DEV Team America Charli Sheen Alpha Squadron 007 2.0

1.      Your math teacher is somewhat upset, so he gives you a completing the square problem without explaining it first. Lucky for you, you’re a math whiz.  

77=5x²+15x-12

89=5x²+15x

89=5(x²+3x+9/4)

401/4=5(x²+3x+9/4)

401/4=5(x+3/2)²

401/20=(x+3/2)²

√401/20 = √(x+3/2)²

+/-√401/20=(x+3/2)

X= -3/2 +/-√401/20

The first step in completing this square would be adding 12 to both sides. This is so you can factor. The right side of the equation factors into 89=5(x²+3x+9/4). 9/4 is half of three squared. You then add 9/4 to the other side, but you must multiply it by five. You then have a perfectly squared factor. Then divide both sides by 5. Then you square root both sides to get rid of the squared on the factor. Then you subtract 3/2 to both sides to get the x be itself.

2.      You find a graph among a stack of papers. Your friend thinks that √ (4x²-4x-24) is the function from which it came, but you’d like to double check.                                                                   

√ (4x²-4x-24)                                                                  

(4x²-4x-24) ≥0                                                

4(x²-x-6) ≥0                                      

4(x-3) (x+2) ≥0

D: (-∞, -2 ] υ [3, ∞)

R: [0, ∞)

When solving this, you first take to function out from underneath the square root and set it equal to zero. Then you can factor it. Once it’s factored, ignore the 4. Then you can find the domain. Make sure to put the negatives first. The range for even radicals is always [0, ∞), unless there’s a number added or subtracted outside the square root.  

3.      The empire is constructing a death star, and for whatever reason, they decide to inlay trenches on the outer layer. They make the sides out of 1500ft. of titanium. What depth will provide the maximum cross-sectional area? What are the dimensions?

1500=2x+y   A= x ∙ y

1500-2x=y

A= x (1500-2x)

A= -2x²+1500x

-1500/2 ∙ -2= 375ft.

A= -2 (375)² + 1500 (375)

A= 281, 250ft.

281,250/375= 750

Dim: 750ft. x 375ft.  

            First you need the equation for the area, then the equation for the perimeter for three sides set equal to 1500ft. The next step is to solve for y in the perimeter, then put y into the area formula. You can convert it to standard; it may be useful later. You then divide –b by 2a (from the formula –b/2a). After you get that, plug it into your standard form area equation to get the total area. That answers to first question. To find the maximum dimensions, divide the total area by the number you got from –b/2a. That should give you 750. 750 by 375 are your maximum dimensions.   

   

We chose these concepts, because these were the ones that we had some trouble with when going through the units. We decided this project could be some extra practice with what we struggled with. We each did the problems we believed that we were the worst at. These aren’t the most complex functions you’re going to see, but they’re within the group’s ability to comprehend. We have a completing the square, domain and range of a radical, “Farmer Ted”, factoring and long division with polynomials problem. We covered are large portion of the trimester with these problems. To be completely honest, other than some extra practice with past concepts, I didn’t gain a whole to from this project. If I were a better math student, I could have taken this project farther than I did, however. I didn’t have many problems with this assignment overall, but I didn’t find the value to match the amount of work. -Summary by Cyrus Pierce

We chose these problems because we had some trouble with them. We figured that besides demonstrating the concepts that we were taught throughout the trimester, we could use the D.E.V. to get some extra practice and make sure that we had everything straight, not just the concepts that we already knew. I feel like I got something out of this project, not a lot but still something. It helped me make sure that I have all of the concepts straight in my head for the final exam, and the creative portion of the project definitely was important, since the situations we created will help me to remember these functions in the future. Overall, I didn't have many problems with the D.E.V., just the trouble with uploading the video, and obviously this summary. If I had it to do over I would definitely make sure that I had the project done well before the due date so that I would have time to deal with any problems I might run into.