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Q(1) A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some...

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Basic Math

Q(1) A natural history museum borrows $2,000,000 at simpleannual interest to purchase new exhibits. Some of the money isborrowed at 6%, some at 7.5%, and some at 8.5%. Use a system oflinear equations to determine how much is borrowed at each rategiven that the total annual interest is $137,000 and the amountborrowed at 7.5% is four times the amount borrowed at 8.5%. Solvethe system of linear equations using matrices.

Q(2) Use a system of equations to find the cubic function f(x) =ax3 + bx2 + cx + d  that satisfiesthe equations. Solve the system using matrices.

f(?1) = 3

f(1) = 5

f(2) = 30

f(3) = 95

Q(3) An object moving vertically is at the given heights at thespecified times. Find the position equation

s = 1/2at2 + v0t + s0 for theobject.

At t = 1 second, s = 136 feet

At t = 2 seconds, s = 108 feet

At t = 3 seconds, s = 48 feet

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