The speed, p, at which a container empties is inversely proportional in the radius squared, r, of its cross-section. If p=5 when r=2, find the value of p when r=5?
Let’s write that relationship as a formula: p = k x (1 / r^2) Where k is the proportion constant we need to find. When p=5 and r=2, let’s find out what k is: 5 = k x ( 1 / 2^2) 5 = k x ( 1 / 4) 5 * 4 = k k = 20 Now that we know what k is, let’s rewrite that formula: P = 20 x (1 / r^2) Now let’s find p when r is 5. P = 20 x (1 / 5^2) p = 20 x (1 / 25) p = 20 / 25 (now lets simplify more) p = 4 / 5 Et voila!
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