# Hotmath

Write an equation of the line through point (2, 1) that is perpendicular to 4
*
x
*
– 2
*
y
*
= 3.

The value of a product in 1998 is $20,400. The value is expected to decrease $2000 per year during the next 5 years. Write a linear equation that gives the dollar value
*
V
*
of the product in terms of the year
*
t
*
. (Let
*
t
*
= 8 represent 1998.)

Use a graphing utility to graph the parabolas and find their points of intersection. Find an equation of the line through the points of intersection and sketch its graph in the same viewing rectangle.

*
y
*
=
*
x
*
^{
2
}

*
y
*
= 4
*
x
*
–
*
x
*
^{
2
}

Find an equation of the graph that consists of all the points (
*
x
*
,
*
y
*
) whose distance from the origin is
*
K
*
times (
*
K
*
1) the distance from (2, 0).

If
*
f
*
(
*
x
*
) = 2
*
x
*
^{
2
}
+ 3
*
x
*
– 4, find
*
f
*
(0),
*
f
*
(2),
*
f
*
(√ 2),
*
f
*
(1 + √ 2),
*
f
*
(–
*
x
*
),
*
f
*
(
*
x
*
+ 1), 2
*
f
*
(
*
x
*
), and
*
f
*
(2
*
x
*
).
*
*

Express the surface area of an open rectangular box with volume 3 m
^{
3
}
and a square base as a function of the length of a side of the base. State the domain of the function.

Biologists have found that the chirping rate of crickets is related to temperature, and that the relationship is close to linear. If one species of cricket chirps 113 times per minute at 70
F and 173 times per minute at 80
F, find a linear equation that models the temperature
*
T
*
as a function of the number
*
N
*
of chirps per minute. What does the slope of this line represent?

Graph the equation

*
y
*
=
*
x
*
^{
2
}
– 4
*
x
*
+ 3

using transformations of the graph of
*
y
*
=
*
x
*
^{
2
}
.

If
*
f
*
(
*
x
*
) = 2
*
x
*
^{
2
}
–
*
x
*
and
*
g
*
(
*
x
*
) = 3
*
x
*
+ 2, find
*
f
*
*
g
*
,
*
g
*
*
f
*
,
*
f
*
*
f
*
, and
*
g
*
*
g
*
, and their domains.

Show that
*
f
*
and
*
g
*
are inverse functions (a) algebraically and (b) graphically.

*
f
*
(
*
x
*
) = 5
*
x
*
+ 1

*
g
*
(
*
x
*
) = (
*
x
*
– 1)/5