Advertisements
Advertisements
Question
Find three repeater machines that will do the same work as a (× 64) machine. Draw them, or describe them using exponents.
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
Mass of earth is 5.97 × 1024 kg and the mass of the moon is 7.35 × 1022 kg. What is the total mass?
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 mass of the planets, the sun and the moon in our solar system.
| Celestial Body |
Mass (kg) | Mass (kg) Standard Notation |
| Sun | 1,990,000,000,000,000,000,000,000,000,000 | 1.99 × 1030 |
| Mercury | 330,000,000,000,000,000,000,000 | |
| Venus | 4,870,000,000,000,000,000,000,000 | |
| Earth | 5,970,000,000,000,000,000,000,000 | |
| Mars | 642,000,000,000,000,000,000,000,000,000 | |
| 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 | |
| Pluto | 12,700,000,000,000,000,000,000 | |
| Moon | 73,500,000,000,000,000,000,000 |
- Write the mass of each planet and the Moon in scientific notation.
- Order the planets and the moon by mass, from least to greatest.
- Which planet has about the same mass as earth?
Suppose you have a stretching machine which could stretch almost anything. For example, if you put a 5 metre stick into a (× 4) stretching machine (as shown below), you get a 20 metre stick. Now if you put 10 cm carrot into a (× 4) machine, how long will it be when it comes out?
Two machines can be hooked together. When something is sent through this hook up, the output from the first machine becomes the input for the second. Which stretching machine does the same work as two (× 2) machines hooked together?
  |
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?
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?
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 | |||
