What is the expression for the distance from the point (8,1) to the curve # y = 1 + x^(3/2)# in terms of the x-coordinate of the point on the curve?

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Answer 1 · 2016-12-31T23:04:48

#d = sqrt(x^3 + x^2 - 16x + 64)#

Use the distance formula:

#d = sqrt((x - x_0)^2 +(y - y_0)^2)#

Substitute #(8,1)# for #(x_0,y_0)# is:

#d = sqrt((x - 8)^2 +(y - 1)^2)#

Substitute the right side of the function for y:

#d = sqrt((x - 8)^2 +(x^(3/2) + 1 - 1)^2)#

#d = sqrt((x - 8)^2 +(x^(3/2))^2)#

#d = sqrt((x - 8)^2 + x^3)#

#d = sqrt(x^3 + x^2 - 16x + 64)#