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vesna_86 [32]
3 years ago
6

Question 17 two trains leave stations 252 miles apart at the same time and travel toward each other. one train travels at 100 mi

les per hour while the other travels at 80 miles per hour. how long will it take for the two trains to meet?
Mathematics
1 answer:
VLD [36.1K]3 years ago
7 0
The distance between them is 252 miles
For meeting they reduce the distance with 252 miles
in an hour they reduce distance with 100+80=180 miles
180 miles...........1 hour
252 miles.............x hours
------------------------------------
x=252 /180=1,4 hours=84 minutes
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The equation for a parabola has the form y=ax2+bx+c, where a, b, and c are constants and a≠0. find an equation for the parabola
IRISSAK [1]

The equation of parabola is

y= ax^2 + bx +c

For point (-1,-9), equation of parabola is

-9 = a(-1)^2 +b(-1)+c
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For point (1,7), equation of parabola is

7 = a(1)^2 + b(1)+c
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7 = a + b +c

For point (-6,-14), equation of parabola is

-14 = a(-6)^2 +b(-6)+c
\\
-14 = 36a -6b +c

So we have three equations , which are

a - b + c =-9,
\\
a + b + c = 7
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36a -6b+c = -14

Subtracting first two equation will give

-2b  = -16
\\
b=8

Subtracting second and third equation gives

a+b+c-36a+6b-c = 7+14
\\
-35a +7b = 21
\\
-5a + b =3

Substituting 8 for b, we will get

-5a + 8 =3
\\
-5a = -5
\\
a =1

back substituting 8 for b and 1 for a, we will get

1+8+c = 7
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c = -2

So we have

a=1, b=8 and c=-2

Therefore required equation is

y= x^2 +8x-2

7 0
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bezimeni [28]

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[4-(-8)]^2+[-1-4]^2}\implies AB=\sqrt{(4+8)^2+(-1-4)^2} \\\\\\ AB=\sqrt{144+25}\implies AB=\sqrt{169}\implies \stackrel{\textit{diameter}}{AB=13}~\hfill \boxed{\stackrel{\textit{radius}}{6.5}} \\\\[-0.35em] ~\dotfill

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3 years ago
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