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 pm Jarvis Hall Science Wing 203
Didn’t pass your Gateway Quiz? Hereare 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, (email@example.com) to set up a date and time
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)
Example of solving a formula for a variable: Understand 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. 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 letx = 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 – 30 = 4x + 30 – 30 (subtract 30 from both sides) (divide both sides by 4) 102 = x + 2x + x + 30 102 = 4x + 30(simplify right side) 72 = 4x(simplify both sides) 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”.)
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 • 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 (divide both sides by mr) (simplify right side)
Example 2: Solve the formula for T (Subtract P from both sides) (Simplify right side) (Divide both sides by PR) (Simplify right side)
Example 3: Solve the formula for P (Factor out P from both terms on the right side) (Divide both sides by 1 + RT) (Simplify the right side)
Reminders: • This homework on Section 2.6 is due at start of next class session. • Make sure you SIGN UP TO TAKE THIS WEEK’S GATEWAYif you haven’t passed it yet. (in open lab) • 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: 155/2 miles (or 127.5)