Coming Up: Today: Lecture on Section 2.5 More word problems!

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Presentation transcript:

Coming Up: Today: Lecture on Section 2.5 More word problems! Next two class sessions after today: Review for Test 1 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 10 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. Math TLC Open Lab Jarvis 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 (One new attempt allowed per week, beginning March 26) During the lab hour time 11:15-12:10 on Tuesdays and Thursdays SIGN UP IN THE MATH TLC OPEN LAB! If you do not want to use your lab hour time, email Amanda Larson, Math TLC Coordinator (JHSW 202E), to set up a date and time.

Any questions on the Section 2.4 homework that was due today?

CLOSE Please YOUR LAPTOPS, and get out your note-taking materials. and turn off and put away your cell phones, and get out your note-taking materials.

Section 2.5 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)

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) (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.

Note: The formula for the volume of a tank like this is V = l∙w∙h 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 simplify each side. Get all terms containing specified variable on the same side, 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)

Problem from today’s homework:

Reminders: This homework on Section 2.5 is due at start of next class session. Make sure you SIGN UP TO TAKE THIS WEEK’S GATEWAY (in open lab) if you haven’t passed it yet. 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.