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Question
For the following repeater machines, how many times the base machine is applied and how much the total stretch is?
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Solution
In machine (a), (× 1002) = 10000 stretch.
Since, it is two times the base machine.
In machine (b), (× 75) = 16807 stretch.
Since, it is fair times the base machine.
In machine (c), (× 57) = 78125 stretch.
Since, it is 7 times the base machine.
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| Sun | 1,990,000,000,000,000,000,000,000,000,000 | 1.99 × 1030 |
| Mercury | 330,000,000,000,000,000,000,000 | |
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| Earth | 5,970,000,000,000,000,000,000,000 | |
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| Jupiter | 1,900,000,000,000,000,000,000,000,000 | |
| Saturn | 568,000,000,000,000,000,000,000,000 | |
| Uranus | 86,800,000,000,000,000,000,000,000 | |
| Neptune | 102,000,000,000,000,000,000,000,000 | |
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| Moon | 73,500,000,000,000,000,000,000 |
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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.
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In a shrinking machine, a piece of stick is compressed to reduce its length. If 9 cm long sandwich is put into the shrinking machine below, how many cm long will it be when it emerges?
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Ajay had a 1 cm piece of gum. He put it through repeater machine given below and it came out `1/(100,000)` cm long. What is the missing value?
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| × 2 | ||||
| 1 | 5 | |||
| 3 | 15 | |||
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