Question

question attempt: 1 of 2
y = 1.5x² - 125.3x + 2675
y = 21.3x + 105.5
y = 0.31x² + 0.82x
(a) which curve fits the data best?
○ figure 1 ○ figure 2 ○ figure 3
(b) use the equation of the best fitting curve from part (a) to predict the distance required to stop the train when it is travelling 30 kilometers per hour. give an exact answer, not a rounded approximation.
try one last time

Explanation:

Part (b) Solution:

Step 1: Identify the equation

The best - fitting curve from part (a) is Figure 3 with the equation \(y = 0.31x^{2}+0.82x\). We need to find the value of \(y\) when \(x = 30\) (since the speed of the train is 30 kilometers per hour).

Step 2: Substitute \(x = 30\) into the equation

Substitute \(x=30\) into \(y = 0.31x^{2}+0.82x\):
First, calculate \(x^{2}\) when \(x = 30\), \(x^{2}=30^{2}=900\).
Then, calculate \(0.31x^{2}\): \(0.31\times900 = 279\).
Next, calculate \(0.82x\): \(0.82\times30=24.6\).
Finally, add the two results together: \(y=279 + 24.6\).

Step 3: Calculate the sum

\(279+24.6=303.6\)

Answer:

The distance required to stop the train when it is traveling at 30 kilometers per hour is \(303.6\) (the unit is not specified in the problem, but it is related to the distance for stopping the train).