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natka813 [3]
3 years ago
10

use algebraic manipulation to find the minimum sum-of-products expression for the function x1x2'x3' + x1x2x4+x1x2'x3x4'

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
7 0

Answer:

sum of products expression = x₁x₂x₃'  +  x₁x₂'x₄  + x₁x₂x₄

Step-by-step explanation:

Given function ( f ) = x₁x₂'x₃'  +  x₁x₂x₄ + x₁x₂'x₃x₄'

using algebraic manipulation

f = x₁ [ x₂'x₃'  +  x₂x₄ + x₂'x₃x₄' ]

 =  x₁ [ x₂'( x₃' + x₃x₄') +  x₂x₄  ]

next apply Boolean rules

a + bc = ( a + b )(a + c )

a' + a =1

hence

minimum sum-of-products expression = x₁x₂x₃'  +  x₁x₂'x₄  + x₁x₂x₄

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Answer:

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Step-by-step explanation:

We are given;

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Assuming the other endpoint is (x,y)

Using the ratio theorem

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Then;

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10=\frac{4}{9}x+\frac{10}{9}

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Also

1=\frac{4}{9}y+\frac{25}{9}

solving for y

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Therefore,

the coordinates of the end point are (20,-4)

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