Solve w= (va)/(r^2+a^2) for a.
is the answer a= sqrt[w(r^2+v^2)/v]?
wr^2 + wa^2 - va=0
a^2 -v/w a -wr^2=0
Now apply the quadratic formula
a= (v/w +- sqrt (v^2/w^2 - 4*(-wr^2)) /2
check my thinking.
I have the answer as a= (v+/- sqrt[v^2+4w^2r^2]/w
To solve for the variable 'a' in the equation w = (va)/(r^2 + a^2), we can follow these steps:
Step 1: Multiply both sides of the equation by (r^2 + a^2) to eliminate the denominator on the right side:
w(r^2 + a^2) = va
Step 2: Expand the equation:
wr^2 + wa^2 = va
Step 3: Rearrange the terms to isolate 'a' on one side:
wa^2 - va + wr^2 = 0
Step 4: This is a quadratic equation in terms of 'a'. To solve quadratic equations, we can apply the quadratic formula:
a = (-b ± √(b^2 - 4ac))/(2a)
Comparing our equation to the quadratic formula, we have:
a = (-v ± √(v^2 - 4wvr^2))/(2w)
Simplifying further, we get:
a = (-v ± √(v^2 - 4wvr^2))/(2w)
So, the correct answer is a = (-v ± √(v^2 - 4wvr^2))/(2w).