# The vector u = <3140, 2750> gives the number of hamburgers and hot dogs, respectively, sold at a fast-food stand in one month.  The vector v = <2.25, 1.75> gives the prices (in dollars) of the food items. a)  Find the dot product u * v and interpret the result in the context of the problem. b) Identify the vector operation used to increase the prices by 2.5%. Lets rearrange the forms of the vectors

The number of hamburgers and hotdogs,

The prices of them, v = 2.25 i + 1.75 j

a) The dot product of u*v

u*v = 3140X2.25 + 2750X1.75

= 7065 + 4812.5 = $11877.5  b) 2.5%... ## See This Answer Now Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime. Lets rearrange the forms of the vectors The number of hamburgers and hotdogs, The prices of them, v = 2.25 i + 1.75 j  a) The dot product of u*v u*v = 3140X2.25 + 2750X1.75  = 7065 + 4812.5 =$11877.5

b) 2.5% increase  in their price can be represented by \$1.025

[(100+2.5)/100 = 1.025]

Second vector v has to be multiplied by the scalar k, i. e., 1.025

therefore v = 1.025(2.25 i + 1.75 j)

= 1.025X2.25i + 1.025X1.75j

 = 2.30625 i + 1.79375j

= 2.31i + 1.79j                (rounded up to two decimals)

The required vector is kv(2.31, 1.79)

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