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x varies directly as the square of y and inversely as the cube root of z and x = 2, when y = 4, z= 8. What is the value of y when x = 3, and z = 27?
- a)6, -6
- b)4, -4
- c)1, -1
- d)5, -5
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
x varies directly as the square of y and inversely as the cube root of...
Given:
Direct variation relationship = x ∝ y2.
Inverse variation relationship = x ∝ 1/z(1/3).
Concept used:
In variation problems, establishing the constant of proportionality allows transformation into equality.
Calculations:
x = k (y2/z(1/3)) where k is the constant of proportionality.
Substituting x = 2, y = 4, and z = 8
⇒ 2 = k((42) ÷ (8(1/3))
⇒ k = 0.25
Now substituting x = 3, z = 27, and k = 0.25
⇒ 3 = 0.25(y2/(27(1/3))).
⇒ 3 = 0.25(y2/3)
⇒ y2 = 900/25
⇒ y2 = ±36.
⇒ y = ±6.
∴ y can be either 6 or -6.
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x varies directly as the square of y and inversely as the cube root of z and x = 2, when y = 4, z= 8. What is the value of y when x = 3, and z = 27?a)6, -6b)4, -4c)1, -1d)5, -5Correct answer is option 'A'. Can you explain this answer?
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