x varies directly as (y² +z²). At y = 1 and z = 2, the value of x is 15.
Posted on 17-02-2023
Ques - x varies directly as (y² +z²). At y = 1 and z = 2, the value of x is 15. Find the value of z, when x = 39 and y = 2.
(a) 2
(b) 3
(c) 4
(d) 6
Solution -
x varies directly as y² +z²
= x ∝ y² +z²
Remove the sign of proportional and and a constent k.
Therefore,
x = k(y² +z²) ___________ (1)
Now,
Put the value of x, y, z in eq. 1.
x = k(y² +z²)
15 = k(1² +2²)
15 = 5k
k = 3
Again,
Put the value of k = 3, x = 39 and y = 2 in eq. 1.
x = k(y² +z²)
39 = 3(2² + z²)
39 = 3(4 + z²)
39 = 12 + 3z²
39 - 12 = 3z²
27 = 3z²
z² = 27/3
z² = 9
z = 3
Hence,
The correct answer is option (b) 3.
Thank You