charlymccormick3766 charlymccormick3766
  • 07-01-2022
  • Mathematics
contestada

All positive integers which can be written as a sum of one or more distinct powers of 3 are written in increasing order. The first four of them are 1, 3, 4, and 9. What is the 81st?

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 08-01-2022

Answer:

   811

Step-by-step explanation:

The place values of digits in base-3 are all powers of 3. The numbers 1, 3, 4, 9 written in base-3 are ...

  1

  10

  11

  100

You will recognize these as successive numbers in base 2. Then the 81st number of interest is written in base-3 the way 81 is written in base-2:

  101 0001

It will be the sum 3^6 +3^4 +3^0 = 729 +81 +1 = 811

The 81st number is 811.

Answer Link

Otras preguntas

In the scarlet Ibis old woman swamp is a symbol of. To doodle and his brother
Which of the functions below could have created this graph? O A. F(x) = - x ^ 0 + x ^ 3 - x ^ 2 O B. F(x) = - x ^ 2 + 4x ^ 3 - 2x ^ 2 C. F(x) = x ^ 9 + 12x ^ 8
r (90 degree) (def) for d (0,5) e (-2,8) f(-3,-5)
if ford mustang costs $30,000 in the us and 40,000 pounds in the uk and the current exchange rate between pound and dollar is $1.2 per pound, then according to
What is the range of y=3sin(x)?
Ramona went to a theme park during spring break. She was there for 6 hours and rode 12 rides. At what rate did Ramona ride rides in rides per hour?
Which of the following best describes the Gentleman's Agreement made between the United States and Japan in the beginning of the 1900s?
If16 = x/20, then x=
2. How many people inhabited the planet in 1950?
What is the squires job in Canterbury tails