Question

System of Equations help?

Answer 1

\[\frac{ 4 }{ 5 }Fac-Fab \cos 30=0\]
\[\frac{ 3 }{ 5 }Fac+Fab \sin 30 - 550=0\]

Answer 2

Solving for both Fac and Fab

Answer 3

My plan was to solve for Fac using the 2nd equation.

Answer 4

so by substitution, what's your question?

Answer 5

\[Fac= \frac{ -5 }{ 3 }Fab+916.669\]

Then sub that equation into first equation.

\[4/5[-5Fab/3+916.669]\]

Answer 6

er
what happened to the sin(30)?

Answer 7

Simplifying,
\[\frac{ -4 }{ 3 }Fab+1222.223-Fabcos30=0\]

Answer 8

double check your first step

Answer 9

\[\frac{ -4 }{ 3 }Fabsin30+1222.223-Fabcos30=0\]

Answer 10

better

Answer 11

this is the part where you grab a calculator and solve for F_ab

Answer 12

Im confused on this part. Would I move the Fab terms to the opther side to make positive and then try to reduce?

Answer 13

combine like terms

Answer 14

\[\frac{ 4 }{ 3 }Fabsin30+Fabcos30=1222.223\]

Answer 15

yes

Answer 16

Could I then pull out a Fab from both terms?

Answer 17

you could do that

Answer 18

you're not allowed to use calculators?

Answer 19

I could but I was not sure what to meant for using the solve?

Answer 20

The solve function under Math?

Answer 21

cos(30 ) = .866...
sin (30) = .5

-4/3 *.5 Fab + .866 Fab = 1222.223

Answer 22

Wouldn't the 4/3 be positive?

Answer 23

gah

you keep making mistakes left and right

Answer 24

one second

Let Fab = x
let Fac = y
\[\frac{4}{5}y-x \cos(30) = 0\]
\[\frac{3}{5}y-x \sin(30) -550= 0\]

solving for y for 2nd equation
\[y=\frac{5}{3}(550+xsin(30))\]


substituting for y into first equation

\[\frac{4}{5}\frac{5}{3}(550+xsin(30))-x cos(30)=0\]

\[\frac{4}{3}(550+xsin(30))-xcos(30)=0\]

Answer 25

\[733.333+ \frac{4}{6} x - \frac{\sqrt{3}}{2} x=0\]

Answer 26

\[x(\frac{4}{6}-\frac{\sqrt{3}}{2})=-733.33333\]

Answer 27

\[x=\frac{-733.33333}{\frac{4}{6}-\frac{\sqrt{3}}{2}}\]

then solve for y


HOPEFULLY I DIDNT MAKE ANY MISTAKES WHEN SOLVING THIS
NOTE, BE VERY CAREFUL WHEN DOING SYSTEMS OF EQUATIONS LIKE THIS AS A SINGLE MISTAKE CAN DRASTICALLY ALTER THE SOLUTION

Answer 28

Wow thanks for the step by step. Im assuming you got root 3/2 from the unit circle?

Answer 29

i have it memorized

cos(30) = .866

Answer 30

when you use it often enough, you tend to memorize these things

Answer 31

Ok I see. Just checked online. cos30= root 3/2.

Thanks for the help!

Answer 32

but that part is the reason why i suggested you grab calculator because the number is not a nice decimal