18. Determine the greatest three-digit number in each of the following bases.
a. Base two
b. Base twelve

If you're asking about the largest number that can be written with 3 digits in the given base:

• In base 2, the largest number with 3 digits is

111₂ = 1•2² + 1•2¹ + 1•2⁰ = 7

• In base 12, the largest number with 3 digits is

bbb₁₂ = 11•12² + 11•12¹ + 11•12⁰ = 1727

(in base 12, a₁₂ = 10 and b₁₂ = 11)

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,