The quantity y is partly constant and partly varies inversely as the square of x. When x = 1, y = 11 and when x = 2, y = 5, find the value of y when…

Question

The quantity y is partly constant and partly varies inversely as the square of x. When x = 1, y = 11 and when x = 2, y = 5, find the value of y when x = 4.

Answer 1

The quantity y is partly constant and partly varies inversely as the square of x. When x = 1, y = 11 and when x = 2, y = 5, find the value of y when x = 4.

3 – 1/2 ✓
4
5 – 2/3
3 – 3/4

Explanation

“Partly constant, partly inversely as x²” gives y = c + k/x².

When x = 1: c + k = 11. When x = 2: c + k/4 = 5. Subtract: 3k/4 = 6, so k = 8, and c = 3.

So y = 3 + 8/x². When x = 4: y = 3 + 8/16 = 3 + 1/2 = 3½.

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