• Today: Lecture on Section 2.6: More word problems!

• Next class session: Review for Test 1 (covers everything since the beginning of the semester, including 2.5 and 2.6 on word problems)

• Class session after that: Test 1

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• Two attempts to pass in class

– If not passed during those two attempts:• One attempt per week

– Eight weeks = eight chances to pass

• Outside of class time

Math TLC Open Lab open M-Th 8:00 am to 7:30 pmJarvis Hall Science Wing 203

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(Beginning Monday, October 29)

• Mondays– 2:30 pm– 3:35 pm

• Tuesdays– 1:25 pm– 3:35 pm

• Wednesdays– 10:10 am– 11:15 am

• Thursdays– 10:10 am– 11:15 am

SIGN UP IN THE MATH TLC OPEN LAB!If NONE of the above times work for you…

email Krystle Mayer, Math TLC Coordinator, (mayerkr@uwstout.edu) to set up a date and time

Any questions on the Section 2.5 homework that

was due today?

Please

CLOSE

YOUR LAPTOPS,and turn off and put away your

cell phones,

and get out your note-taking materials.

Section 2.6

A formula is an equation that states a relationship among two or more variables.

Examples of Formulas

A = lw (Area of a rectangle = length · width)

I = PRT (Simple Interest = Principal · Rate · Time)

P = a + b + c (Perimeter of a triangle = side a + side b + side c)

d = rt (distance = rate · time)

V = lwh (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:

Example of solving a formula for a variable:

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

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.

DRAW A PICTURE!!!

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)

4

4

4

72 x (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

number 1.5 into the mixed fraction .)

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”.)

5 10

1

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 formulas1) Multiply to clear fractions.

2) Use distributive property to remove grouping symbols like parentheses.

3) Combine like terms to simply each side.

4) Get all terms containing specified variable on the same time, other terms on opposite side.

5) Isolate the specified variable by dividing by its number coefficient on both sides of the equation.

Example: Solve the following formula for n

mnrT

mr

mnr

mr

T (divide both sides by mr)

nmr

T (simplify right side)

Example 2: Solve the formula for T

PRTPA PRTPPPA (Subtract P from both sides)

PRTPA (Simplify right side)

PR

PRT

PR

PA

(Divide both sides by PR)

TPR

PA

(Simplify right side)

Example 3: Solve the formula for P

PRTPA )1( RTPA (Factor out P from both terms on

the right side)

RT

RTP

RT

A

1

)1(

1(Divide both sides by 1 + RT)

PRT

A

1(Simplify the right side)

Problem from today’s homework:

Problem from today’s homework:

Problem from today’s homework:

Reminders:1. This homework on Section 2.6 is due

at start of next class session.2. Make sure you SIGN UP TO TAKE

THIS WEEK’S GATEWAY if you haven’t passed it yet. (in open lab)

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.

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: