SOLUTION: The repulsive force f between the north poles of two magnets is inversely proportional to the square of the distance d between them. If the repulsive force is 29 lb when the distan

Question 951584: The repulsive force f between the north poles of two magnets is inversely proportional to the square of the distance d between them. If the repulsive force is 29 lb when the distance is 25 in., find the repulsive force when the distance is 5 in.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for inverse variation between force and distance is:

f = k / d^2

when f = 29 and d = 25, the formula becomes:

29 = k / 25^2

solve for k to get k = 29 * 25^2 = 18125.

k always stays the same which is why it's called the constant of variation.

when d = 5, the formula of y = k / d^2 becomes y = 18125 / 5^2.

solve for y to get y = 725.

when the distance between the objects is 5, the repulsive force is equal to 725 pounds.

when the distance became 1/5 as much, the repulsive force became 25 times as high.

29 = 18125 / 25^2

725 = 18125 / 5^2

when you solve for k in the formula of f = k / d^2, you get k = f*d^2.

f * d^2 will always be equal to k which will always be equal to 18125, based on the fact that, when f = 29, d was equal to 25.

29 * 25^2 = 29 * 625 = 18125.

725 * 5^2 = 725 * 25 = 18125.

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