To evaluate the function [tex]\( p(x) = \left\lfloor \frac{60}{x} \right\rfloor \)[/tex] at [tex]\( x = 7 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 7 \)[/tex] into the function [tex]\( p(x) \)[/tex]:
[tex]\[
p(7) = \left\lfloor \frac{60}{7} \right\rfloor
\][/tex]
2. Calculate the division inside the floor function:
[tex]\[
\frac{60}{7}
\][/tex]
Performing the division yields approximately:
[tex]\[
\frac{60}{7} \approx 8.5714
\][/tex]
3. Apply the floor function:
The floor function, denoted by [tex]\( \left\lfloor \cdot \right\rfloor \)[/tex], returns the greatest integer less than or equal to the given number. In this case:
[tex]\[
\left\lfloor 8.5714 \right\rfloor
\][/tex]
4. The greatest integer less than or equal to [tex]\( 8.5714 \)[/tex] is [tex]\( 8 \)[/tex].
Therefore, the value of [tex]\( p(7) \)[/tex] is:
[tex]\[
p(7) = 8
\][/tex]
