Visualize the following procedure: tear in half a square piece of paper with an area of one square unit. then tear it in half again. predict the area of one of the resulting rectangles after 5 tears.

square units

Step-by-step explanation:

To predict the area of the piece of paper after 5 tears we can use a geometric sequence.

Each time a piece is torn, half of the previous area is lost. If the area of the first piece is 1 square unit then:

square units

= 0.0625 in²

Step-by-step explanation:

Area of a piece of paper = 1 unit²

then we tear this paper into half.

So area becomes 0.5 unit²

In this way the sequence formed will be

1, 0.5, 0.25, .........

This sequence is a geometric sequence

as

common ratio r = 0.5

We have to find the 5th term of this sequence

Explicit formula of a geometric sequence is represented by

Now      

                   = (0.5)⁴

                   = 0.0625 in²

After 5 tears area would be  0.0625 in²

step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: