Pythagoras Theorem and Financial polynomials Essay

                  Ahmed and Vanessa have interest in locating a treasure, which is buried. It is my responsibility to help the two locate it. First, I will help them locate it by the use of Pythagorean quadratic. As per Ahmed’s half, the treasure is buried in the desert (2x + 6) paces form the Castle Rock while as per Vanessa’s half she has to walk (x) paces to the north then walk (2x + 4) paces to the east. According to the Pythagorean theorem, every right angled triangle with length (a) and (b) as well as a hypotenuse (c), has a relationship of (a2 + b2 = c2) (Larson & Hostetler, 2009).                  In Ahmed and Vanessa’s case, I will let a=x, b =2x+4 and then c=2x+6. To follow, will be my efforts to put the measurements above into the real Pythagoras theorem equation as follows: X2+ (2x+4)2=(2x+6)2 this is the equation formed out of the Pythagoras Theorem X2+4Ãâ€"2+16x+16 = 4Ãâ€"2+ 24x+36 are the binomials squared x2 & 4Ãâ€"2 on both sides can be subtracted out. X2+16x+16 = 24x +36 subtract 16x from both sides X2+16 = 8x+36 now subtract 36 from both sides X2-20 = 8x X2-8x-20=0 I will use to solve the function by factoring using the zero factor. (x-) (x+) the coefficient of x2 Application and selection from the following (-2, 10: -10,2: -5,4; -4, -5) In this case, it seems that I am going to use -10 and 2 is as per how the expression looks like this (x-10)(x+2)=0 X-10=0 or x+2=0 creation of a complex equation x=10 or x=-2 these are the two probable resolutions to this equation.                     One of the two calculated solutions is an extraneous solutions, as it do not work with such sceneries. The remaining solution I only have is (X=10) as the number of paces Ahmed and Vanessa have to accomplish to find the lost treasure. As a result the treasure is 10 paces to the north 2x+4 connect the 10, now its 2(10)+4=24 paces to the east of Castle Rock, or 2x+6= 2(10)+6=26 paces from Castle Rock. Financial polynomial                   For the case of financial polynomials, I have first to write the polynomial without the parenthesis. Following the above, I have to solve for p= 2000 + r = 10% for part A and then solve for p= $5670 + r = 3.5% for part B, without the parenthesis as follows: P + P r + P r2/4 (the original polynomial) to reach this I followed the following steps: (1 + r/2)2 This is because it looks as if it is foil P(1 + r/2) P (1+r/2)(1+r/2) After the two equations I combine like terms. Because I am multiplying by 2 on r/2, it cancels out both 2’s and I then get left with is r as follows; P(1+ r/2 + r/2 + r2/4) P(1 + 2(r/2) + r2/4) I then write in descending order (P + Pr + Pr2) To solve for P=2000 and r=10% the following follows; P + Pr + Pr2/4 2000 + 2000 Ãâ€"(0.10) +2000Ãâ€" 0.1024 2000 + 200 + 5 = $2205 P(1+ r/2)2 2000Ãâ€"( 1 + .10)2 2000Ãâ€"(1.05)2 2000Ãâ€"( 1.1025) = $2205 For part B I will solve for P=5670 and r= 3.5% P + Pr + P Ãâ€"(r2/4) 5670 + 5670Ãâ€" (0.035) + 5670 Ãâ€" 0.0352 5670 + 198.45 + 1.7364375 = 5870.1864375 This is approximately ($5870.19) The problem 70 on page 311 has the following steps; (-9Ãâ€"3 + 3Ãâ€"2 – 15x) à · (-3x) The Dividend is (-9Ãâ€"3 + 3Ãâ€"2 – 15x), and the Divisor is (-3x). The Dividend is (-9Ãâ€"3 + 3Ãâ€"2 – 15x), and the Divisor is (-3x). -9Ãâ€"3 + 3Ãâ€"2 – 15x -3xAfter I divide -9 by -3 which equals +3. The x on the bottom cancels the x from the top. -9Ãâ€"3 + 3Ãâ€"2 – 15x -3x -3x -3x -9* x*x* x I am now left with 3Ãâ€"2 for the first part of the polynomial. -3 * x -9*x *x * x -3 * x I first divide 3 by -3, which equals -1 and the x from the bottom cancels out one of the x’s from the top. -9Ãâ€"3 + 3Ãâ€"2 – 15x -3x -3x -3x 3 *x *x At this point I am left with -1x, which simplifies to just –x, as the second part of the polynomial. Then -3 *x 3 *x * x -3 * x Then I divide -15 by -3, which equals positive 5, and the x on the bottom cancels out the x on the top, so you do not have any x’s to carry onto the answer of the equation. -9Ãâ€"3 + 3Ãâ€"2 – 15x -3x -3x -3x -15 *x At this point I am left with only 5 for the last part of the polynomial, and the answer is 3Ãâ€"2 – x + 5. -3 * x -15 * x -3 * x                   The negative sign from the -3 x changes the plus sign in the equation to a minus sign, it changes the minus sign to a plus sign in the final answer, and the equation is in Descending order. Reference Larson, R., & Hostetler, R. P. (2009). Elementary and intermediate algebra. Boston, Mass: Houghton Mifflin Source document