3 years ago

Ahahhajdockdndn help

Mathematics

1 answer:

Elina [12.6K]3 years ago

6 0

Domain: 6,-5,-1
Range: 2, 0, 2

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

3 0

3 years ago

What is the range of y = sinx in the interval - π ≤ x ≤ 0?

Kaylis [27]

Answer:

$-1 \le y \le 1$

Step-by-step explanation:

Let be $y = \sin x$ , the range of the function corresponds to the set of values of $y$ . The sine function is a bounded function between -1 and 1. Hence, the range of the function is: