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kondor19780726 [428]
3 years ago
6

Find the coordinates of the point 7/10 of the way from A to B. a=(-3,-6) b=(12,4)

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

Answer:

The coordinates of M are x = \frac{15}{2} and y = 1.

Step-by-step explanation:

Let be A = (-3,-6) and B = (12, 4) endpoints of segment AB and M a point located 7/10 the way from A to B. Vectorially, we get this formula:

\overrightarrow {AM} = \frac{7}{10}\cdot \overrightarrow {AB}

\vec M - \vec A = \frac{7}{10}\cdot (\vec B - \vec A)

By Linear Algebra we get the location of M:

\vec M = \vec A + \frac{7}{10}\cdot (\vec B - \vec A)

\vec M = \vec A +\frac{7}{10}\cdot \vec B - \frac{7}{10}\cdot \vec A

\vec M = \frac{3}{10}\cdot \vec A + \frac{7}{10}\cdot  \vec B

If we know that \vec A = (-3,-6) and \vec B = (12, 4), then:

\vec M = \frac{3}{10}\cdot (-3,-6)+\frac{7}{10}\cdot (12,4)

\vec M = \left(-\frac{9}{10},-\frac{9}{5}  \right)+\left(\frac{42}{5} ,\frac{14}{5} \right)

\vec M =\left(-\frac{9}{10}+\frac{42}{5} ,-\frac{9}{5}+\frac{14}{5}   \right)

\vec M = \left(\frac{15}{2} ,1\right)

The coordinates of M are x = \frac{15}{2} and y = 1.

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Average speed is 3 kilometers an hour

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2 years ago
Find the distance from the point (1, 4) to the line y = 1/3x – 3.
Otrada [13]

Answer: Distance between line and point =

4√5 -3/2√10

Step-by-step explanation:

Distance between the line is

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Half of the line = 3/2√10

Distance of one side of the line and the point.

= √((9-1)²+(0-4)²)

= √((8)²+(-4)²)

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Distance between line and point =

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8 0
2 years ago
Solve each system by substitution. please help me<br> 2x{+y=6<br> x{+y=3
saw5 [17]
1. x= 3/Y as a fraction btw

2. Same thing
6 0
3 years ago
Please help
ehidna [41]

Answer:

The length between the two points is RT = 1.3 units

Step-by-step explanation:

The coordinates of the point R and T are R(2,1.2) and T(2,2.5).

Now, by DISTANCE FORMULA:

The distance between two coordinates  P and Q with coordinate P(a,b)  and Q(c,d) is given as:

PQ  = \sqrt{(a-c)^2   + (b-d)^2}

So, here the distance RT = \sqrt{(2-2)^2  + (2.5 - 1.2)^2}   = \sqrt{0^2  + (1.3)^2}   = 1.3

or, RT = 1.3 units

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2 years ago
Two trains leave stations 560 miles apart at the same time and travel toward each other. One train travels at 90 miles per hour
lana [24]

Answer: the two trains will meet in 2.8 hours

Step-by-step explanation:

Step 1

Speed of train A  = 90mph

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Since both trains  are travelling towards each other , their effective speed will be= 90 mph + 110mph= 200mph

Step 2

we know that Speed = distance / time

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Distance = 560 miles

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Time = 560miles / 200mph

2.8 hours

5 0
2 years ago
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