Question

Q1. a uniform circular track is the area bounded by two concentric circles if the area of track is 1144 metre square and its width is 14 M find the diameter of the two circles.
Q2. If a=2+2^2/3+2^1/3. Prove that x^2+1/x^2=x^3+1/x^3=x4+1/x^4

Answer 1

Q1. Let the radii of inner circle be x and Thor outer circle be x+14.
WKT,
area of the track =pi(R^2-r^2)
1144=22/7[(x+14)^2-(x)^2]
1144*7/22=[x^2+14^2+2(x)(14)]-x^2
364=x^2+196+28x-x^2
364=196+28x
364-196=28x
168=28x
168/28=x
x=6
Therefore,radius of inner circle =6m
radius of outer circle=20m
Diameter of inner circle =12m
Diameter of outer circle =40m

Answer 2

Ans1 : Diameter of outer circle = 40 m

           Diameter of inner circle = 14 m

Step-by-step explanation:

Q1 : Given : Area of track = 1144 sq m

                    Width of track = 14 m

             Radius of outer circle = R

             Radius of inner circle r = R - 14 m

Area of outer circle -  Area of inner circle = π R² - π(R-14)²

                                                                    = π (R² - (R² + 196 - 28 R)

                                                                   = π (R² - R² - 196 + 28 R)

                                                                   = (28R - 196)22/7

                                                                   = 28× 22/7(R-7)

                                                                   = (R-7)88

Area of track = (R-7)88/7

1144 = (R-7)88

1144/88 = R - 7

13 = R-7

R =20 m

So, Radius of outer circle = 20 m

    Diameter of outer circle = 40 m

Radius of inner circle = 7 m

    Diameter of inner circle = 14 m

Q2. Wrong wording.