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zhenek [66]
3 years ago
5

One airplane is 78 miles due south of a control tower. Another airplane is 52 miles from the control tower at a heading of N 38

degrees E. To the nearest tenth of a mile, how far apart are the two airplanes?
Mathematics
1 answer:
kow [346]3 years ago
4 0

Answer:

123.2 miles

Step-by-step explanation:

Given that One airplane is 78 miles due south of a control tower. Another airplane is 52 miles from the control tower at a heading of N 38 degrees E. To the nearest tenth of a mile, how far apart are the two airplanes?

The angle Ø = 90 + 52 = 142 degree

Or 180 - 28 = 142 degree

Using cosine formula

D^2 = 78^2 + 52^2 - 2(78)(52)Cos142

D^2 = 6084 + 2704 - 8112Cos142

D^2 = 8788 + 6392.34

D^2 = 15180.34

D = 123.2 miles

Therefore, the two planes are 123.2 miles apart.

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Gnesinka [82]

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

$5\left|x-2\right|>4$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$

$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

5 0
3 years ago
a man retires at age 50 with $625,000 in savings.after 7 years of retirement, he has spent $259,000 of his savings and is consid
vaieri [72.5K]
Im not entirely sure what you are looking for, but if you are trying to find out how much he has left, you would take 625,000-259,000=366,000

He would have $366,000 left from his retirement.

Hope this helps! :)
3 0
3 years ago
Y = x – 6 x = –4 what is the solution to the system of equations? (–8, –4) (–4, –8) (–4, 4) (4, –4
fredd [130]

Answer:

(- 4, - 10 )

Step-by-step explanation:

Given the 2 equations

y = x - 6 → (1)

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Substitute x = - 4 into (1) for corresponding value of y

y = - 4 - 6 = - 10

Solution is (- 4, - 10 )

4 0
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Lapatulllka [165]

Answer:

Divide each side of 18/4 by 2 to get <u>9/2.</u>

5 0
3 years ago
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Slope of (-1,-6 and (1,-8)
Mars2501 [29]
<h2>Answer: m = -1</h2>

Step-by-step explanation:

If you follow the formula : y2 - y1 / x2 - x1

You will get m=\frac{-8-(-6)}{-1-(-1)}

m = -1

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3 years ago
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