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°
The answer is A in my opinion
Answer:1obtuse ghi h igh 2.acute rqp prq q 3.complementary 4.sorry it’s not visible but if the angle is flat which I asume it’s supplementary
Step-by-step explanation:
Answer:
Volume of cylinder = 360.010cubic inches
Step-by-step explanation:
Volume of a cone
V = πr^2h/3
V - volume
π - pie
r - radius
h - height
Given
V = 120 inches cubic
π - 3.142
120 = 3.142 * r^2 * h/3
120 = 3.142r^2h/3
120 = 3.142/3 * r^2h
120 = 1.0473r^2h
r^2h = 120 / 1.0473
= 114.580
Make h the subject of the formula
h = 114.580 / r^2
Gotten the value for h, substitute h into the formula for volume of a cylinder
Since the cone and the cylinder has the same base and height
V = πr^2h
h = 114.580/r^2
π - 3.142
V = 3.142 * r^2 * (114.580/r^2)
V = 3.142 * r^2 * 114.580/r^2
r^2 divides r^2
V = 3.142 * 114.580
V = 360.010 cubic inches
Answer:
![A'(-3,0),B'(8,3),C'(2,-9)](https://tex.z-dn.net/?f=A%27%28-3%2C0%29%2CB%27%288%2C3%29%2CC%27%282%2C-9%29)
Step-by-step explanation:
we know that
the triangle is translated 4 units right and 6 units down
so
The rule for the translation is
![(x,y) -----> (x+4,y-6)](https://tex.z-dn.net/?f=%28x%2Cy%29%20-----%3E%20%28x%2B4%2Cy-6%29)
Applying the rule for the translation find the image of each vertex
1) ![A(-7,6) -----> A'(-7+4,6-6)](https://tex.z-dn.net/?f=A%28-7%2C6%29%20-----%3E%20A%27%28-7%2B4%2C6-6%29)
![A(-7,6) -----> A'(-3,0)](https://tex.z-dn.net/?f=A%28-7%2C6%29%20-----%3E%20A%27%28-3%2C0%29)
2) ![B(4,9) -----> B'(4+4,9-6)](https://tex.z-dn.net/?f=B%284%2C9%29%20-----%3E%20B%27%284%2B4%2C9-6%29)
![B(4,9) -----> B'(8,3)](https://tex.z-dn.net/?f=B%284%2C9%29%20-----%3E%20B%27%288%2C3%29)
3) ![C(-2,-3) -----> C'(-2+4,-3-6)](https://tex.z-dn.net/?f=C%28-2%2C-3%29%20-----%3E%20C%27%28-2%2B4%2C-3-6%29)
![C(-2,-3) -----> C'(2,-9)](https://tex.z-dn.net/?f=C%28-2%2C-3%29%20-----%3E%20C%27%282%2C-9%29)