Sure, let's solve the given equation step-by-step to find [tex]\( t \)[/tex] in terms of [tex]\( p \)[/tex], [tex]\( s_1 \)[/tex], and [tex]\( s_2 \)[/tex].
Given equation:
[tex]\[ p = s_1 t - s_2 t \][/tex]
First, combine the terms on the right-hand side that involve [tex]\( t \)[/tex]:
[tex]\[ p = (s_1 - s_2) t \][/tex]
Next, to isolate [tex]\( t \)[/tex], divide both sides of the equation by [tex]\( (s_1 - s_2) \)[/tex]:
[tex]\[ t = \frac{p}{s_1 - s_2} \][/tex]
So, the equation solved for [tex]\( t \)[/tex] is:
[tex]\[ t = \frac{p}{s_1 - s_2} \][/tex]
Among the given options:
- [tex]\( t=p(s_1-s_2) \)[/tex]
- [tex]\( f=p-s_1+s_2 \)[/tex]
- [tex]\( t=\frac{\rho}{s_1-s_2} \)[/tex]
- [tex]\( t=\frac{p}{s_1+s_2} \)[/tex]
The correct option is:
[tex]\[ t=\frac{p}{s_1-s_2} \][/tex]
