A binary search is to be performed on the list: 1 , 5 ,10 , 13 , 48 , 68 , 100 , 101 How many comparisons would it take to the find the number 101?

3 comparisons

Step-by-step explanation:

Given:

Required

Determine the number of comparisons to get to 101

The length of the list is 8. So, the first index is 0 and the last is 7.

We have:

Initially:

-- first index

--- last index

Start by calculating the mid-item

--- approximated.

The mid-index is 4 and the item is:

101 is on the right of 48.

So, we calculate the new begin index.

Calculate mid

The mid-index is 6 and the item is:

101 is on the right of 100.

So, we calculate the new begin index.

Calculate mid

At this point, the mid-index is at 101

i.e.

This implies that, we have located 101.

So far, we made 3 comparisons

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x