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%.

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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%...

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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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