Sure, let's go through the problem step-by-step to solve for [tex]\( v \)[/tex].
### Step 1: Understand the Equation
Given:
[tex]\[ v = \sqrt{\frac{2 \times 145}{76}} \][/tex]
We need to rearrange and solve this equation to find the value of [tex]\( v \)[/tex].
### Step 2: Calculate the Numerator
First, calculate the value in the numerator:
[tex]\[ 2 \times 145 = 290 \][/tex]
So the equation simplifies to:
[tex]\[ v = \sqrt{\frac{290}{76}} \][/tex]
### Step 3: Divide the Numerator by the Denominator
Next, perform the division inside the square root:
[tex]\[ \frac{290}{76} \approx 3.8157894736842106 \][/tex]
Now the equation is:
[tex]\[ v = \sqrt{3.8157894736842106} \][/tex]
### Step 4: Calculate the Square Root
Finally, calculate the square root of the result:
[tex]\[ \sqrt{3.8157894736842106} \approx 1.9534045852521722 \][/tex]
### Conclusion
Therefore, the value of [tex]\( v \)[/tex] is approximately [tex]\( 1.953 \)[/tex] (rounded to three decimal places).
Thus, we have rearranged the equation and calculated the value step-by-step.
