For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
For Exercises 111-114, use the graph of y = f x to answer the following. (See Example 10) a . Determine f − 2 . b . Determine f 3 . c . Find all x for which f x = − 1. d . Find all x for which f x = − 4. e . Determine the x -intercept s . f . Determine the y -intercept . g . Determine the domain of f . h . Determine the range of f
For Exercises 111-114, use the graph of
y
=
f
x
to answer the following. (See Example 10)
a
. Determine
f
−
2
.
b
. Determine
f
3
.
c
. Find all
x
for which
f
x
=
−
1.
d
. Find all
x
for which
f
x
=
−
4.
e
. Determine the
x
-intercept
s
.
f
. Determine the
y
-intercept
.
g
. Determine the domain of
f
.
h
. Determine the range of
f
A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?
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