Advertisements
Advertisements
Question
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?

Advertisements
Solution
According to the question, if we put a 5 m stick into a (× 4) stretching machine, then machine produces 20 m stick.
Similarly, if we put 10 cm carrot into a (× 4) stretching machine, then machine produce 10 × 4 = 40 cm stick.
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 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?
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?
Find three repeater machines that will do the same work as a (× 64) machine. Draw them, or describe them using exponents.
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?
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?

Shikha has an order from a golf course designer to put palm trees through a (× 23) machine and then through a (× 33) machine. She thinks she can do the job with a single repeater machine. What single repeater machine should she use?

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.

A particular star is at a distance of about 8.1 × 1013 km from the Earth. Assuring that light travels at 3 × 108 m per second, find how long does light takes from that star to reach the Earth.
