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Both x and y are said to vary ______ with each other if for some positive number k, xy = k
Solution:
The table below depicts a relationship described by the expression xy = k.
x |
0.002 |
0.004 |
0.008 |
0.016 |
0.05 |
y |
500 |
250 |
125 |
62.5 |
31.25 |
xy = k only if
x ∝ 1/y
From the table we find,
xy = 0.002 × 500 = 0.004 × 250 = 0.008 × 125 = 0.06 × 62.5 = 0.05 × 31.25 = 1 = k
Hence x and y are inversely proportional to each other.
✦ Try This: Establish the type of proportionality between the variables p and q.
p |
1 |
2 |
3 |
4 |
5 |
q |
7 |
14 |
21 |
28 |
35 |
To establish the type of proportionality between the two variables we have to ascertain one of the two types given below:
1) x ∝ 1/y
2) x ∝ y
If x ∝ y, then
x/y = k where k is a +ve proportionality constant
x/y = 1/7 = 2/14 = 3/21 = 4/28 = 5/35 = 1/7 = k
If x ∝ 1/y, then
xy = 1 × 7 ≠ 2 × 14 ≠ 3 × 21 ≠ 4 × 28 ≠ 5 × 35 ≠ k
Hence we can conclude that x and y are directly proportional.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13
NCERT Exemplar Class 8 Maths Chapter 10 Problem 21
Both x and y are said to vary ______ with each other if for some positive number k, xy = k
Summary:
Both x and y are said to vary inversely with each other if for some positive number k, xy = k
☛ Related Questions:
- x and y are said to vary directly with each other if for some positive number k, ______ = k
- Two quantities are said to vary ______ with each other if they increase (decrease) together in such . . . .
- Two quantities are said to vary ______ with each other if an increase in one causes a decrease in t . . . .
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