For all exercises in this exercise set, use a graphing calculator. Find the accumulated present value of each continuous income stream at rate R ( t ) , for the given time T and interest rate k , compounded continuously. R ( t ) = $ ( 2000 t + 7 ) , T = 30 yr , k = 4.5 %
For all exercises in this exercise set, use a graphing calculator. Find the accumulated present value of each continuous income stream at rate R ( t ) , for the given time T and interest rate k , compounded continuously. R ( t ) = $ ( 2000 t + 7 ) , T = 30 yr , k = 4.5 %
Solution Summary: The author calculates the accumulated present value of a continuous income stream at rate (2000t+7), for the time 30 years and interest rate 4.5% compound
For all exercises in this exercise set, use a graphing calculator.
Find the accumulated present value of each continuous income stream at rate
R
(
t
)
,
for the given time T and interest rate k, compounded continuously.
R
(
t
)
=
$
(
2000
t
+
7
)
,
T
=
30
yr
,
k
=
4.5
%
A company specializing in lubrication products for vintage motors produce two
blended oils, Smaza and Nefkov. They make a profit of K5,000.00 per litre of
Smaza and K4,000.00 per litre of Nefkov. A litre of Smaza requires 0.4 litres of
heavy oil and 0.6 litres of light oil. A litre of Nefkov requires 0.8 litres of heavy oil
and 0.2 litres of light oil. The company has 100 litres of heavy oil and 80 litres of
light oil. How many litres of each product should they make to maximize profits
and what level of profit will they obtain? Show all your workings.
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).
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