: Marianne puts her favorite Backstreet Boys disc in her CD player. If it spins with a frequency of 1800 revolutions per minute, what is the period of spin of the compact disc

According to the question,

then,

→

hence,

The time period of spin will be:

=

=

Thus the approach above is right.

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The period of spin of the compact disc is approximately 0.033 seconds.

Explanation:

From Rotation Kinematics we must remember that a period of spin is the time needed by the compact disk to make one revolution. Period can be found by using the following equation:

(Eq. 1)

Where:

- Period, measured in seconds.

- Angular velocity, measured in radians per second.

At first we need to convert angular velocity into radians per second:

If we know that , then the period of spin of the compact disc is:

The period of spin of the compact disc is approximately 0.033 seconds.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .