Question

Q(1): An object moving vertically is at the given heights at the specified times. Find the position equation

s = 1/2at² + v₀t + s₀

for the object At

t = 1 second, s = 141 feet

t = 2 seconds, s = 93 feet

t = 3 seconds, s = 13 feet

Q(2):

Find the equation

y = ax² + bx + c

of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

(0, 3), (1, 4), (2, 3)

Q(3):

A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 5%, some at 6.5%, and some at 7.5%. Use a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $129,750 and the amount borrowed at 6.5% is four times the amount borrowed at 7.5%. Solve the system of linear equations using matrices.

Answer 1