Answer:
the answer is C.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that angle A is in IV quadrant
So A/2 would be in II quadrant.
sin A = -1/3
cos A = ![\sqrt{1-sin^2 A} =\frac{2\sqrt{2} }{3}](https://tex.z-dn.net/?f=%5Csqrt%7B1-sin%5E2%20A%7D%20%3D%5Cfrac%7B2%5Csqrt%7B2%7D%20%7D%7B3%7D)
(cos A is positive since in IV quadrant)
Using this we can find cos A/2
![cosA = 2cos^2 \frac{A}{2} -1\\Or cos \frac{A}{2} =-\sqrt{\frac{1+cosA}{2} } =-\sqrt{\frac{3+2\sqrt{2} }{6} }](https://tex.z-dn.net/?f=cosA%20%3D%202cos%5E2%20%5Cfrac%7BA%7D%7B2%7D%20-1%5C%5COr%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%3D-%5Csqrt%7B%5Cfrac%7B1%2BcosA%7D%7B2%7D%20%7D%20%3D-%5Csqrt%7B%5Cfrac%7B3%2B2%5Csqrt%7B2%7D%20%7D%7B6%7D%20%7D)
Answer:
1. C. cylindrical coordinates
2 A. spherical coordinates
3. A. spherical coordinates
4. D. Cartesian coordinates
5 B. polar coordinates
Step-by-step explanation:
USE THE BOUNDARY INTERVALS TO IDENTIFY
1. ∭E dV where E is:
x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0 -- This is A CYLINDRICAL COORDINATES SINCE x>= 0, y>= 0, z>= 0
2. ∭E z^2 dV where E is:
-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2 This is A SPHERICAL COORDINATES
3. ∭E z dV where E is:
1 <= x <= 2, 3<= y <= 4,5 <= z <= 6 -- This is A SPHERICAL COORDINATES
4. ∫10∫y^20 1/x dx ---- This is A CARTESIAN COORDINATES
5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4 This is A POLAR COORDINATES
900 is the answer of 2 squared times 15 squared
Answer:
![\huge{ \boxed{ \sf{ \frac{4}{3} }}}](https://tex.z-dn.net/?f=%20%5Chuge%7B%20%5Cboxed%7B%20%5Csf%7B%20%5Cfrac%7B4%7D%7B3%7D%20%7D%7D%7D)
Step-by-step explanation:
![\star{ \sf{ \: Let \: the \: points \: be \: A \: and \: B}}](https://tex.z-dn.net/?f=%20%5Cstar%7B%20%5Csf%7B%20%5C%3A%20Let%20%5C%3A%20the%20%5C%3A%20points%20%5C%3A%20be%20%5C%3A%20A%20%5C%3A%20and%20%5C%3A%20B%7D%7D)
![\star{ \sf{ \: Let \: a(2,-1) \: be \: (x1 \:, y1) \: and \: b (5,3) \: be \: (x2 \:, y2)}}](https://tex.z-dn.net/?f=%20%5Cstar%7B%20%5Csf%7B%20%5C%3A%20Let%20%5C%3A%20a%282%2C-1%29%20%20%5C%3A%20be%20%5C%3A%20%28x1%20%5C%3A%2C%20y1%29%20%5C%3A%20and%20%5C%3A%20b%20%285%2C3%29%20%20%5C%3A%20be%20%5C%3A%20%28x2%20%5C%3A%2C%20y2%29%7D%7D)
![\underline{ \sf{Finding \: the \: slope \: of \: the \: line}}](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Csf%7BFinding%20%5C%3A%20the%20%5C%3A%20slope%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20line%7D%7D)
![\boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1} }}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Csf%7BSlope%20%3D%20%20%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D%20%7D%7D)
![\mapsto{ \sf{Slope = \frac{3 - ( - 1)}{5 - 2} }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7BSlope%20%3D%20%20%5Cfrac%7B3%20-%20%28%20-%201%29%7D%7B5%20-%202%7D%20%7D%7D)
![\mapsto{ \sf{Slope = \frac{3 + 1}{5 - 2}}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7BSlope%20%3D%20%20%5Cfrac%7B3%20%2B%201%7D%7B5%20-%202%7D%7D%7D%20)
![\mapsto{ \sf{Slope = \frac{4}{3} }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7BSlope%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%7D%7D)
Hope I helped!
Best regards! :D
~![\text{TheAnimeGirl}](https://tex.z-dn.net/?f=%20%5Ctext%7BTheAnimeGirl%7D)