the answers are clear if you use priority and equation rules.
- q=11
- u=2
- a=13
- l=8
- s=12
Step-by-step explanation:
42 is your answer according to bodmas
Answer:
![\beta=45\degree\:\:or\:\:\beta=135\degree](https://tex.z-dn.net/?f=%5Cbeta%3D45%5Cdegree%5C%3A%5C%3Aor%5C%3A%5C%3A%5Cbeta%3D135%5Cdegree)
Step-by-step explanation:
We want to solve
, where
.
We rewrite in terms of sine and cosine.
![\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20%5Cbeta%7D%7B%5Ccos%20%5Cbeta%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7B%5Ccos%20%5Cbeta%7D%20%3D%5Csqrt%7B2%7D)
![\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20%5Cbeta%7D%7B%5Ccos%5E2%5Cbeta%7D%3D%5Csqrt%7B2%7D)
Use the Pythagorean identity:
.
![\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20%5Cbeta%7D%7B1-%5Csin%5E2%5Cbeta%7D%3D%5Csqrt%7B2%7D)
![\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)](https://tex.z-dn.net/?f=%5Cimplies%20%5Csin%20%5Cbeta%3D%5Csqrt%7B2%7D%281-%5Csin%5E2%5Cbeta%29)
![\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta](https://tex.z-dn.net/?f=%5Cimplies%20%5Csin%20%5Cbeta%3D%5Csqrt%7B2%7D-%5Csqrt%7B2%7D%5Csin%5E2%5Cbeta)
![\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7B2%7D%5Csin%5E2%5Cbeta%2B%5Csin%20%5Cbeta-%20%5Csqrt%7B2%7D%3D0)
This is a quadratic equation in
.
By the quadratic formula, we have:
![\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%28%5Csqrt%7B2%7D%29%28-%5Csqrt%7B2%7D%20%29%20%7D%20%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%20%7D)
![\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2%2B4%282%29%20%7D%20%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%20%7D)
![\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B9%7D%20%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%20%7D)
![\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D%5Cfrac%7B-1%5Cpm3%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%20%7D)
or ![\sin \beta=\frac{-4}{2\cdot \sqrt{2} }](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D%5Cfrac%7B-4%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%20%7D)
or ![\sin \beta=-\frac{2}{\sqrt{2} }](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D-%5Cfrac%7B2%7D%7B%5Csqrt%7B2%7D%20%7D)
or ![\sin \beta=-\sqrt{2}](https://tex.z-dn.net/?f=%5Csin%20%5Cbeta%3D-%5Csqrt%7B2%7D)
When
, ![\beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )](https://tex.z-dn.net/?f=%5Cbeta%3D%5Csin%20%5E%7B-1%7D%28%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D%20%29)
on the interval
.
When
,
is not defined because ![-1\le \sin \beta \le1](https://tex.z-dn.net/?f=-1%5Cle%20%5Csin%20%5Cbeta%20%5Cle1)
Answer:
The answer is 37.
Step-by-step explanation:
#Hope it helps uh.......
Answer:
I think it is C 8,-4
Step-by-step explanation:
I think