can sone one give me Variations whole chapter notes for 8th class cbse
Answers
Explanation:
Question 1:
Write the following statements using the symbol of variation.
(1) Circumference (c) of a circle is directly proportional to its radius (r).
(2) Consumption of petrol (l) in a car and distance travelled by that car (d) are in direct variation.
ANSWER:
(1)
Circumference (c) of a circle is directly proportional to its radius (r). This statement is written as
c∝r
(2)
Consumption of petrol (l) in a car and distance travelled by that car (d) are in direct variation. This statement is written as
l∝d
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Question 2:
Complete the following table considering that the cost of apples and their number are in direct variation.
Number of apples (x) 1 4 ... 12 ...
Cost of apples (y) 8 32 56 ... 160
ANSWER:
It is given that the cost of apples (y) and number of apples (x) are in direct variation.
∴y∝x⇒y=kx, where k is constant of variation
When x = 1, y = 8.
∴ 8 = k × 1
⇒ k = 8
So, the equation of variation is
y = 8x
When y = 56,
56 = 8x
⇒ x = 7
When x = 12,
y = 8 × 12 = 96
When y = 160,
160 = 8x
⇒ x = 20
The complete is given below.
Number of apples (x) 1 4 7 12 20
Cost of apples (y) 8 32 56 96 160
Question 3:
If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14
ANSWER:
It is given that m∝n.
∴ m = kn, where k is constant of variation
When m = 154, n = 7.
∴ 154 = k × 7
⇒ k = 1547 = 22
Therefore, the equation of variation is m = 22n.
When n = 14,
m = 22 × 14 = 308
Thus, the value of m is 308.
Question 4:
If n varies directly as m, complete the following table.
m 3 5 6.5 ... 1.25
n 12 20 ... 28 ...
ANSWER:
It is given that n varies directly as m i.e. n∝m.
∴ n = km, where k is constant of variation
When m = 3, n = 12.
∴ 12 = k × 3
⇒ k = 4
So, the equation of variation is n = 4m.
When m = 6.5,
n = 4 × 6.5 = 26
When n = 28,
28 = 4n
⇒ n = 7
When m = 1.25,
n = 4 × 1.25 = 5
The complete table is given below.
m 3 5 6.5 7 1.25
n 12 20 26 28 5
Answer: