Certainly! Let's break down the given function [tex]\( f(t) \)[/tex]:
1. Understanding the Function:
The function is given as:
[tex]\[
f(t) = \frac{9}{2} t^5 + \frac{4}{3} t^4 - \frac{3}{4} t^3 - 5 t
\][/tex]
2. Simplify the Coefficients:
To make it easier to understand, let's convert the coefficients to decimal form where necessary:
- [tex]\(\frac{9}{2}\)[/tex] is 4.5
- [tex]\(\frac{4}{3}\)[/tex] is approximately 1.333333
- [tex]\(\frac{3}{4}\)[/tex] is 0.75
- [tex]\(-5\)[/tex] remains [tex]\(-5\)[/tex]
So, the function becomes:
[tex]\[
f(t) = 4.5 t^5 + 1.333333 t^4 - 0.75 t^3 - 5 t
\][/tex]
3. Writing Down the Simplified Function:
Thus, we can rewrite the function clearly with decimal coefficients:
[tex]\[
f(t) = 4.5 t^5 + 1.333333 t^4 - 0.75 t^3 - 5 t
\][/tex]
This detailed breakdown ensures clarity in understanding each step of the transition from the original mathematical representation to its simplified form.
