Suppose y varies inversely with x and y = 5 when x = 7
Part A) Write an equation that models the variation.
Part B) Find x when y = 140.
Part A) The equation that models the variation is y = k/x, where k is the constant of variation. To find the value of k, we can use the initial values given when y = 5 and x = 7:
5 = k/7
5 * 7 = k
35 = k
Therefore, the equation that models the variation is y = 35/x.
Part B) To find x when y = 140, plug in y = 140 into the equation y = 35/x:
140 = 35/x
140x = 35
x = 35/140
x = 1/4
Therefore, when y = 140, x is equal to 1/4.