Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a (× 2⁴) machine is the same as putting it through a (× 2) machine four times. So, if you send a 3 cm piece of wire through a (× 2⁴) machine, its length becomes 3 × 2 × 2 × 2 × 2 = 48 cm. It can also be written that a base (2) machine is being applied 4 times.
What will be the new length of a 4 cm strip inserted in the machine?
Solution:
Given, a repeater machine is a hypothetical machine which automatically enlarges items several times.
Sending a piece of wire through a (× 2⁴) machine is the same as putting it through a (× 2) machine four times.
We have to find the new length of a 4 cm strip inserted in the machine.
Given, 3 × 2⁴ = 3 × 2 × 2 × 2 × 2
= 3 × 16
= 48 cm
Similarly, 4 × 2⁴ = 4 × 2 × 2 × 2 × 2
= 4 × 16
= 64 cm
Therefore, the new length will be 64 cm.
✦ Try This: Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a (× 2⁴) machine is the same as putting it through a (× 2) machine four times. What will be the new length of a 5 cm strip inserted in the machine?
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 149
Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a (× 2⁴) machine is the same as putting it through a (× 2) machine four times. So, if you send a 3 cm piece of wire through a (× 2⁴) machine, its length becomes 3 × 2 × 2 × 2 × 2 = 48 cm. It can also be written that a base (2) machine is being applied 4 times.
Summary:
Similarly, repeater machine is a hypothetical machine which automatically enlarges items several times. For example, sending a piece of wire through a (× 2⁴) machine is the same as putting it through a (× 2) machine four times. So, if you send a 3 cm piece of wire through a (× 2⁴) machine, its length becomes 3 × 2 × 2 × 2 × 2 = 48 cm. It can also be written that a base (2) machine is being applied 4 times. The new length of a 4 cm strip inserted in the machine will be 64 cm.
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