hi.... i ve got this exercice here, 0.1=1/1+(1-w^2*0.1*0.01/w*10*0.01) how should i proceed? thanks

Question

0.1=                        1                    

        1+(1-w²*0.1*0.01/w*10*0.01)

Answer 1

if the question is solve for w, then I would do some of the multiplications to start.

 

in the denominator    1 + (1 - .001w²)/.1w

 

get a common denominator and combine fractions

 

.1w/.1w + (1 - .001w²)/.1w = (.1w + 1 - .001w²)/.1w

 

instead of dividing by this fraction, multiply by the reciprocal

 

1(.1w/(.1w + 1 - .001w²)    so this is the right side of the equation

 

.1 = .1w/(.1w + 1 - .001w²)    cross multiply

 

.1(.1w + 1 - .001w² )= .1w     divide by .1

 

.1w + 1 -.001w² = w

 

.001w² + .9w - 1 = 0     multiply by 1000

 

w² + 900w - 1000 = 0    solve using quadratic formula