Franz borrowed a total of $10,000 . Part of the money was borrowed from a lending institution that charged 5.5 % simple interest. The rest of the money was borrowed from a friend to whom Franz paid 2.5 % simple interest. Franz paid his friend back after 9 months (0.75 yr) and paid the lending institution after 2 yr. If the total amount Franz paid in interest was $735 , how much did he borrow from each source?
Franz borrowed a total of $10,000 . Part of the money was borrowed from a lending institution that charged 5.5 % simple interest. The rest of the money was borrowed from a friend to whom Franz paid 2.5 % simple interest. Franz paid his friend back after 9 months (0.75 yr) and paid the lending institution after 2 yr. If the total amount Franz paid in interest was $735 , how much did he borrow from each source?
Franz borrowed a total of
$10,000
. Part of the money was borrowed from a lending institution that charged
5.5
%
simple interest. The rest of the money was borrowed from a friend to whom Franz paid
2.5
%
simple interest. Franz paid his friend back after 9 months (0.75 yr) and paid the lending institution after 2 yr. If the total amount Franz paid in interest was
$735
, how much did he borrow from each source?
6. Solve the system of differential equations using Laplace Transforms:
x(t) = 3x₁ (t) + 4x2(t)
x(t) = -4x₁(t) + 3x2(t)
x₁(0) = 1,x2(0) = 0
3. Determine the Laplace Transform for the following functions. Show all of your work:
1-t, 0 ≤t<3
a. e(t) = t2, 3≤t<5
4, t≥ 5
b. f(t) = f(tt)e-3(-) cos 4τ dr
4. Find the inverse Laplace Transform Show all of your work:
a. F(s) =
=
2s-3
(s²-10s+61)(5-3)
se-2s
b. G(s) =
(s+2)²
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