Understanding the definition of words - Speech or Presentation Example

Part Discussion 1. In your own words, define the word “function.”   Function pertains to a relation established by coordinates in ordered pairs (x, y) consisting of the domain (x-values) and the range (y-values) where each value of ‘y’ corresponds to a distinct value of ‘x’.2. Give your own example of a function using a set of at least 4 ordered pairs. Example: (4, -7) (0, -3) (1, 2) (3, 5) 3. Explain why your example models a function.   The given example models a function because for each unique value of ‘x’ in the domain, there corresponds a value of ‘y’ so that the relationship basically shows a one-to-one correspondence.

No value of ‘x’ appears more than once in the example and this is a necessary condition for a relation to be considered a ‘function’.4. Give your own example of at least four ordered pairs that does not model a function. Example: (3, -11) (7, 0) (5, 1) (3, 4) 5. Explain why your example does not model a function.  It does not represent a function because the value of ‘x’ repeats on (3, -11) and (3, 4) and this does not satisfy the definition and correspondence of one-to-one.Part 26. Select any two integers between -12 and +12 which will become solutions to a system of two equations.

Two integers: 5 and 77. Write two equations that have your two integers as solutions. Show how you built the equations using your integers. Your solution and equations should not be the same as those of other students or the textbook. There are infinite possibilities.Step 1: Come up with two equations, multiplying each of 5 and 7 by two separate constants to make one equation as follows: 3(5) + (-2)(7) = 1 and 4(5) + 2(7) = 34Step 2: Write each equation in ax + by = c form, such that: Equation 1: 3x - 2y = 1 and Equation 2: 4x + 2y = 348.

Solve your system of equations by the addition/subtraction method. Make sure you show the necessary 5 steps. Use the example on page 426 of Mathematics in Our World as a guide. By the method of addition: 3x - 2y = 1 4x + 2y = 34 7x + 0 = 35 --- 7x = 35Then dividing each side by 7 --- x = 5And substituting this into one of the original equations: 4(5) + 2y = 34 --- 20 + 2y = 34 then 20 may be subtracted (each side) to have 2y = 14 where upon division by 2 (both sides) -- y = 79.

Respond to at least two of your classmates’ postings. Do you agree or disagree that their examples model functions? Follow their 5 steps. Do their calculations follow the correct rules of algebra? Yes. Their examples demonstrate what we can expect of functions by definition and their calculations are patterned after the correct algebraic rules.Week Three Discussion 2This Discussion tests your ability to use a ruler and convert from Standard English measure to Metrics. You will then apply your knowledge of the geometric measurements of area and volume through real world problems. 1. Choose a room in your house.

Measure the length, the width, and the height. Make sure you use feet and inches. Convert the measurements to all inches for step 2, and then convert back to square feet for step 3.Length = 23’5” ; Width = 18’7’’ ; Height = 20’3” 2. Record your dimensions and, using the appropriate formula, find the surface area of the room. Since 1 foot = 12 inchesLength = (23*12) in. + 5 in. = 281 inchesWidth = (18*12) in. + 7 in. = 223 inchesHeight = (20*12) in. + 3 in. = 243 inchesSurface Area = 2(LW) + 2(HL) + 2(HW) = 2(281)(223) + 2(243)(281) + 2(243)(223) = 125326 in.

2 + 136566 in.2 + 108378 in.2Surface Area = 370270 in.2 and converting to ft2 = (370270 in.2) * (1 ft2 / 144 in.2) Surface Area = 2,571.32 ft2 3. A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon.Since 1 gallon ≡ 350 ft2 then2,571.32 ft2 * (1 gallon / 350 ft2) = 7.35 ≈ 7 gallons4. If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room?Cost = 7 gallons * ($22.

95 / 1 gallon) + (0.08)*($22.95) = $162.49 5. One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.Length = 281 inches * (2.54 cm / 1 inch) --- Length = 713.74 cm.Width = 223 inches * (2.54 cm / 1 inch) --- Width = 566.42 cm.Height = 243 inches * (2.54 cm / 1 inch) --- Height = 617.22 cm. 6. Find the volume in cubic centimeters. Be neat and precise. Volume = (713.74 cm.) * (566.42 cm.) * (617.22 cm.) Volume = 249,527,609.7 cm37. If each dimension (length, width, and height) is doubled, what happens to the volume of the room?

Show your work.If L = 2(713.74) = 1427.48 cm, W = 2(566.42) = 1132.84 cm., and H = 2(617.22) = 1234.44 cm. which makesVolume = (1427.48 cm.)*(1132.84 cm.)*(1234.44 cm.) = 1,996,220,878 cm3So, the new volume is 8 times as much as the original volume when dimensions are doubled. 8. Respond to at least two of your classmates’ postings. Review their calculations and determine if their results seem reasonable for the size of the room. Reviewing the calculations carried out in their work, I can say that the results obtained are reasonable for a room’s size.

Most of the room sizes are relative in values with each other.