Answer :

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].