9514 1404 393
Answer:
7.0
Step-by-step explanation:
The relationship of interest is ...
Tan = Opposite/Adjacent
tan(25°) = x/15
x = 15·tan(25°) ≈ 6.9946
x ≈ 7.0
Answer: 
or ![y=\sqrt[3]{8x} -1](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B8x%7D%20-1)
Step-by-step explanation:
To find the inverse, you switch y with x and x with y. Then, you solve for y.
[switch y with x and x with y]
[multiply both sides by 8]
[cube both sides]
![\sqrt[3]{8x} =y+1](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8x%7D%20%3Dy%2B1)
[subtract both sides by 1]
or
<span>cos 2x + sqrt(2) sinx=1
</span><span>
Note that: cos 2x = cos^2x - sin^2x = (1-sin^2x) - sin^2x = 1 - 2sin^2x.
So, when alternatively written, you have the following equation:
</span>- 2sin^2x + sqrt(2)sinx + 1 = 1
- 2sin^2x + sqrt(2)sinx = 0
Then, let z=sin(x). So you get,
- 2z^2 + sqrt(2)z = 0
z(- 2z + sqrt(2)) = 0
Either z=0, or - 2z + sqrt(2) = 0 ---> z=sqrt(2)/2.
Then, since z=0 or z=sqrt(2)/2, therefore sin(x)=0, or sin(x)=sqrt(2)/2.
Then, for you remains just to list the angles. (Let me know if this is not fair or if you got questions.)
Answer:
x = 35, x = 27
Step-by-step explanation:
(9)
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
141° is an exterior angle, thus
x + 24 + 2x + 12 = 141 , that is
3x + 36 = 141 ( subtract 36 from both sides )
3x = 105 ( divide both sides by 3 )
x = 35
-----------------------------------------------------------
(11)
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180, that is
2x - 9 + 3x + 2x = 180
7x - 9 = 180 ( add 9 to both sides )
7x = 189 ( divide both sides by 7 )
x = 27
