Two circular flower beds have a combined area of (29¥)/2m^2. The sum of the circumferences of the flower beds is 10¥m. Determine the radius of each bed........
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If the two radii are x and y, then
π(x^2+y^2) = 29π/2
2π(x+y) = 10π
factoring out the π,
x^2+y^2 = 29/2
x+y = 5
Now you should be able to solve for x and y
To solve this problem, let's assume the radius of the first circular flower bed is "r1" and the radius of the second circular flower bed is "r2".
We are given two pieces of information:
1. The combined area of the flower beds is (29¥)/2 square meters.
The area of a circle is given by the formula A = πr^2. Therefore, the area of the first circular bed is πr1^2 and the area of the second circular bed is πr2^2. So we have the equation:
πr1^2 + πr2^2 = (29¥)/2
2. The sum of the circumferences of the flower beds is 10¥ meters.
The formula for the circumference of a circle is C = 2πr. Therefore, the circumference of the first circular bed is 2πr1 and the circumference of the second circular bed is 2πr2. So we have the equation:
2πr1 + 2πr2 = 10¥
Now, we have a system of two equations:
πr1^2 + πr2^2 = (29¥)/2
2πr1 + 2πr2 = 10¥
To solve this system, we can use substitution or elimination method. Let's use the substitution method.
From the second equation, we can solve for r1:
2πr1 = 10¥ - 2πr2
r1 = (10¥ - 2πr2) / (2π)
Now, substitute this value of r1 into the first equation:
π[(10¥ - 2πr2) / (2π)]^2 + πr2^2 = (29¥)/2
Simplify and solve for r2. This will give us the radius of the second circular flower bed.
Once we have the value of r2, substitute it back into the equation for r1 to find the radius of the first circular flower bed.