Coming Up:
Today: Lecture on Section 2.5
More word problems!
Next two class sessions after today:
1.
2.
Review for Test 1
Test 1 on Mon. November 9th (MW) or
Thursday November 12th (T/TH)
Test 1 is on all sections covered this semester up to
this point (including material covered on Quizzes 1 and
2, plus sections 2.4 and 2.5)
REMINDER:
If you haven’t passed the Gateway, you can
retake it once each week until you do.
Gateway Quiz Retake Facts
• MUST pass with 100% to pass Math 010
• So far: Two attempts to pass in class
– If not passed during one of those two attempts:
• One attempt per week for rest of semester
– Eight weeks = eight chances to pass
• Outside of class time: scheduled times will be given
today and posted on bulletin boards.
Didn’t pass your Gateway Quiz?
Here are the next steps:
• Go over the incorrect answers on your previous
attempts with a TA (and get their signature) in
the Math TLC Open Lab (JHSW 203).
• Take another Practice Gateway Quiz.
– Go over any incorrect answers on the practice
attempts with a TA in the Math TLC Open Lab
• Have a TA in the Math TLC Open Lab sign you
up for a retake time
Gateway Quiz Retake Times
(One new attempt allowed per week, beginning November 2)
• Mondays
– 1:25 pm
– 2:30 pm
• Tuesdays
– 1:25 pm
– 3:35 pm
• Wednesdays
– 10:10 am
– 11:15 am
• Thursdays
– 10:10 am
– 11:15 pm
SIGN UP IN THE MATH TLC OPEN LAB!
If NONE of the above times work for you…
email Krystle Mayer, Math TLC Coordinator (JHSW 201),
to set up a date and time.
Any questions on the
Section 2.4 homework
that was due today?
Please
CLOSE
YOUR LAPTOPS,
and turn off and put away your
cell phones,
and get out your notetaking materials.
Section 2.5
A formula is an equation that states a
relationship among two or more variables.
Examples of Formulas
A = lw
I = PRT
(Area of a rectangle = length · width)
(Simple Interest = Principal · Rate · Time)
P=a+b+c
d = rt
V = lwh
(Perimeter of a triangle = side a + side b + side c)
(distance = rate · time)
(Volume of a rectangular solid = length · width · height)
Examples of Using a Formula:
Problem: Find the area of a rectangle with a length of 5 inches and a
width of 10 inches using the formula A = lw :
Solution: l = 5 and w = 10, so A = 5·10 = 50 square inches
Problem: Find the distance traveled in 4 hours by an airplane flying
at a speed of 720 mph using the formula d = rt :
Solution: r = 720 and t = 4, so d = 720·4 = 2880 miles
(distance = rate · time)
Problem from today’s homework:
A flower bed is in the shape of a triangle with one side
twice the length of the shortest side, and the third side is
30 feet more than the length of the shortest side. Find the
dimensions if the perimeter is 102 feet.
Understand
DRAW A PICTURE!!!
Read and reread the problem. Recall that the formula for the
perimeter of a triangle is P = a + b + c .where a, b and c represent the
lengths of the three sides of the triangle.
If we let x = the length of the shortest side, then
2x = the length of the second side, and
x + 30 = the length of the third side.
Example (cont.)
Translate
Formula: P = a + b + c
x = the length of the shortest side (a)
2x = the length of the second side (b)
x + 30 = the length of the third side (c)
P = perimeter = 120 feet (given in the problem statement.)
Substitute these items into the formula to get:
102 = x + 2x + x + 30
Example (cont.)
Solve
102 = x + 2x + x + 30
102 = 4x + 30
(simplify right side)
102 – 30 = 4x + 30 – 30
(subtract 30 from both sides)
72 = 4x
(simplify both sides)
72 4 x

4
4
(divide both sides by 4)
18 = x
(simplify both sides)
Example (cont.)
Interpret
Check: If the shortest side of the triangle is 18
feet, then the second side is 2(18) = 36 feet, and the
third side is 18 + 30 = 48 feet. This gives a
perimeter of P = 18 + 36 + 48 = 102 feet, the
correct perimeter. Always check your answer!
State: The three sides of the triangle have lengths
of 18 feet, 36 feet, and 48 feet.
Problem from today’s homework:
(As we do this problem, we will review adding and multiplying
decimal numbers without using a calculator.)
Problem from today’s homework:
(To do this problem without using a calculator, convert the decimal
5
1
number 1.5 into the mixed fraction 10 .)
Note: The formula for the volume of a tank like this is
V = l∙w∙h
where V = volume, l = length, w = width and h = height.
(You will not have to memorize formulas for tests or quizzes – we will
give them to you. If you need a formula for a homework problem, click
“help me solve this”.)
It is often necessary to rewrite a formula so that
it is solved for one of the variables.
This is accomplished by isolating the designated
variable on one side of the equal sign.
Steps for solving formulas
1)
2)
3)
4)
5)
Multiply to clear fractions.
Use distributive property to remove grouping
symbols like parentheses.
Combine like terms to simply each side.
Get all terms containing specified variable on
the same time, other terms on opposite side.
Isolate the specified variable by dividing by its
number coefficient on both sides of the
equation.
Example: Solve the following formula for n
T  mnr
T
mnr

mr mr
T
n
mr
(divide both sides by mr)
(simplify right side)
Example 2: Solve the formula for T
A  P  PRT
(Subtract P from both sides)
A  P  P  P  PRT
(Simplify right side)
A  P  PRT
A  P PRT
(Divide both sides by PR)

PR
PR
A P
(Simplify right side)
T
PR
Example 3: Solve the formula for P
A  P  PRT
A  P (1  RT )
(Factor out P from both terms on
the right side)
A
P(1  RT )
(Divide both sides by 1 + RT)

1  RT
1  RT
A
(Simplify the right side)
P
1  RT
Problem from today’s homework:
Problem from today’s homework:
Problem from today’s homework:
Reminders:
This homework on Section 2.5 is due
at start of next class session.
2. Make sure you SIGN UP TO TAKE
THIS WEEK’S GATEWAY (in open
lab) if you haven’t passed it yet.
3. You can start taking Practice Test 1
any time now, and you can take it as
many times as you want before the
test which will be given the class
session after next.
1.
Note to instructors:
The remaining slides contain additional problems from today’s homework that you
may want to cover if time allows.
Problem from today’s homework:
Problem from today’s homework:
155/2 miles (or 127.5)
Problem from today’s homework:
Problem from today’s homework: