Question - Solving for v in terms of u and finding a specific value
Solution:
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 $$ 14 $$.
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