Wednesday, January 29, 2020

Pythagoras Theorem and Financial polynomials Essay Example for Free

Pythagoras Theorem and Financial polynomials Essay Pythagoras Theorem and Financial polynomials Introduction                   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+42+16x+16 = 42+ 24x+36 are the binomials squared x2 42 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; (-93 + 32 – 15x) à · (-3x) The Dividend is (-93 + 32 – 15x), and the Divisor is (-3x). The Dividend is (-93 + 32 – 15x), and the Divisor is (-3x). -93 + 32 15x -3xAfter I divide -9 by -3 which equals +3. The x on the bottom cancels the x from the top. -93 + 32 – 15x -3x -3x -3x -9* x*x* x I am now left with 32 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. -93 + 32 – 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. -93 + 32 – 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 32 – 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

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