- Here Is The Nutritional Information For 20 Fl Oz Of Original Coke Vanilla Coke Pepsi And Pepsi Next Represented 1 (162.21 KiB) Viewed 49 times
- Here Is The Nutritional Information For 20 Fl Oz Of Original Coke Vanilla Coke Pepsi And Pepsi Next Represented 2 (170.01 KiB) Viewed 49 times
Here is the nutritional information for 20 fl oz of Original Coke®, Vanilla Coke®, Pepsi Ⓡ and Pepsi Next ®, represented as nutritional vectors with the respective amount of Calories, Sodium (mg) and Carbs (g): 240 (.. 65 noc where the coefficients are and npN 70 The nutritional vector for original coke is noc can be expressed as a linear combination of vectors of the other colas: noc=anvc+Bnp+mpN α = 1/2 , nvc 260 - ().- 70 = Calories Sodium (mg) Carbs (g) 1/3 Note: this may be a tricky calculation, see hints below. ,np = Table 1. Ingredients and Nutritional Information 250 55 The main ingredients of cola are Carbonated Water, High Fructose Corn Syrup (HFCS) and Caramel Colour. The nutritional content for these ingredients is in the table below Carbonated Water (1 fl oz) 0 5 0 A = HFCS (1 fl oz) 25 1 5 We can represent this nutritional information by the matrix A: 0 25 25 5 1 20 0 5 38 100 (). 25 Y = 4/15 Caramel Colour (1 fl oz) 25 20 38
We can represent this nutritional information by the matrix A: 0 25 25 1 20 0 5 38 The matrix A defines a linear map from ingredient vectors to nutritional vectors. For example, we can compute the nutritional value of a mixture of 5 fl oz of Carbonated Water, 6 fl oz of HFCS and 4fl oz of Caramel Colour as: 5 +() A 4 A = 5 6 - <250,111,182> But with the power of linear algebra, we can also go backwards and compute the following valuable trade secrets (see hints below, and give your answers to two significant figures): • The ingredient vector for Vanilla Coke is A-¹ nvc= • The ingredient vector for Pepsi is A¯¹np= • The ingredient vector for Pepsi Next is A-¹nPN -1 7.8 9.9 .55 Hints • the Maple command for finding the reduced row-echelon form of a matrix M is LinearAlgebra [ReducedRowEchelon Form] (M); • the Maple command to compute the inverse N of the matrix M is N := LinearAlgebra [MatrixInverse] (M) ; • the Maple command to compute the product of a matrix N and vector v, evaluated to two significant figures, is