IDNLearn.com: Your trusted source for accurate and reliable answers. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

Mason is a captain of a tourist cruise to the Statue of Liberty. He modeled a few of the relationships.

\begin{tabular}{lll}
Function & Input & Output \\
\hline
[tex]$P$[/tex] & Duration of the cruise, [tex]$r$[/tex] & Average number of photos taken by each passenger, [tex]$P(r)$[/tex] \\
[tex]$S$[/tex] & Current of the river, [tex]$x$[/tex] & Speed of the ship, [tex]$S(x)$[/tex] \\
[tex]$D$[/tex] & Speed of the ship, [tex]$k$[/tex] & Duration of the cruise, [tex]$D(k)$[/tex] \\
\end{tabular}

According to Mason's findings, which of the following represents the average number of photos taken per passenger as a function of the speed of the ship?

Choose one answer:
A. [tex]$P(D(k))$[/tex]
B. [tex]$P(S(k))$[/tex]
C. [tex]$D(P(r))$[/tex]
D. [tex]$S(P(r))$[/tex]


Sagot :

To determine which function represents the average number of photos taken per passenger as a function of the speed of the ship, we need to follow the relationships outlined in the problem:

1. Duration of the cruise, [tex]\( r \)[/tex]: The duration of the cruise [tex]\( r \)[/tex] is a function of the speed of the ship [tex]\( k \)[/tex]—this relationship is represented by [tex]\( D \)[/tex]. Therefore, the duration of the cruise [tex]\( r \)[/tex] can be expressed as [tex]\( D(k) \)[/tex].

2. Average number of photos taken per passenger, [tex]\( P \)[/tex]: This is a function of the duration of the cruise [tex]\( r \)[/tex], which is expressed as [tex]\( P(r) \)[/tex].

Given that [tex]\( r \)[/tex] is determined by [tex]\( k \)[/tex] through the function [tex]\( D \)[/tex], we need to substitute [tex]\( r \)[/tex] with [tex]\( D(k) \)[/tex] in the function [tex]\( P(r) \)[/tex].

Therefore, the function that represents the average number of photos taken per passenger as a function of the speed of the ship [tex]\( k \)[/tex] is: [tex]\( P(D(k)) \)[/tex].

So the correct answer is:

(A) [tex]\( P(D(k)) \)[/tex]

When referencing the choices given:
- (A) [tex]\( P(D(k)) \)[/tex] correctly represents the average number of photos taken per passenger as a function of the speed of the ship.
- (B) [tex]\( P(S(k)) \)[/tex] is incorrect because [tex]\( S \)[/tex] represents the speed of the ship as a function of the current of the river, not the speed of the ship provided.
- (C) [tex]\( D(P(r)) \)[/tex] and (D) [tex]\( S(P(r)) \)[/tex] are incorrect as they incorrectly relate the functions.

Hence, the answer is:
1