he half-life of a certain radioactive substance is 14 days. There are 6.6 grams of the substance present initially. Which equati
on represents the number of grams of the radioactive substance on day 42 ?
2 answers:
Answer:
Step-by-step explanation:
half-life of 14 days, basically means it reduces by 50% or half every 14 days.
This can generally be expressed as: , where h=half life, and t=time, where the unit of time for t and half-life is the same. also a is the initial value.
So we can express this half-life equation as: where t=days.
So plugging in 42 days in here, we get:
The reason for this is because 42 days is 3 half-lives.
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Answer:
and
Step-by-step explanation:
Let's first isolate the trig function.
Add 1 one on both sides:
Divide both sides by :
Now recall .
or
The first ratio I have can be found using in the first rotation of the unit circle.
The second ratio I have can be found using you can see this is on the same line as the
so you could write
as
.
So this means the following:
is true when
where is integer.
Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.
So now we have a linear equation to solve:
Add on both sides:
Find common denominator between the first two terms on the right.
That is 24.
(So this is for all the solutions.)
Now I just notice that it said find all the solutions in the interval .
So if and we let
, then solving for
gives us:
( I just added
on both sides.)
So recall .
Then .
Subtract on both sides:
Simplify:
So we want to find solutions to:
with the condition:
That's just at and
So now adding to both gives us the solutions to:
in the interval:
.
The solutions we are looking for are:
and
Let's simplifying:
and
and
and
Answer:
A=384
Step-by-step explanation:
A =2(wl+hl+hw)
A=2(8*8+8*8+8*8)
A=2(64+64+64)
A=2(192)
A=384