Posted by **Callie** on Wednesday, August 17, 2011 at 9:50pm.

The rate of transmission r in a telephone cable is obseed to be approximately r(x)=x^2*ln(1/x, where x is the ratio of the radius of the core to the thickness of the insulation. Due to manufacturing constraints, the only possible ratios are 1/4<=x<=1. What value of x gves the maximum rate of transmission?

No idea where to even start! Any help at all is appreciated! Thanks so much!

- Calculus 1, Help! -
**bobpursley**, Wednesday, August 17, 2011 at 9:54pm
take drate/dx= 2x ln(1/x)+x=0

solve for x

ln(1/x)=1/2

1/x=sqrte

x= 1/sqrte

- Calculus 1, Help! -
**Callie**, Wednesday, August 17, 2011 at 10:04pm
isn't the derivative of the rate x*2ln(1/x)-1??

- Calculus 1, Help! -
**Callie**, Wednesday, August 17, 2011 at 10:08pm
nevermind, it doesn't change the answer. thankyou very much!

## Answer this Question

## Related Questions

- Calc - A metal cable has radius r and is covered by insulation, so that the ...
- astronomy - Using the densities below, find what percentage of the Earth's mass ...
- Physics - A 100.0 meter long transmission cable is suspended between two towers...
- CAL-Help on dr/dt - A circular oil slick of uniform thickness is caused by a ...
- Physic - The composite bar BCD in the figure is composed of an inner aluminum ...
- Thermodynamics and Heat Transfer - A steam pipe is 75 mm external diameter and ...
- Elements of Structures MIT 2.02 - In this problem The composite beam AB, of ...
- CALCULUS - A ruptured oil tanker causes a circular oil slick on the surface of ...
- calculus - A hole of a radius of 1cm is pierced in a sphere of a 4cm radius. ...
- Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...