Solve for the indicated variable:
A = 2(pi)r^2 + 2(pi)rh, for positive r
(and by pi i mean 3.14...)
This is what I have so far:
A = 2pi(r^2+rh)
A/2pi=r^2 + rh
?
Thanks!
isn't it a quadratic?
r^2 + rh - A/2PI =0
ax^2+bx+c=0
r= (-h +-sqrt(h^2+4A/2PI))/2
To solve for the indicated variable, we need to isolate "r" in the equation A = 2(pi)r^2 + 2(pi)rh.
Here's how we can do that:
Step 1: Start with the equation A = 2(pi)r^2 + 2(pi)rh.
Step 2: Subtract 2(pi)rh from both sides of the equation to move it to the other side:
A - 2(pi)rh = 2(pi)r^2
Step 3: Divide both sides of the equation by 2(pi) to solve for r:
(A - 2(pi)rh) / (2(pi)) = r^2
Simplifying further:
A / (2(pi)) - (2(pi)rh) / (2(pi)) = r^2
A / (2(pi)) - rh = r^2
Step 4: Rearrange the equation to isolate r:
rh = A / (2(pi)) - r^2
Step 5: Move the term containing r^2 to the other side of the equation:
rh + r^2 = A / (2(pi))
Step 6: Factor out r on the left side of the equation:
r(h + r) = A / (2(pi))
Step 7: Divide both sides of the equation by (h + r) to solve for r:
r = (A / (2(pi))) / (h + r)
Now, we have the equation to solve for r:
r = A / [2(pi)(h + r)]
Please note that this final equation for r is in terms of A, h, and r itself. So, it cannot be easily solved algebraically for a specific value of r. However, you can use this equation to calculate the value of r numerically by substituting the known values of A and h into the equation and solving for r using numerical methods such as iterations or a graphing calculator.