Answer:
r=5 units
Step-by-step explanation:
we have
Convert the equation of the circle in standard form
Complete the square twice. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
center (0,2)
radius r=5 units
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
Where <em>A₀</em> is the initial amount, <em>t</em> is the time that has passes (in this case seconds), <em>d</em> is the half-life, and <em>A</em> is the amount after <em>t</em> seconds.
Since the half-life of the element is 30 seconds, <em>d</em> = 30. Our initial sample has nine grams, so <em>A₀</em> is 9. Substitute:
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let <em>A</em> = 0.72 and solve for <em>t: </em>
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Divide both sides by 9:
We can take the natural log of both sides:
By logarithm properties:
Solve for <em>t: </em>
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So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.