i got help with this problem a couple days ago. the answer and explanation given made sense to me but on my list of answers it said the the answer is suppose to be:
r=[-pih+sqrt(pi^2h^2+2piA)]/2pi
if anyone can figure out how to get that thanks so much.
the original problem is:
A=2pir^2 + 2pirh
*solve for positive r
It is directly from the quadratic equation.
i still don't understand what you are saying. can someone show me the work.
To solve for positive r in the equation A = 2πr^2 + 2πrh, we can follow these steps:
Step 1: Start with the equation A = 2πr^2 + 2πrh.
Step 2: Group the terms that contain r together. We can rewrite the equation as A = 2πr^2 + 2πrh = 2π(r^2 + rh).
Step 3: Divide both sides of the equation by 2π to isolate the term in parentheses. Now we have A/(2π) = r^2 + rh.
Step 4: Move the rh term to the other side of the equation. Subtracting rh from both sides gives A/(2π) - rh = r^2.
Step 5: Rearrange the equation to put it in quadratic form. We now have r^2 - rh + (A/(2π) - rh) = 0.
Step 6: Apply the quadratic formula to solve for r, which is given by r = (-b ± √(b^2 - 4ac)) / (2a).
Comparing this formula to the equation in step 5, we can see that a = 1, b = -h, and c = A/(2π) - rh.
Step 7: Substitute the values of a, b, and c into the quadratic formula to get r = (-(-h) ± √((-h)^2 - 4(1)(A/(2π) - rh))) / (2(1)).
Step 8: Simplify the expression inside the square root. We have r = (h ± √(h^2 - 4(A/(2π) - rh))) / 2.
Step 9: Expand the expression inside the square root. We get r = (h ± √(h^2 - 4(A/(2π)) + 4r^2h)) / 2.
Step 10: Distribute the 4r^2h term. We now have r = (h ± √(h^2 - 4(A/(2π)) + 4r^2h)) / 2.
Step 11: Move the 4r^2h term to the other side of the equation. We can rewrite the equation as r - (h ± √(h^2 - 4(A/(2π)))) / 2r = 0.
Step 12: Factor out r from the numerator. Now we have r = [(h ± √(h^2 - 4(A/(2π)))) / 2r]r.
Step 13: Simplify the equation by canceling out the r terms in the numerator and denominator. This gives us r = (h ± √(h^2 - 4(A/(2π)))) / 2.
Step 14: Multiply both the numerator and denominator by 1/(2π) to obtain the final answer, which is:
r = [h ± √(h^2 - 4(A/(2π)))] / (2π).
Therefore, the correct answer for positive r is r = [h + √(h^2 - 4(A/(2π)))] / (2π).