Write a general formula to describe the variation:

Mathematics

1 answer:

kap26 [50]3 years ago

6 0

Answer:

Idk

Step-by-step explanation:

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A sample of tritium-3 decayed to 94.5% of its original amount after a year.

Zolol [24]

(a) If $y(t)$ is the mass after $t$ days and $y(0) = A$ then $y(t) = Ae^{kt}.$

$y(1) = Ae^k = 0.945A \implies e^k = 0.945 \implies k = \ln 0.945$

$\text{Then } Ae^{(\ln 0.945)t} = \frac{1}{2}A\ \Leftrightarrow\ \ln e^{(\ln 0.945)t} = \ln \frac{1}{2}\ \Leftrightarrow\ ( \ln 0.945) t = \ln \frac{1}{2} \Leftrightarrow \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 12.25 \text{ years}$

(b)
$Ae^{(\ln 0.945) t} = 0.20 A \ \Leftrightarrow\ (\ln 0.945) t \ln \frac{1}{5}\ \implies \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 28.45\text{ years}$

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4 years ago

Y = 2x + 5 and 3x + y = 40

Sophie [7]

ANSWER: x=7, y=19

Steps

1. Substitute y=2x+5

3x+2x+5=40

2. For y=2x+5 , Substitute x=7

y=2 * 7+5

3. 2 * 7+5=19

y=19

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3 years ago

Explain why the sum of a rational number and an irrational number is always irrational

grandymaker [24]

Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.

(write this in your own words)

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How to turn 7/20 into a decimal and percent

lilavasa [31]

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