Answer:
![\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%2B%5Csqrt%20%7B2%7D%7D%7B4%7D)
Step-by-step explanation:
We can use the following trigonometrical identity:
(1)
Where
,
are angles, measured in sexagesimal degrees.
If we know that
and
, then the value of the given function is:
![\sin 105^{\circ} = \sin 135^{\circ}\cdot \cos 30^{\circ} - \cos 135^{\circ}\cdot \sin 30^{\circ}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Csin%20135%5E%7B%5Ccirc%7D%5Ccdot%20%5Ccos%2030%5E%7B%5Ccirc%7D%20-%20%5Ccos%20135%5E%7B%5Ccirc%7D%5Ccdot%20%5Csin%2030%5E%7B%5Ccirc%7D)
![\sin 105^{\circ} = \left(\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{\sqrt{3}}{2}\right)-\left(-\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{1}{2}\right)](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright%29-%5Cleft%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29%5Ccdot%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29)
![\sin 105^{\circ} = \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B4%7D%2B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B4%7D)
![\sin 105^{\circ} = \sqrt{\frac{6}{16} }+\sqrt{\frac{2}{16} }](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B6%7D%7B16%7D%20%7D%2B%5Csqrt%7B%5Cfrac%7B2%7D%7B16%7D%20%7D)
![\sin 105^{\circ} = \sqrt{\frac{3}{8} }+\sqrt{\frac{1}{8} }](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B3%7D%7B8%7D%20%7D%2B%5Csqrt%7B%5Cfrac%7B1%7D%7B8%7D%20%7D)
![\sin 105^{\circ} = \frac{\sqrt{3}+1}{2\cdot \sqrt{2}}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%2B1%7D%7B2%5Ccdot%20%5Csqrt%7B2%7D%7D)
![\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}](https://tex.z-dn.net/?f=%5Csin%20105%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B6%7D%2B%5Csqrt%20%7B2%7D%7D%7B4%7D)
Answer:
80%
Step-by-step explanation:
Answer:
1) ![5r + 2 < s](https://tex.z-dn.net/?f=5r%20%2B%202%20%3C%20s)
2) ![12t + 6s < 960](https://tex.z-dn.net/?f=12t%20%2B%206s%20%3C%20960)
3) ![p - q > 30](https://tex.z-dn.net/?f=p%20-%20q%20%3E%2030)
Step-by-step explanation:
1) Length of a ruler = r
Height of Shiela = s
According to the question ,
5 times the length of a ruler increased by 2 .
⇒ ![5r + 2](https://tex.z-dn.net/?f=5r%20%2B%202)
Also , 5r + 2 is less than height of Shiela.
Hence , the linear inequality is ⇒ ![5r + 2 < s](https://tex.z-dn.net/?f=5r%20%2B%202%20%3C%20s)
2) Let the cost of each t-shirt be 't' & cost of each short be 's'.
⇒ Cost of dozen of t-shirts = 12t and Cost of half a dozen shorts = 6s
According to the question ,
12t & 6s is not greater than Php 960.
Hence the linear inequality is ⇒ ![12t + 6s < 960](https://tex.z-dn.net/?f=12t%20%2B%206s%20%3C%20960)
3) Let the number of Php 100-peso tickets be 'p' and let the number of Php 50-peso tickets be 'q'.
According to the question ,
Difference of p & q is not less than 30
Hence the linear inequality is ⇒![p - q > 30](https://tex.z-dn.net/?f=p%20-%20q%20%3E%2030)
Answer: Choice A
This is a 3 by 1 matrix, which can be written "3 x 1 matrix".
There are 3 rows and 1 column. The number of rows is listed first.