Answer:
The solutions are 0° and 3π
Step-by-step explanation:
On solving the equation given;
![sin(\frac{3\pi}{2}+x )+ sin(\frac{3\pi}{2}+x ) = -2\\2sin(\frac{3\pi}{2}+x ) = -2\\sin(\frac{3\pi}{2}+x ) = -1\\\frac{3\pi}{2}+x = sin^{-1}-1\\ \frac{3\pi}{2}+x = -\frac{\pi}{2} \\x = -\frac{\pi}{2} -\frac{3\pi}{2} \\x = \frac{-4\pi}{2} \\x = -2\pi\\](https://tex.z-dn.net/?f=sin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%2B%20sin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%20%3D%20-2%5C%5C2sin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%20%3D%20-2%5C%5Csin%28%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%29%20%3D%20-1%5C%5C%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%20%3D%20sin%5E%7B-1%7D-1%5C%5C%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%2Bx%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5C%5Cx%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%5C%5Cx%20%3D%20%20%5Cfrac%7B-4%5Cpi%7D%7B2%7D%20%5C%5Cx%20%3D%20-2%5Cpi%5C%5C)
<u>Since sin is negative in the 3rd and 4th quadrant, </u>
In the 3rd quadrant;
x =180°+2π
x = π + 2π
x = 3π
In the 4th quadrant;
x = 360°-2π
x = 2π-2π
x = 0°
Answer:
Two measurements on a graph meet at a axis
Hello!
![\large\boxed{\text{B. } k(x) = (-x + 3)^{\frac{1}{2} }}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7BB.%20%7D%20k%28x%29%20%3D%20%28-x%20%2B%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%7D%7D)
We can look at each answer choice to verify whether it has a restricted domain or not:
A. ![f(x) = (3x)^{\frac{1}{5}} - 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%283x%29%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%20-%204)
This is a function similar to a cubic root function. Its domain is (-∞, ∞), so it has no restriction.
B. ![k(x) = (-x + 3)^{\frac{1}{2}}](https://tex.z-dn.net/?f=k%28x%29%20%3D%20%28-x%20%2B%203%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
This is a square root function. This graph only consists of x-values in the interval (3, ∞) because you cannot take the square root of a negative number. This function has a restricted domain.
C.
This is a cubic function, so it has an interval of (-∞, ∞)
D. ![h(x) = (4x)^{2} - 5](https://tex.z-dn.net/?f=h%28x%29%20%3D%20%284x%29%5E%7B2%7D%20-%205)
This is a quadratic function, which has no domain restriction.
Therefore, the correct answer is B.
Answer:
1: x > -5
2: n > 4
3: x > -2
Step-by-step explanation:
Answer:
33/2
Step-by-step explanation:
6 * 11/4 = 66/4 = 33/2