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x varies directly as y and x varies inversely as the square of z, when y = 75 and x = 6, then z = 5. Find the value of x, when y = 24 and z = 4.
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?
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x varies directly as y and x varies inversely as the square of z, when...
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x varies directly as y and x varies inversely as the square of z, when...
Given that x varies directly as y and inversely as the square of z.
We can write the equation as:
x = k * y / z^2
where k is the constant of proportionality.

When y = 75 and x = 6, we can substitute these values in the equation and solve for k:
6 = k * 75 / 5^2
k = 6 * 25 / 75
k = 2

Now we can use this value of k to find x when y = 24 and z = 4:
x = 2 * 24 / 4^2
x = 3

Therefore, the value of x when y = 24 and z = 4 is 3.

Summary:
- x varies directly as y and inversely as the square of z.
- Using the given values of x, y, and z, we can solve for the constant of proportionality k.
- Then, we can use this value of k to find the value of x when other values of y and z are given.
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x varies directly as y and x varies inversely as the square of z, when y = 75 and x = 6, then z = 5. Find the value of x, when y = 24 and z = 4.a)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?
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