9514 1404 393
Answer:
vertex: (-2, 4)
Step-by-step explanation:
Use your regression calculator to find the parameters of the quadratic model.
The vertex form equation is ...
y = -3(x +2)^2 +4
so the vertex is (-2, 4).
__
The standard form equation is the expansion of the above:
y = -3x^2 -12x -8
4(4) - 6 = 10
r = 10
11(4) + 9 = 53
h = 53
V = πr²h is the formula
V = π 10² (53)
V = π 100(53)
V = 530πin. or 1,665in
<h2>
Answer: 816 years</h2>
This problem can be solved using the <u>Radioactive Half Life Formula:
</u>
<u />
(1)
Where:
is the final amount of the material
is the initial amount of the material
is the time elapsed (the quantity we are asked to find)
is the half life of americium-241
Knowing this, let's find
from (1):
Applying natural logarithm in both sides:
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<u>Finally:</u>
To add fractions, find the LCD and then combine.
Exact form:
9/2
Decimal form:
4.5
Mixed number form:
4 1/2
So, answer is
4 1/2
Hope this helps!