x y
4 1
8 2
12 3
16 4
Compare the table of Object A and the equation y =
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 1.25Object B by a factor of 1.25
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To compare the speed of Object A and Object B, we can look at the rate of change of their y-values with respect to their x-values.
For Object A, the rate of change can be calculated by taking the difference in y-values (Δy) and dividing by the difference in x-values (Δx) for any two points.
For example, using the first two points (4, 1) and (8, 2), we have:
Δy_A = 2 - 1 = 1
Δx_A = 8 - 4 = 4
The rate of change for Object A is Δy_A/Δx_A = 1/4 = 0.25
For Object B, the equation is y = x. The rate of change is the coefficient of x, which is 1.
Comparing the rate of change for Object A (0.25) and Object B (1), we see that Object B has a greater rate of change, indicating that it has a greater speed.
To find the factor by which Object B's speed is greater than Object A's, we can divide the rate of change for Object B by the rate of change for Object A.
Object B's rate of change = 1
Object A's rate of change = 0.25
Factor = Object B's rate of change / Object A's rate of change = 1 / 0.25 = 4
Rounded to the nearest hundredth, the factor is 4. Therefore, Object B has a greater speed than Object A by a factor of 4.
The correct answer is D) Object B by a factor of 1.25