Evaluate \frac{T_3}{T_2}
(\frac{T_2}{T_1} = -3)
To find the value of \frac{T_3}{T_2}, we can use the given ratio \frac{T_2}{T_1} = -3 to write T_1 in terms of T_2 and then substitute into the expression for T_3.
Starting with the given ratio, we find:
\frac{T_2}{T_1} = -3
This can be rearranged to isolate T_1:
T_1 = -\frac{T_2}{3}
Now we can substitute T_1 into the expression for T_3:
T_3 = 2T_1 + 5T_2
T_3 = 2(-\frac{T_2}{3}) + 5T_2
T_3 = -\frac{2}{3}T_2 + 5T_2
T_3 = \frac{13}{3}T_2
Finally, we can find \frac{T_3}{T_2}:
\frac{T_3}{T_2} = \frac{\frac{13}{3}T_2}{T_2} = \frac{13}{3}
Therefore, the value of \frac{T_3}{T_2} is \frac{13}{3}.