Question

System of eq help - MEDAL
[1] 0 = xcos30 - ycos45
[2] 0 = xsin30 + ysin45 - 9.81*m

[1] x = ycos45/cos30
substitution
0 = (sin30)ycos45/cos30 + ysin45 - 9.81*m
0 = y(-.299) - 9.81*m

...what happened?!

Answer 1

Where you want help?

Answer 2

Reduce your equations a little bit from Trigonometry..

Answer 3

\[\frac{\sqrt{3}}{2}x - \frac{1}{\sqrt{2}}(y) = 0 \implies \sqrt{3} x - 2y = 0\]

Answer 4

\[\frac{\sqrt{3}}{2}x - \frac{1}{\sqrt{2}}(y) = 0 \implies \sqrt{3} x - \sqrt{2}y = 0\]

Answer 5

\[\frac{1}{2}x + \frac{1}{\sqrt{2}}y - 9.81m = 0 \implies x + \sqrt{2}y = 9.81m\]

Answer 6

Add both the equations, you will get \(x\) as :
\[(\sqrt{3} + 1)x = 9.81m \\ x = \frac{9.81m}{\sqrt{3} +1}\]

Answer 7

But that's 3.59, not 7.18

Answer 8

Yes, that is wrong written there.

Answer 9

Good.. :)

Answer 10

Wait, the answer book is wrong?

Answer 11

\(\large\color{black}{ \displaystyle 0 = x\cos(30) - y\cos(45) }\)
\(\large\color{black}{ \displaystyle 0 = x\sin30 - y\sin(45) }\)

cos(45)=sin(45), do you know that?

Answer 12

I don't know what the other 9.81m is

Answer 13

what is 9.81m supposed to be? is that another constant at the end, or what?

You want me to solve for 3 variables in only 2 equations? I am not that good at math-:(

Answer 14

the attachement?

Answer 15

yes, so I guess your answer is in terms of m.

Answer 16

So, that means that the coefficients of y are equivalent.

\(\large\color{black}{ \displaystyle 0 = x\cos(30) - y\cos(45) }\)
\(\large\color{black}{ \displaystyle 0 = x\sin30 - y\sin(45) }\)

for convenience, I will multiply the first eq. times -1,

\(\large\color{black}{ \displaystyle 0 = -x\cos(30) + y\cos(45) }\)
\(\large\color{black}{ \displaystyle 0 = x\sin30 - y\sin(45)-9.81m }\)

Answer 17

Now, add the equations

Answer 18

your y's will go away, because SOMETHING - SOMETHING =0

Answer 19

0 = x(sin30 - cos30) - 9.81m
9.81m = x
x = -26.8

Answer 20

with m

Answer 21

sin(30) is not the same thing cos(30)

Answer 22

oh, weauit

Answer 23

\(\large\color{black}{ \displaystyle 0 = -x\cos30 +x\sin30 - 9.81m}\)

\(\large\color{black}{ \displaystyle 0 = -x(\cos30 -\sin30) - 9.81m}\)

\(\large\color{black}{ \displaystyle 0 = -x(\frac{\sqrt{3} }{2} -\frac{1 }{2}) - 9.81m}\)

\(\large\color{black}{ \displaystyle 0 = -x(\frac{\sqrt{3}-1 }{2}) - 9.81m}\)

Answer 24

and on...

Answer 25

0 = -0.366x - 9.81m
x = 26.8m ?
How is the answer for x, 7.18 then?

Answer 26

\(\large\color{black}{ \displaystyle \frac{-9.81m}{\frac{\sqrt{3}-1 }{2}} = x }\)

\(\large\color{black}{ \displaystyle \frac{-19.62m}{\sqrt{3}-1 } = x }\)

times sqrt(3)+1 on top and bottom

\(\large\color{black}{ \displaystyle \frac{-19.62m(\sqrt{3}+1)}{3-1 } = x }\)

\(\large\color{black}{ \displaystyle \frac{-19.62m(\sqrt{3}+1)}{2 } = x }\)

\(\large\color{black}{ \displaystyle -9.81m(\sqrt{3}+1) = x }\)

Answer 27

this is what I am getting

Answer 28

I am not very good, or let me put it differently, I am really bad at science. This math question although is math, I don't really get the science side where it is coming from....
(not that I am good at math, either)

Answer 29

so I should intentionally get it wrong?