Question

it is given that A=B² if A=100± 0.20 then B is equal to​

Answer 1

Answer:

B = +/-(10 +/- 0.01)

Explanation:

it is given that A=B² if A=100± 0.20 then B is equal to

let say B = X +/- y

then B^2 = (X +/- y)^2

= X^2 +/- 2xy

X^2 = 100

=> X = +/- 10

2Xy = 0.2

2 (10)y = 0.2

=> y = 0.01

B = +/-(10 +/- 0.01)

Answer 2

answer : 10 ± 0.01

explanation : it is given that, A = 100 ± 0.20

expression is A = B² ......(1)

differentiating both sides,

dA = 2B.dB

or, dA/A = 2B.dB/A

or, dA/A = 2B.dB/B² [ from equation (1), ]

or, dA/A = 2dB/B

or we can write it ∆A/A = 2∆B/B

now to find error (i.e., ∆B) in B we have to find first B,

B = √A = √(100) = 10

now, ∆B = (∆A/A) × (B/2)

here, A = 100, ∆A = 0.2 and B = 10

so, ∆B = (0.2/100) × (10/2) = 0.01

hence, appropriate value of B = B ± ∆B

= 10 ± 0.01 [ answer ]