Assuming that y varies directly as the fourth power of x, fill in the missing values in the table of ordered pairs.
x 18.3 74.5 ?
y 29.6 ? 155
To solve this problem, we need to use the direct variation formula, which states that y varies directly as the fourth power of x. The formula can be written as y = kx^4, where k is the constant of variation.
To find the constant of variation, we can use any pair of values from the table. Let's choose the first pair, (18.3, 29.6):
29.6 = k(18.3)^4
Now, we can solve for k:
k = 29.6 / (18.3)^4
k ≈ 0.000018201
Now that we have found the constant of variation k, we can use it to fill in the missing values in the table.
For the second pair, we can use the formula to find y:
y = 0.000018201 * (74.5)^4
y ≈ 815.5
For the third pair, we can use the formula again:
y = 0.000018201 * (155)^4
y ≈ 82486
Therefore, the missing values in the table are:
x 18.3 74.5 155
y 29.6 815.5 82486