A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and theposition of the ball was measured each time. The coordinates obtained are shown in the table. (x and y are measured in feet.)Horizontal distance, x1530Height, y6.09.812.5(a) Use a system of equations to find the equation of the parabola y = ax2 + bx +c that passes through the three points. Solve the systemusing matrices. (Round each coefficient to four decimal places.)y =(b) Use a graphing utility to graph the parabola. (c) Graphically approximate the maximum height of the ball and the point at which the ball struck the ground. (Round your answers to thenearest whole number.)maximum heightftpoint at which the ball strikes the groundft(d) Analytically find the maximum height of the ball and the point at which the ball struck the ground. (Round your answers to three decimalplaces.)maximum heightftpoint at which the ball strikes the groundft(e) Compare your results from parts (c) and (d).The results are similar.The results are considerably different.

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A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (x and y are measured in feet.) Horizontal distance, x 15 30 Height, y 6.0 9.8 12.5 (a) Use a system of equations to find the equation of the parabola y = ax2 + bx + c that passes through the three points. Solve the system using matrices. (Round each coefficient to four decimal places.) y = (b) Use a graphing utility to graph the parabola.

A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. (x and y are measured in feet.) Horizontal distance, x 15 30 Height, y 6.0 9.8 12.5 (a) Use a system of equations to find the equation of the parabola y = ax2 + bx + c that passes through the three points. Solve the system using matrices. (Round each coefficient to four decimal places.) y = (b) Use a graphing utility to graph the parabola.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the
position of the ball was measured each time. The coordinates obtained are shown in the table. (x and y are measured in feet.)
Horizontal distance, x
15
30
Height, y
6.0
9.8
12.5
(a) Use a system of equations to find the equation of the parabola y = ax2 + bx +c that passes through the three points. Solve the system
using matrices. (Round each coefficient to four decimal places.)
y =
(b) Use a graphing utility to graph the parabola.

(c) Graphically approximate the maximum height of the ball and the point at which the ball struck the ground. (Round your answers to the
nearest whole number.)
maximum height
ft
point at which the ball strikes the ground
ft
(d) Analytically find the maximum height of the ball and the point at which the ball struck the ground. (Round your answers to three decimal
places.)
maximum height
ft
point at which the ball strikes the ground
ft
(e) Compare your results from parts (c) and (d).
The results are similar.
The results are considerably different.

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