Juan borrows $ 100 , 000 to pay for medical school. He borrows part of the money from the school whereby he will pay 4.5 % simple interest. He borrows the rest of the money through a government loan that will charge him 6 % interest. In both cases, he is not required to pay off the principal or interest during his 4 yr of medical school. However, at the end of 4 yr , he will owe a total of $ 19 , 200 for the interest from both loans. How much did he borrow from each source?
Juan borrows $ 100 , 000 to pay for medical school. He borrows part of the money from the school whereby he will pay 4.5 % simple interest. He borrows the rest of the money through a government loan that will charge him 6 % interest. In both cases, he is not required to pay off the principal or interest during his 4 yr of medical school. However, at the end of 4 yr , he will owe a total of $ 19 , 200 for the interest from both loans. How much did he borrow from each source?
Solution Summary: The author calculates the amount of money borrowed by Juan from the school and the government that will charge him 6% interest.
Juan borrows
$
100
,
000
to pay for medical school. He borrows part of the money from the school whereby he will pay
4.5
%
simple interest. He borrows the rest of the money through a government loan that will charge him
6
%
interest. In both cases, he is not required to pay off the principal or interest during his
4
yr
of medical school. However, at the end of
4
yr
, he will owe a total of
$
19
,
200
for the interest from both loans. How much did he borrow from each source?
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
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