simoner
  • simoner
find the acute angle between the lines x+2y=7 and 5x-y=2
Mathematics
jamiebookeater
  • jamiebookeater
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simoner
  • simoner
I did\[\tan^{-1} \left( 5 \right)=78.69 degrees\]
simoner
  • simoner
and \[\tan^{-1} \left( -.5 \right)=-26.75 degrees\] so arent yu supposed to subtract that from 180 to get 153.43 degrees
simoner
  • simoner
then you subtract 153.43 degrees from 78.69 degrees to get 75.74 degrees?

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simoner
  • simoner
can anyone tell me if this is correct?
triciaal
  • triciaal
|dw:1440901646597:dw|
simoner
  • simoner
is what i did correct? i just need to know if the answer i got is correct
triciaal
  • triciaal
I don't know sorry but the intersection is (1,3)
triciaal
  • triciaal
|dw:1440902711014:dw|
anonymous
  • anonymous
2y=-x+7 \[y=-\frac{ 1 }{ 2 }x+\frac{ 7 }{ 2 }\] slope\[m _{1}=-\frac{ 1 }{ 2 }\] y=5x-7 its slope\[m _{2}=5\] let theta be the angle between them. \[\tan \theta =\left| \frac{ m _{1}-m _{2} }{ 1+m _{1}m _{2} } \right|\] \[\tan \theta=\left| \frac{ -\frac{ 1 }{ 2 }-5 }{ 1+\left( -\frac{ 1 }{ 2 } \right)*5 } \right|\] \[\tan \theta=\left| \frac{ \frac{ -11 }{ 2 } }{ 1-\frac{ 5 }{ 2 } } \right|=\left|\frac{ -11 }{ 2 }\times \frac{ -2 }{ 3 } \right|\] \[=\frac{ 11 }{ 3 }\] \[\theta=\tan^{-1} \left( \frac{ 11 }{ 3 } \right)\] =74.74degree
triciaal
  • triciaal
interesting 72, 75, 78 as in 75 +/- 3
anonymous
  • anonymous
correction y=5x-2

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