A football was punted. Its height h above the ground at time t is given by the following table and can be modeled by a parabola of the form h(t)=at2+bt+c Time t (seconds) Height h (feet) t=0.5 31 t=1 51 t=2 67 (a) Write three equations using the given information. (b) Find the equation of the parabola. Show the matrix setup. (Note: RREF method may not be used here.) (c) Find the time and the height of the ball when it is at its maximum height. (d) Find the hang time of the punt (the time it takes before the ball hits the ground). Write an appropriate equation that leads to your answer.
A football was punted. Its height h above the ground at time t is given by the following table and can be modeled by a parabola of the form h(t)=at2+bt+c
| Time t (seconds) | Height h (feet) |
| t=0.5 | 31 |
| t=1 | 51 |
| t=2 | 67 |
(a) Write three equations using the given information.
(b) Find the equation of the parabola. Show the matrix setup. (Note: RREF method may not be used here.)
(c) Find the time and the height of the ball when it is at its maximum height.
(d) Find the hang time of the punt (the time it takes before the ball hits the ground). Write an appropriate equation that leads to your answer.
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QC: The Fresh Sandwich specializes in chicken, fish, and ham sandwiches. In April, May, and June 2012, they sold the following quantities. Write three equations using the given information and then find the selling price of each of the three types of sandwiches using appropriate matrix operations. Show the matrix setup. (Note: RREF method may not be used here.)
| Sale volume in | hundreds | ||
| april | may | june | |
|
chicken |
8 | 7 | 4 |
| fish | 11 | 8 | 6 |
| ham | 6 | 7 | 3 |
| monthly revenue in hundreds from the sale of these sandwhiches | $164 | $141 | $86 |
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