Answer:
![\fbox{\begin{minipage}{5em}13. 0.830\\14. 0.800\\15. 0.391\\16. 0.750\end{minipage}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%7Bminipage%7D%7B5em%7D13.%200.830%5C%5C14.%200.800%5C%5C15.%200.391%5C%5C16.%200.750%5Cend%7Bminipage%7D%7D)
Step-by-step explanation:
A right triangle with 3 sides: adjacent side, opposite side and hypotenuse (as shown in attached picture)
According to the trigonometric properties:
![sin(theta) = \frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=sin%28theta%29%20%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
![cos(theta) = \frac{adjacent}{hypotenuse}](https://tex.z-dn.net/?f=cos%28theta%29%20%3D%20%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D)
![tan(theta) = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=tan%28theta%29%20%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%7D)
![(adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}](https://tex.z-dn.net/?f=%28adjacent%29%5E%7B2%7D%20%2B%20%28opposite%29%5E%7B2%7D%20%3D%20%28hypotenuse%29%5E%7B2%7D)
![(adjacent)^{2} = (hypotenuse)^{2} - (opposite)^{2}](https://tex.z-dn.net/?f=%28adjacent%29%5E%7B2%7D%20%3D%20%28hypotenuse%29%5E%7B2%7D%20-%20%28opposite%29%5E%7B2%7D)
![(opposite)^{2} = (hypotenuse)^{2} - (adjacent)^{2}](https://tex.z-dn.net/?f=%28opposite%29%5E%7B2%7D%20%3D%20%28hypotenuse%29%5E%7B2%7D%20-%20%20%28adjacent%29%5E%7B2%7D)
Use the above formulas with corresponding sides:
![13) cos(theta) = \frac{9}{3\sqrt{13} } = 0.83](https://tex.z-dn.net/?f=13%29%20cos%28theta%29%20%3D%20%5Cfrac%7B9%7D%7B3%5Csqrt%7B13%7D%20%7D%20%3D%200.83)
![14) sin(theta) = \frac{\sqrt{5^{2}-3^{2} } }{5} = \frac{4}{5} = 0.8](https://tex.z-dn.net/?f=14%29%20sin%28theta%29%20%3D%20%5Cfrac%7B%5Csqrt%7B5%5E%7B2%7D-3%5E%7B2%7D%20%20%7D%20%7D%7B5%7D%20%3D%20%5Cfrac%7B4%7D%7B5%7D%20%3D%200.8)
![15) sin(theta) = \frac{9}{\sqrt{(8\sqrt{7}) ^{2} + 9^{2} } } = 0.391](https://tex.z-dn.net/?f=15%29%20sin%28theta%29%20%3D%20%5Cfrac%7B9%7D%7B%5Csqrt%7B%288%5Csqrt%7B7%7D%29%20%5E%7B2%7D%20%2B%209%5E%7B2%7D%20%7D%20%7D%20%20%3D%200.391)
![16) tan(theta) = \frac{3}{4} = 0.75](https://tex.z-dn.net/?f=16%29%20tan%28theta%29%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20%3D%200.75)
Hope this helps!
:)
C) 2x^2 + 3/2x - 5
Just add the two functions.
9514 1404 393
Answer:
A: 144 cm
B: 64 cm
C: 36 cm
Step-by-step explanation:
The volume of a cone is given by ...
V = (1/3)πr²h
Solving for h, we get ...
3V/(πr²) = h
Filling in the given values, we get ...
3(192π)/(πr²) = h
576/r² = h
Then the heights of the different cones are ...
A: r = 2, h = 576/4 = 144 . . . cm
B: r = 3, h = 576/9 = 64 . . . cm
C: r = 4, h = 576/16 = 36 . . . cm
I am sorry but I might not be able to show my work. But the answer is a trapezoid. This is what I did. I looked through my geometry angles, lines and shapes flash cards and saw the trapezoid. It only has one pair of parrelell sides. ( in a regular one it would be the top and bottom) and it has four sides so it is a quadrilateral. And so the answer is a trapezoid. I hope this helped you!