Suppose that of approximately 4 , 224 , 100 individuals of age 40 in the United States, 8038 die before the age of 41 and 4 , 216 , 062 survive. Determine the probability that a 40 -yr -old will live to age 41 .
Suppose that of approximately 4 , 224 , 100 individuals of age 40 in the United States, 8038 die before the age of 41 and 4 , 216 , 062 survive. Determine the probability that a 40 -yr -old will live to age 41 .
Solution Summary: The author calculates the probability that a 40-year-old will live up to age 41 if the number of 40 years old individuals is 4,224,100 in the United States, 8038 die before the age of 41, and
Suppose that of approximately
4
,
224
,
100
individuals of age
40
in the United States,
8038
die before the age of
41
and
4
,
216
,
062
survive. Determine the probability that a
40
-yr
-old will live to age
41
.
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).
University Calculus: Early Transcendentals (4th Edition)
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