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vladimir2022 [97]
3 years ago
7

Find the equation of a line with a slope of 1 and passing through (11;3)

Mathematics
1 answer:
romanna [79]3 years ago
3 0

Step-by-step explanation:

slope(m)=(Y-Y1)/X-X1

here,

M=1

(X1,Y1)=(11,3)

NOW,

m=(Y-Y1)/(X-X1)

1=(Y-3)/(X-11)

1×(X-11)=Y-3

X-11=Y-3

X-Y-11+3=0

X-Y-8=0

X-Y=0 is the required equation.

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Answer:

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed = \frac{distance}{time}

Sarah's speed = 6 km/hr = 1.6667 m/s

Emily's speed = 10 km/hr = 2.7778 m/s

The measure of angle between their bearings = 105^{o}

After 30 minutes (1800 seconds);

distance = speed x time

Sarah would have covered a distance = 1.6667 x 1800

                               = 3000 m

                               = 3 km

Emily would have covered a distance = 2.7778 x 1800

                               = 5000 m

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The distance between them, a, can be determined by applying the cosine rule;

a^{2} = b^{2} + c^{2} - 2bcCos A

   = 5000^{2} + 3000^{2} -2(5000 x 3000) Cos 105

   = 5000^{2} + 3000^{2} -2(5000 x 3000) x (-0.2588)

   = 2.5 x 10^{7} + 9 x 10^{6} + 7764000

   = 41764000

a = \sqrt{41764000}

  = 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

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Answer:

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Step-by-step explanation:

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