The rate of transmission in a telegraph cable is observed to be proportional to x^22ln(1/x) where x is the ratio of the radius of the core to the thickness of the insulation (0

x = 0.606

Step-by-step explanation:

Data provided in the question:

rate of transmission is proportional to

or

rate of transmission, R =

here, C is the proportionality constant

Now,

for point of maxima

differentiating the function with respect to 'x'

R' =

using the product rule, we get\

R' =

or

R' =  

Now,

R' = 0         [for point of maxima]

OR

= 0

or

-x²¹ = 0 or   = 0

or

ln(x) =

or

x = 0.606

Since,

0 < x < 1

Hence,

accepted value of x = 0.606

ian gonna lie that is way to much

you didn't give me the choices, so i will just give you the graph so you can look at your choices and choose the right one.