example
In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 6 lbs of pressure to break a board 3 feet long, how many pounds of pressure will it take to break a board that is 8 feet long?
a) Set up the formula.
b) Find the missing constant, k, using the first set of data given.
c) Using the formula and constant, k, find the missing value in the problem.
Solution
a) Here we're to find the amount of force needed to break a board. k, is the constant and l, is the length of the board.
b) 6 lbs is the amount of pounds of pressure to break a board of 3 feet which is the given. Plug in the given values to the appropriate variables. By multiplying the reciprocal of k over 3, k = 18
c) Now we know the constant, which is 18, next we plug in the constant in to the formula. Then plug in the 8 for l. By dividing 18 by 8 we get 2.25 lbs of pressure
EQUATION, TABLE, AND GRAPH
reflection
In this example, what we are trying to find is the amount of force that is need to break a certain length of a board. The problem is asking what amount of force is needed to a board that is the length of 8 feet long. The formula is needed is f=k/l. The variables are 'f' for the force, 'l' for length, and 'k' for the coefficient. In an inverse variation, the values of the two variables change in an opposite manner - as one value increases, the other decreases. To find the 'k' variable, we have to substitute 6 for 'f' and 3 for 'l', so we get 6=k/3, then we multiple the reciprocal. We get k=18. To answer the problem, we substitute 18 for 'k' and 8 for 'l'. Dividing the 18 by 8 and we get 2 1/4 which equals to 2.25 lbs of pressure. To break a board with a length of 8 feet we need 2.25 lbs of pressure. This problem is fairly simple with a formula that is easy to understand and not too complicated. Overall this problem is good for inverse variation.