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marissa [1.9K]
3 years ago
7

NO LINKS - death valley is the hottest place in the united states. the highest temperature ever recorded there was 134F the lowe

st temperature recorded there was 15F write two inequalities that would describe the temperature, in degrees fahrenheit, in death valley at any time since temperatures have been recorded
Mathematics
1 answer:
Darina [25.2K]3 years ago
5 0

Answer:

134F>15F and 15F< 134F

Step-by-step explanation:

if you flip the first one then you have the second

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Radioactive Decay
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Answer:

Percentage of (226Ra) after 900 years is 68%

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Half life of (226 Ra) = 1599 years

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Decay i amount of radioactive substance is related to time t as

\frac{dP}{dt}=kP(t)\\\\\frac{1}{P}\,dP=kdt\\\\Integrating\,\, both\,\,sides\\\\ln|P|=kt+c\\\\P(t)=Ce^{kt}\\\\at \,\, t=0\,\, P(0)=P_{o}\\\\P(0)=Ce^{k0}\\\\P_{o}=C\\\\then\\\\P(t)=P_{o}e^{kt}

To find value of k

at\,\, t=1599\,years\\\\P(1599)=\frac{P_{o}}{2}\\\\then\\\\\frac{P_{o}}{2} =P_{o}e^{k(1599)}\\\\\frac{1}{2} =e^{k(1599)}\\\\ln|\frac{1}{2}|=k(1599)\\\\k=\frac{ln|\frac{1}{2}|}{1599}=-4.3\times 10^{-3}\\\\\implies P(t)=P_{o}e^{-4.3\times 10^{-3}t}\\\\at\,\, t=900 \\\\P(900)=P_{o}e^{-4.3\times 10^{-3}(900)}\\\\P(900)=0.68P_{o}

Percentage of radioactive element is:

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