Chapter 4.2, Problem 20PPE

To determine

To determine whether given statements are right or not.

Answer to Problem 20PPE

Both of them are right.

Explanation of Solution

Given: During projection of a movie, a certain number of frames passes through the projector in one minute. A person argues that the length of the movie in minutes is a function of the number of frames projected. Another person says that the number of frames projected is a function of the length of the movie in minutes. Correctness of both the statements needs to be checked.

Let, number of frames which passes through the projector in a minute which is constant = k

Number of total frames projected= P

Length of the movie in minutes= T

Now, length of the movie = (number of total frames projected / k) minutes

  $\Rightarrow T=\frac{P}{\text{k}}$

Thus we can see that T is a function of P . So the first statement is correct. Length of the movie is a function of the number of the frames projected.

Now, from the above equation;

  $\begin{array}{l}T=\frac{P}{\text{k}}\\ \Rightarrow P=\text{k}T\end{array}$

Thus we can see that, number of frames projected is also a function of the length of the movie.

Hence, Both the arguments/statements are right.