The force, F, needed to break a board in a martial arts class varies inversely with the length, L, of the board. If it takes 24 pounds of pressure to break a board 2.5 feet long, how many pounds of pressure would it take to break a board that is 18 inches long?
LF=k, so you want F such that
18F = (2.5*12)*24
watch the units -- you cannot just plug in inches and feet without making adjustments
To solve this problem, we can use the concept of inverse variation. Inverse variation is represented by the equation F = k/L, where F is the force, L is the length, and k is the constant of variation.
We are given that the force, F, needed to break a board varies inversely with the length, L. Thus, we can set up the proportional relationship as follows:
F = k/L
To find the constant of variation, k, we can substitute the given values:
24 = k/2.5
Let's solve for k:
k = 24 * 2.5
k = 60
Now that we have the constant of variation, we can use it to find the force needed to break a board that is 18 inches long.
F = k/L
Converting 18 inches to feet gives us 1.5 feet:
F = 60/1.5
F = 40
Therefore, it would take 40 pounds of pressure to break a board that is 18 inches long.
To solve this problem, we need to use the concept of inverse variation. In inverse variation, when one variable increases, the other variable decreases and vice versa. Mathematically, we can express inverse variation as:
F = k/L
Where F is the force needed to break the board, L is the length of the board, and k is a constant.
To find the constant of variation, k, we can plug in the given values:
24 = k/2.5
To solve for k, multiply both sides of the equation by 2.5:
2.5 * 24 = k
k = 60
Now that we have the constant of variation, we can use it to find the force, F, needed to break a board that is 18 inches long:
F = 60/18
Simplifying this equation, we find:
F = 20/6
Therefore, it would take approximately 3.33 pounds of pressure to break a board that is 18 inches long.