Answer :
To solve the equation [tex]\(\frac{v k}{D + y} = 5\)[/tex] for [tex]\(y\)[/tex], follow these steps:
1. Rewrite the equation: Start by isolating the variable term on one side of the equation:
[tex]\[ \frac{v k}{D + y} = 5 \][/tex]
2. Clear the fraction: Multiply both sides of the equation by [tex]\(D + y\)[/tex] to eliminate the denominator:
[tex]\[ v k = 5(D + y) \][/tex]
3. Distribute the right-hand side: Expand the right-hand side of the equation:
[tex]\[ v k = 5D + 5y \][/tex]
4. Isolate the variable term: Subtract [tex]\(5D\)[/tex] from both sides to isolate the term containing [tex]\(y\)[/tex]:
[tex]\[ v k - 5D = 5y \][/tex]
5. Solve for [tex]\(y\)[/tex]: Finally, divide both sides of the equation by 5:
[tex]\[ y = \frac{v k - 5D}{5} \][/tex]
This solution can be simplified to:
[tex]\[ y = -D + \frac{k v}{5} \][/tex]
So the solution for [tex]\(y\)[/tex] is:
\[
y = -D + \frac{k v}{5}
1. Rewrite the equation: Start by isolating the variable term on one side of the equation:
[tex]\[ \frac{v k}{D + y} = 5 \][/tex]
2. Clear the fraction: Multiply both sides of the equation by [tex]\(D + y\)[/tex] to eliminate the denominator:
[tex]\[ v k = 5(D + y) \][/tex]
3. Distribute the right-hand side: Expand the right-hand side of the equation:
[tex]\[ v k = 5D + 5y \][/tex]
4. Isolate the variable term: Subtract [tex]\(5D\)[/tex] from both sides to isolate the term containing [tex]\(y\)[/tex]:
[tex]\[ v k - 5D = 5y \][/tex]
5. Solve for [tex]\(y\)[/tex]: Finally, divide both sides of the equation by 5:
[tex]\[ y = \frac{v k - 5D}{5} \][/tex]
This solution can be simplified to:
[tex]\[ y = -D + \frac{k v}{5} \][/tex]
So the solution for [tex]\(y\)[/tex] is:
\[
y = -D + \frac{k v}{5}