Assignment 5 1

Assignment 5
DeJuan Stanley
MAT 221
Prof Timothy Kilgore
June 2, 2014

MAT 221 Week 5 Assignment Buried treasure. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x? The key to solving this equation is to use the Pythagorean Theorem which has a right angle in the equation with a & b equaling side c. Based on the example we know that we will have to use the formula A^2 + B^2 = C^2. What we know is that Ahmed’s half of the map is 2x + 6 = treasure, which would be how far he would need to walk, (A^2). Vanessa’s map needs to show her how to get to the North of Castle Rock, which is 2x + 4, (C^2). We are trying to solve for X (side B). Vanessa is forming a 90 degree angle from point B and walk (2x + 4) until she made it to C. The formula we would use to solve for X is the following:
(2x + 6)^2 = x^2 + (2x + 4)^2
4x^2 + 24x + 36 = x^2 +4x^2 + 16x + 16
The next step would be to combine like terms, multiplying, adding, and subtracting.
24x + 36 = x^2 + 16x + 16
-24x -24x

36 = x^2 – 8x + 16
-36 -36

Now we have a quadratic equation. Treasure = x^2 – 8x – 20. We have simplified the equation, now we can solve for X. Inside the quadratic equation, x^2 – 8x – 20 = 0, we can solve by factoring and using the zero factor. This is called the compound equation, because we know that the two factors we have are 10 and -2, so we can solve for each binomial. The equation is (x-a)(x+b)=0 or (x – 10)(x + 2). The answer would be x = 10 and x = -2. One of the rules is that we cannot have a negative number in our equation, because you cannot take negative paces. The only number we are now left with is 10. Now we can plug 10 into our original equation. In Ahmed’s map, we have (2x + 6) or (20 + 6) = 26. Vanessa’s paces would be (2x + 4) or (20 + 4) = 24

Reference
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:
McGraw-Hill Publishing.