, to find the quantity of silicone-32 remaining we apply the above equation
22.38 g of silicone-32 will be present in 300 years.
We want to find a scalar function 
such that 
.
So we need to have
Integrating both sides with respect to
gives
Differentiating with respect to
gives
So we find that
By the fundamental theorem of calculus, we then know the line integral depends only on the values of at the endpoints of the path. Therefore
So we need to have
Integrating both sides with respect to
Differentiating with respect to
So we find that
By the fundamental theorem of calculus, we then know the line integral depends only on the values of