Question 951584
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.