if z varies directly as cude x and inversely as the square y when z=10 when x=2 and y=5,find z when x=3 and y=2
Answer:
Here's a step-by-step solution to find the value of z when x=3 and y=2 using the given equation:
1. Start with the equation: z = k * (x^3 / y^2)
2. Substitute the given values: z = k * (2^3 / 5^2)
3. Simplify the exponents: z = k * (8 / 25)
4. Multiply both sides of the equation by 25/8 to solve for k:
(25/8) * z = k * (8 / 25) * (25/8)
(25/8) * z = k
5. Substitute the given values to find k: 10 = k * (2^3 / 5^2)
6. Simplify the equation: 10 = k * (8 / 25)
7. Multiply both sides of the equation by 25/8 to solve for k:
(25/8) * 10 = k * (8 / 25) * (25/8)
31.25 = k
8. Now that we have the value of k, substitute it back into the original equation:
z = 31.25 * (3^3 / 2^2)
9. Simplify the exponents: z = 31.25 * (27 / 4)
10. Multiply the numbers: z = 31.25 * 6.75
11. Calculate the final result: z ≈ 210.94
Therefore, when x=3 and y=2, the value of z is approximately 210.94.
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