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lana66690 [7]
2 years ago
6

The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?

Mathematics
1 answer:
adell [148]2 years ago
3 0

Answer: 129.33 g

Step-by-step explanation:

$$Let $p=A \cdot e^{n t}$ \\$(p=$ present amount, $A=$ initial amount, $n=$ decay rate, $t=$ time)

\begin{aligned}&\Rightarrow \text { Given } p=\frac{A}{2} \ a t  \ t=1590 \\&\Rightarrow \frac{1}{2}=e^{1590n} \Rightarrow n=\frac{\ln (1 / 2)}{1590}=-0.00043594162\end{aligned}

$$If $A=200 \mathrm{mg}$ and $t=1000$ then,$$\begin{aligned}P &=200 e^{\left(\frac{\ln \left(1/2\right)}{1590}\right) \cdot 1000} \text \\\\&=129.33 \text { grams}\end{aligned}$$

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Answer:

5000 students appeared in the examination.

Step-by-step explanation:

We solve this question using Venn probabilities.

I am going to say that:

Event A: Passed in Mathematics

Event B: Passed in English.

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This means that 100 - 5 = 95% pass in at least one, which means that P(A \cup B) = 0.95

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This means that P(A) = 0.8, P(B) = 0.75

Proportion who passed in both:

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P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.8 + 0.75 - 0.95 = 0.6

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3000 is 60% of the total t. So

0.6t = 3000

t = \frac{3000}{0.6}

t = 5000

5000 students appeared in the examination.

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2 years ago
The radius of the large sphere is double the radius of the small sphere. How many times is the volume of the large sphere than t
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