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a cable company is connecting a new customer to its cable network. on a site plan, the customer's house has coordinates H(7,17). the equation y= 1/2x+4 represents the existing trunk cable. the cable company wants to keep the branch to the customer's house as short as possible. where should the cable company make the connection to the trunk cable?

Respuesta :

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d^2=(y2-y1)^2+(x2-x1)^2

d^2=(17-x/2-4)^2+(7-x)^2)

d^2=(169-13x+x^2/4)+49-14x+x^2)

d^2=1.25x^2-27x+218

dd^2/dx=2.5x-27, dd^2/dx=0 when 2.5x=27, x=10.8

y(10.8)=5.4+4=9.4

So the connection to the trunk cable should be made at the point (9.4, 10.8)

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