lroxoxkmAmberrayne lroxoxkmAmberrayne
  • 22-03-2017
  • Mathematics
contestada

Find two positive numbers whose product is 81 and whose sum is a minimum.

Respuesta :

irspow
irspow irspow
  • 26-03-2017
ab=81, a=81/b

s=a+b using a from above in this we get:

s(b)=81/b +b

s(b)=(81+b^2)/b

ds/db=(2b*b-81-b^2)/b^2

ds/db=(2b^2-81-b^2)/b^2

ds/db=(b^2-81)/b^2

d2s/db2=(2b^3-2b^3+81)/b^4

d2s/db2=81/b^4 since b is positive we know that the acceleration is positive so that when ds/db=0 it is a minimum for s(b)

ds/db=0 only when b^2-81=0, b^2=81, b=9

The two positive numbers are 9 and 9.


Answer Link

Otras preguntas

who's sus?????????????????????????????????/
What are the equations of the lines with the given slope and y-intercept 1. Slope:2, y-intercept: -3 2. Slope: 4, y-intercept: -2
Simplified form of this expression 5z-8-4z-3z+6
the diameter of a penny is 19.05 mm and it is 1.52 mm thick. what is the mass od the penny?​
How did the development of new technologies and industries in the late 19th century affect the US economy?
hoy es lunes pasodo manana es
In which region on the map would you find the country South Africa?
hujknjk jk jjkjj help
Why are city streets so vital to the functioning of a city, as well as the people living within it?
Sandel Company makes 2 products, footballs and baseballs. Additional information follows: Footballs Baseballs Units 4,000 2,500 Sales $60,000 $25,000 Variable