Sure, let's solve the equation step-by-step.
We start with the given equation:
[tex]\[
\tau \cdot 2r^2 = 50
\][/tex]
Our goal is to solve for [tex]\(\tau\)[/tex].
1. Isolate [tex]\(\tau\)[/tex]:
To isolate [tex]\(\tau\)[/tex], we need to get [tex]\(\tau\)[/tex] by itself on one side of the equation. We can do this by dividing both sides of the equation by [tex]\(2r^2\)[/tex].
[tex]\[
\tau = \frac{50}{2r^2}
\][/tex]
2. Simplify the right side of the equation:
Now, simplify the fraction on the right-hand side.
[tex]\[
\tau = \frac{50}{2r^2} = \frac{50 \div 2}{r^2} = \frac{25}{r^2}
\][/tex]
So, the solution to the equation [tex]\(\tau \cdot 2 r^2 = 50\)[/tex] is:
[tex]\[
\tau = \frac{25}{r^2}
\][/tex]
Thus, [tex]\(\tau\)[/tex] in terms of [tex]\(r\)[/tex] is [tex]\(\frac{25}{r^2}\)[/tex].
