Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a $ 60 , 000 taxable value in a municipality with a 19 mil tax rate would require 0 .019 $60,000 =$1140 in property taxes. In one county, homeowners pay a flat tax of $172 plus a rate of 19 mil on the taxable value of a home. a. Write a linear function that represents the total property tax T x for a home with a taxable value of x dollars. b. Evaluate T 80 , 000 and interpret the meaning in the context of this problem.
Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a $ 60 , 000 taxable value in a municipality with a 19 mil tax rate would require 0 .019 $60,000 =$1140 in property taxes. In one county, homeowners pay a flat tax of $172 plus a rate of 19 mil on the taxable value of a home. a. Write a linear function that represents the total property tax T x for a home with a taxable value of x dollars. b. Evaluate T 80 , 000 and interpret the meaning in the context of this problem.
Millage rate is the amount per
$1000
that is often used to calculate property tax. For example, a home with a
$
60
,
000
taxable value in a municipality with a 19 mil tax rate would require
0
.019
$60,000
=$1140
in property taxes. In one county, homeowners pay a flat tax of
$172
plus a rate of 19 mil on the taxable value of a home.
a. Write a linear function that represents the total property tax
T
x
for a home with a taxable value of
x
dollars.
b. Evaluate
T
80
,
000
and interpret the meaning in the context of this problem.
A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related
rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt=
feet/sec.
(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt=
feet/sec.
Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z²
= x²+
+12
x
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
2z
dz
dt
dx
2x.
+2y
dt
dx
dy
dz
x
+y
dt
dt
dt
2z
dy
dt
×
dx
(x+y
dt
dy
dt
An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters.
9
ground level
Assume that x is increasing at a rate of 3 meters/sec.
(a) Write as a function of x: 0=
(b) When x=10, the angle is changing at a rate of
rad/sec.
(c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R?
○ Yes
○ No
College Algebra with Modeling & Visualization (5th Edition)
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