r_2 ≈ 1.69256875064327 feet, approximately

I need help with math word problems I am not good with them.i just need help

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pi r_1^2 + pi r_2^2 = 130 ft^2

pi r_1^2 - pi r_2^2 =112 ft^2

Add the equations:

2 pi r_1^2 = 242

pi r_1^2 = 121 => r_1 = sqrt(121/pi) = 11/sqrt(pi) feet, exactly

Using calculator with built-in pi value:

r_1 ≈ 6.20608541902532 feet, approximately

121 + pi r_2^2 = 130

pi r_2^2 = 130 - 121 = 9

r_2 = sqrt(9/pi) = 3/sqrt(pi) feet, exactly

Using calculator with built-in pi value:

r_2 ≈ 1.69256875064327 feet, approximately

r_2 ≈ 1.69256875064327 feet, approximately

Hi Willie,Let radius of ist circle is r1 & radius of 2nd circle is r2.

Area of first circle = Pie *r1^2

Area of 2nd circle = pie*r2^2

Now sum of areas of two circles=pie(r1^2+r2^2)=130.....Eq-1

Diff of areas=pie(r1^2 -r2^2)=112........Eq-2

adding Eq-1 & Eq-2, We get,2pie*r1^2=242 ( value of pie = 22/7)

2*22/7*r1^2=242

r1^2=242*7/2*22= 38.5

r1= sq root of 38.5=6.2ft

Now substituting the value of r1^2 inti Eq-1,

pie(r1^2+r2^2)=130

22/7(38.5+r2^2)=130

38.5+r2^2=130*7/22

r2^2=41.36-38.5=2.86

r2= sq root of 2.86=1.7ft

Ans: radius of one circle is 6.2ft & radius 2nd circle is 1.7ft.

Meena from Strongsville,OH

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

∏ r_{1}^2 + ∏r_{2}^2 = 130 ft^{2}

∏ r_{1}^2 - ∏r_{2}^2 = 112 ft^2

r_{1^2 +} r_{2} ^ 2 = 130 /∏ =41.4

r_{1^2 - }r_{2 ^ 2 = }112/ ∏=35.7

2 r_{1}^2 = 77.1

r_{1 ^ 2 = 38.6 }

r_{1} = √38.6 = 6.2 ft

r_{2} ^ 2 = 44.4 - 35.7 = 8.7

r_{2 = }√8.7 = 2.9 ft

Area of a circle = pi x R2

As per question

(pi x R12) + ( pi x R22) = 130

(pi x R12) - (pi x R22) = 112

=> R12 + R22 = 130/pi equation 1

R12 - R22 = 112/pi equation 2

=> R12 = 112/pi + R22 Substitute this value of R12 in equation 1

=> 112/pi + R22 + R22 = 130/pi

=> 2 R22 = 130/pi - 112/pi = 18/pi

=> R22 = 18/2pi = 9/pi

=> R2 = √(9/pi) = 3/√pi = 3/1.77 = 1.69 ft

Substitute this value of R2 in equation 2

R12 - 9/pi = 112/pi

R12 = 112/pi + 9/pi = 121/pi

R1 = √(121/pi) = 11/√pi = 6.21 ft

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