Advertisements
Advertisements
Question
y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.
Solution
It is given that y varies directly as square root of x i.e. `y α sqrtx`
∴ \[y = k\sqrt{x}\] , where k is constant of variation
When x = 16, y = 24.
∴ \[\ 24 = k \times \sqrt{16}\]
⇒ 24 = 4k
⇒ k = 6
So, the equation of variation is \[y = 6\sqrt{x}\]
Thus, the constant of variation is 6 and the equation of variation is \[y = 6\sqrt{x}\].
RELATED QUESTIONS
Write the following statement using the symbol of variation.
Circumference (c) of a circle is directly proportional to its radius (r).
Write the following statement using the symbol of variation.
Consumption of petrol (l) in a car and distance travelled by that car (d) are in direct variation.
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 |
If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14
If n varies directly as m, complete the following table.
| m | 3 | 5 | 6.5 | ______ | 1.25 |
| n | 12 | 20 | ______ | 28 | ______ |
The total remuneration paid to labourers, employed to harvest soyabeen is in direct variation with the number of labourers. If remuneration of 4 labourers is ₹ 1000, find the remuneration of 17 labourers.
If x and y vary directly, find the values of x, y, and z:
| x | 3 | x | y | 10 |
| y | 36 | 60 | 96 | z |
A truck consumes 28 litres of diesel for moving through a distance of 448 km. How much distance will it cover in 64 litres of diesel?
For 100 km, a taxi charges ₹ 1,800. How much will it charge for a journey of 120 km?
If 27 identical articles cost ₹ 1,890, how many articles can be bought for ₹ 1,750?
