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3 years ago

Find x so the distance between (x,2) and (1,4) is square root 13.

Mathematics

1 answer:

AlekseyPX3 years ago

5 0

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have the points (x, 2) and (1,4) and the distance d = √13.

Substitute:

$\sqrt{(1-x)^2+(4-2)^2}=\sqrt{13}\\\\\sqrt{(1-x)^2+2^2}=\sqrt{13}\\\\\sqrt{(1-x)^2+4}=\sqrt{13}\iff(1-x)^2+4=13\qquad|-4\\\\(1-x)^2=9\iff1-x=\pm\sqrt9\\\\1-x=-3\ \vee\ 1-x=3\qquad|-1\\\\-x=-4\ \vee\ -x=2\qquad|\text{change the signs}\\\\\boxed{x=4\ \vee\ x=-2}$

<h3>Answer: x = -2 or x = 4.</h3>

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3 years ago

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Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

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