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.
(a) Which two machines hooked together do the same work a (×10²) machine does? Is there more than one arrangement of two machines that will work?
(b) Which stretching machine does the same work as two (× 2) machines hooked together?
Solution:
Given, 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.
We have to find the two machines hooked together to do the same work as ( ×10²) machine.
We have to find if there is more than one arrangement of two machines that will work.
Let the input be x.
So, x × 10²
Output = x100
To get the same work as the (×10²) machine, hook (×2²) and (×5²) machine.
Input = x
Output = x × 2² × 5²
= x × 4 × 25
=100x
To get the same work as the (×10²) machine, hook (×50¹) and (×2¹) machine.
Input = x
Output = x × 50¹ × 2¹
= x × 50 × 2
= 100x
From the two examples, it is clear that more than one arrangement will work.
We have to find which stretching machine does the same work as two (× 2) machines hooked together.
According to the question,
Two machines of (×2) are hooked together, with input of first as output of second.
Input of first machine = x
Output = x × 2 × 2
= x × 4
= 4x
We observe that the (×4) machine will work exactly the same as two (× 2) machines hooked together.
✦ Try This: 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 two machines hooked together do the same work a ( ×10³) machine does? Is there more than one arrangement of two machines that will work?
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12
NCERT Exemplar Class 8 Maths Chapter 8 Problem 148
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. (a) Which two machines hooked together do the same work a (×10²) machine does? Is there more than one arrangement of two machines that will work, (b) Which stretching machine does the same work as two (× 2) machines hooked together?
Summary:
(a) Two machines (×2²) and (×5²) hooked together do the same work a ( ×10²) machine does. There is more than one arrangement of two machines that will work, (b) (×4) stretching machine does the same work as two (× 2) machines hooked together.
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