x y
4 1
8 2
12 3
16 4
Compare the table of Object A and the equation y = 1/5 x of Object B. Which of the two moving objects has greater speed and by what factor? (round to nearest hundredth)
Responses
A Object A by a factor of 1.05Object A by a factor of 1.05
B Object B by a factor of 1.05Object B by a factor of 1.05
C Object A by a factor of 1.25Object A by a factor of 1.25
D Object B by a factor of 1.25
To determine the speed of the two objects, we need to compare the rates at which their y-values are changing with respect to the x-values.
For Object A:
The change in y (Δy) for every change in x (Δx) is:
Δy = 1 - 4 = -3
Δx = 4 - 0 = 4
For Object B:
The equation is y = (1/5)x, so the rate of change is the coefficient of x, which is 1/5.
Comparing the two rates of change:
Object A: Δy/Δx = -3/4
Object B: Rate of change = 1/5
The rate of change of Object A (Δy/Δx = -3/4) is greater than the rate of change of Object B (1/5). This means that Object A has a greater speed than Object B.
To find the factor by which Object A's speed is greater than Object B's, we can take the absolute value of the ratio of their rates of change:
Factor = |-3/4| / |1/5| = 15/4 ≈ 3.75
Rounded to the nearest hundredth, Object A has a greater speed by a factor of approximately 3.75.
The answer options are:
A Object A by a factor of 1.05Object A by a factor of 1.05.
B Object B by a factor of 1.05Object B by a factor of 1.05
C Object A by a factor of 1.25Object A by a factor of 1.25
D Object B by a factor of 1.25
Apologies for the confusion. Comparing the rates of change, we can determine the factor by which one object's speed is greater than the other.
Object A: Δy/Δx = -3/4
Object B: Rate of change = 1/5
Since Object A's rate of change is greater than Object B's rate, Object A will have a greater speed. However, the factor by which Object A's speed is greater or smaller is not provided in the options. Without the correct options, we cannot determine the exact factor. So, none of the given answer options are correct based on the provided information.