The population P of a culture of Pseudomonas aeruginoso bacteria is given by P = − 1718 t 2 + 82 , 000 t + 10 , 000 , where t is the time in hours since the culture was started. Determine the time(s) at which the population was 600,000. Round to the nearest hour.
The population P of a culture of Pseudomonas aeruginoso bacteria is given by P = − 1718 t 2 + 82 , 000 t + 10 , 000 , where t is the time in hours since the culture was started. Determine the time(s) at which the population was 600,000. Round to the nearest hour.
Solution Summary: The author calculates the population of Pseudomonas aeruginosa bacteria, based on t(s), which is given by P=-1718t
The population P of a culture of Pseudomonas aeruginoso bacteria is given by
P
=
−
1718
t
2
+
82
,
000
t
+
10
,
000
, where t is the time in hours since the culture was started. Determine the time(s) at which the population was 600,000. Round to the nearest hour.
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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