Solving for v in terms of u and finding a specific value
To express \( v \) in terms of \( u \), we will start with the given equation \( u = \sqrt{2v - 3} \) and solve for \( v \).
Here are the steps:
(a) Express \( v \) in terms of \( u \):
1. Square both sides of the equation to eliminate the square root:
\( u^2 = (\sqrt{2v - 3})^2 \)
2. This simplifies to:
\( u^2 = 2v - 3 \)
3. Now add 3 to both sides to isolate the \( v \) term:
\( u^2 + 3 = 2v \)
4. Finally, divide both sides by 2 to solve for \( v \):
\( v = \frac{u^2 + 3}{2} \)
(b) Find the value of \( v \) if \( u = 5 \):
To find the value of \( v \) when \( u = 5 \), substitute \( u \) with 5 in the equation from part (a):
\( v = \frac{5^2 + 3}{2} \)
\( v = \frac{25 + 3}{2} \)
\( v = \frac{28}{2} \)
\( v = 14 \)
So, the value of \( v \) when \( u = 5 \) is \( 14 \).
