The radius of a circular rug is 4 feet. How much ribbing will you need to buy to go around the rug? Use 3 for Ñ
1 answer:
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Answer:
6 billion years.
Step-by-step explanation:
According to the decay law, the amount of the radioactive substance that decays is proportional to each instant to the amount of substance present. Let be the amount of
and
be the amount of
after
years.
Then, we obtain two differential equations
where and
are proportionality constants and the minus signs denotes decay.
Rearranging terms in the equations gives
Now, the variables are separated, and
appear only on the left, and
appears only on the right, so that we can integrate both sides.
which yields
,
where and
are constants of integration.
By taking exponents, we obtain
Hence,
,
where and
.
Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition
Substituting 0 for in the general solution gives
Similarly, we obtain and
The relation between the decay constant and the half-life is given by
We can use this fact to determine the numeric values of the decay constants and
. Thus,
and
Therefore,
We have that
Hence,
Solving for yields
, which means that the age of the universe is about 6 billion years.
Answer:
3 seconds.
Step-by-step explanation:
We have been given that Sandra throws an object straight up into the air with initial velocity of 38 ft per second from platform that is 30 ft above the ground.
To find the time it will take for object to hit the ground, we will use formula:
, where,
represents initial velocity and
represents initial height.
Upon substituting our given initial velocity and initial height, we will get:
We know that object will hit the ground, when height will be 0, so we will equate object's height equal to 0 and solve for t as:
Divide by 2:
Upon using quadratic formula, we will get:
Since time cannot be negative, therefore, it will take 3 seconds for object to hit the ground.