The depreciation rate for a car is given by r = 1 − − S C 1 / π , where S is the value of the car after n years, and C is the initial cost. Determine the depreciation rate for a car that originally cost $ 22 , 990 and was valued at $ 11 , 500 after 4 yr. Round to the nearest tenth of a percent.
The depreciation rate for a car is given by r = 1 − − S C 1 / π , where S is the value of the car after n years, and C is the initial cost. Determine the depreciation rate for a car that originally cost $ 22 , 990 and was valued at $ 11 , 500 after 4 yr. Round to the nearest tenth of a percent.
Solution Summary: The author calculates the depreciation rate of a car by the formula: r=1-(SC)1/n.
The depreciation rate for a car is given by
r
=
1
−
−
S
C
1
/
π
,
where
S
is the value of the car after
n
years, and
C
is the initial cost. Determine the depreciation rate for a car that
originally cost
$
22
,
990
and was valued at
$
11
,
500
after 4 yr. Round to the nearest tenth of a percent.
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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