Answer:
Time period,
Explanation:
We have,
The frequency of an FM radio station is 89.3 MHz.
It is required to find the period of the wave.
The reciprocal of frequency is called time period of a wave. It can be given by :
So, the period of the wave is .
Answer:
The average angular acceleration is 0.05 radians per square second.
Explanation:
Let suppose that Ferris wheel accelerates at constant rate, the angular acceleration as a function of change in angular position and the squared final and initial angular velocities can be clear from the following expression:
Where:
,
- Initial and final angular velocities, measured in radians per second.
- Angular acceleration, measured in radians per square second.
,
- Initial and final angular position, measured in radians.
Then,
Given that ,
and
, the angular acceleration is:
Now, the time needed to accelerate the Ferris wheel uniformly is described by this kinematic equation:
Where is the time measured in seconds.
The time is cleared and obtain after replacing every value:
If ,
and
, the required time is:
Average angular acceleration is obtained by dividing the difference between final and initial angular velocities by the time found in the previous step. That is:
If ,
and
, the average angular acceleration is:
The average angular acceleration is 0.05 radians per square second.
Explanation:
The half-life of a radioactive isotope refers to its decay period, which is the average lifetime of an atom before it disintegrates.
In this case, we are given the half life of two elements:
beryllium-13:
beryllium-15:
As we can see, the half-life of beryllium-15 is greater than the half-life of beryllium-13, but how great?
We can find it out by the following expression:
Where is the amount we want to find:
Finally:
Therefore:
The half-life of beryllium-15 is <u>400 times greater than</u> the half-life of beryllium-13.