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**Proportion Inverse proportion Y is Inversely proportional to x**

Y varies inversely as x

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Inverse proportion Y is inversely proportional to the square of x Y varies inversely as the square of x

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Inverse proportion 1 Y is inversely proportional to the square root of x Y varies inversely as the square root of x

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2 If y is inversely proportional to the square of x and y = 2 when x = 3, find (i) y when x = 12 (ii) x when y = 0.5

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3 The Pressure P of a given mass of gas varies inversely as the volume V. When P = 250 N/m2, V = 4 m3. a) Find the volume when the pressure is 400 N/m2 b) Find the pressure when the Volume is 20 m3.

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4 Example The force F between two magnets is inversely proportional to the square of the distance x between them. If F = 9 when x = 2, find F when x = 3.

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5 Example The Force of attraction F between two magnets varies inversely as the square of the distance d, between them. When the magnets are 3cm apart the force of attraction is 12 newtons. How far apart are they if the attractive force is 18 newtons?

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6 Example The life expectancy of a rat varies inversely as the square of the density d of poison distributed around the home. When the density of poison distributed is 1 g/m2 the life expectancy is 50 days. How long will he survive if the density of poison is 5 g/m2?

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**7 Example y is inversely proportional to the square of x.**

When y = 3, x = 2 Find the value of y when x = 4

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**8 Example y is inversely proportional to the square root of x.**

When y = 10, x = 4. Find the value of y when x = 25.

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**9 Example y is inversely proportional to the cube of x.**

When y = 18, x = 3. Find the value of y when x = 6.

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10 Example The illumination, L, provided by a torch is inversely proportional to the square of the distance, d, from the torch. When L = 2, d = 10. (a) Find an equation expressing L in terms of d. (b) Find the value of L when d = 2. (c) Find the value of d when L = 8.

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11 Example M and G are positive quantities. M is inversely proportional to G. When M = 90, G = 40. Find the value of M when G = M.

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12 Example y is inversely proportional to the square root of x. When x = 16, y = 2 What is the value of y when x = 0.25?

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13 Example In a circuit, the resistance, R ohms, is inversely proportional to the current, I amps. When the resistance is 12 ohms, the current in the circuit is 8 amps. Find an equation connecting R and I. Find the current when the resistance in the circuit is 6.4 ohms.

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