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प्रश्न
Find three repeater machines that will do the same work as a (× 64) machine. Draw them, or describe them using exponents.
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उत्तर
We know that, the possible factors of 64 are 2, 4, 8. :
If 26 = 64, 43 = 64 and 82 = 64
Hence, three repeater machines that would work as a (× 64) will be (× 26), (× 43) and (× 82).
The diagram of (× 26), (× 43) and (× 82) is given below.
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संबंधित प्रश्न
The diameter of the Sun is 1.4 × 109 m and the diameter of the Earth is 1.2756 × 107 m.
The table shows the average distance from each planet in our solar system to the sun.
| Planet | Distance from Sun (km) |
Distance from Sun (km) Standard Notation |
| Earth | 149,600,000 | 1.496 × 108 |
| Jupiter | 778,300,000 | |
| Mars | 227,900,000 | |
| Mercury | 57,900,000 | |
| Neptune | 4,497,000,000 | |
| Pluto | 5,900,000,000 | |
| Saturn | 1,427,000,000 | |
| Uranus | 2,870,000,000 | |
| Venus | 108,200,000 |
- Complete the table by expressing the distance from each planet to the Sun in scientific notation.
- Order the planets from closest to the sun to farthest from the sun.
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?
For the following repeater machines, how many times the base machine is applied and how much the total stretch is?
What will the following machine do to a 2 cm long piece of chalk?
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?
Sanchay put a 1 cm stick of gum through a (1 × 3–2) machine. How long was the stick when it came out?
Neha needs to stretch some sticks to 252 times their original lengths, but her (× 25) machine is broken. Find a hook-up of two repeater machines that will do the same work as a (× 252) machine. To get started, think about the hookup you could use to replace the (× 25) machine.
Find three machines that can be replaced with hook-ups of (× 5) machines.
The left column of the chart lists the lengths of input pieces of ribbon. Stretching machines are listed across the top. The other entries are the outputs for sending the input ribbon from that row through the machine from that column. Copy and complete the chart.
| Input Length | Machine | |||
| × 2 | ||||
| 1 | 5 | |||
| 3 | 15 | |||
| 14 | 7 | |||
