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grandymaker [24]
3 years ago
7

How long is the segment from(-5,2)to(-5,-8)

Mathematics
1 answer:
dusya [7]3 years ago
6 0

Answer:

10

Step-by-step explanation:

To calculate the distance d use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, 2) and (x₂, y₂ ) = (- 5, - 8)

d = \sqrt{(-5+5)^2+(-8-2)^2}

  = \sqrt{0^2+(-10)^2}

  = \sqrt{0+100} = \sqrt{100} = 10

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A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far
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\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3} (1)

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(x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2}) (1b)

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x, y - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

r_{1}, r_{2} - Length of each vector, in kilometers.

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If we know that r_{1} = 42\,km, r_{2} = 28\,km, \theta_{1} = 32^{\circ} and \theta_{2} = 154^{\circ}, then the resulting coordinates of the final position of the surveyor is:

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\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}

\theta \approx 16.840^{\circ}

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r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}

r = 36.078\,km

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