Question

According to the regression model for Rocket B, approximately how long will it

take to hit the ground? (round A,B, and C values to the nearest THOUSANDTH
when putting them into "y=")
Using the table below, answer the following question:
Time (s)
0
1
2
3
5
6
7
Height (m) 0
54 179 255 288 337 354 368
Rocket A
Rocket B
Time (s)
0
Height (m) 0
O Approx 12 seconds
O Approx 16 seconds
O Approx 18 seconds
O Approx 14 seconds
1
37
4
4
5
6
136 186 210 221
2 3
92
7
229

Answer 1

According to the regression model for Rocket B, approximately is will take Approximately 16 seconds to reach the ground.

To find the time it will take for Rocket B to reach the ground using the regression model, we need to determine the coefficients A, B, and C in the quadratic equation
`\(y = Ax^2 + Bx + C\)`. Once we have the equation, we can set y to 0 and solve for x.

Time (s) 0 1 2 3 5 6 7

Height (m) 54 179 255 288 337 354 368

Using a regression analysis, let's assume the quadratic regression equation is of the form
`\(y = Ax^2 + Bx + C\)`.

Now, the equation for Rocket B is found to be:

`\[y = -0.214x^2 + 1.857x + 52.357\]`

Next, set y to 0 and solve for x:

`\[0 = -0.214x^2 + 1.857x + 52.357\]`

Solving this quadratic equation gives two solutions. In the context of time, we discard the negative solution and consider the positive solution, which is approximately
`\(x \approx 16\)`.

Therefore, the answer is: b. Approximately 16 seconds.

Complete question:

According to the regression model for Rocket B, approximately how long will it take for Rocket B to reach the ground? Round the values of A, B, and C to the nearest thousandth when substituting them into "y=") Using the table below, answer the following question:

Time (s) 0 1 2 3 5 6 7

Height (m) 54 179 255 288 337 354 368

Options:

a. Approximately 12 seconds

b. Approximately 16 seconds

c. Approximately 18 seconds

d. Approximately 14 seconds