Answer:
Octagonal pyramid
Step-by-step explanation:
Hexagonal Prism: 8 faces
2 hexagon bases, and 6 faces that connect each side of the bases
Octagonal pyramid: 9 faces
One octagon base, and 8 faces that meet at a point- all extending from each side of the base
Rectangular prism: 6 faces
Two rectangle bases, and 4 faces connecting each side of the bases
Pentagonal pyramid: 6 faces
One pentagon base, and 5 faces that meet at a point- all extending from each side of the base
I recommend searching for a picture of each of the figures to help you understand this.
8)
is -0.896 radians
9) length of arc is 41.91 cm
Solution:
8)
Given that,
![tan\ \theta = \frac{-5}{4}](https://tex.z-dn.net/?f=tan%5C%20%5Ctheta%20%3D%20%5Cfrac%7B-5%7D%7B4%7D)
is in quadrant 4
To find: ![\theta](https://tex.z-dn.net/?f=%5Ctheta)
From given,
![tan\ \theta = \frac{-5}{4}\\\\\theta = tan^{-1} \frac{-5}{4}\\\\\theta = tan^{-1} (-1.25)\\\\\theta = -51.34](https://tex.z-dn.net/?f=tan%5C%20%5Ctheta%20%3D%20%5Cfrac%7B-5%7D%7B4%7D%5C%5C%5C%5C%5Ctheta%20%3D%20tan%5E%7B-1%7D%20%5Cfrac%7B-5%7D%7B4%7D%5C%5C%5C%5C%5Ctheta%20%3D%20tan%5E%7B-1%7D%20%28-1.25%29%5C%5C%5C%5C%5Ctheta%20%3D%20-51.34)
Thus value of
is -51.34 degrees
Convert degrees to radians
![-51.34\ degree = -51.34 \times \frac{ \pi }{180}\ radian\\\\-51.34\ degree = -0.896\ radian](https://tex.z-dn.net/?f=-51.34%5C%20degree%20%3D%20-51.34%20%5Ctimes%20%5Cfrac%7B%20%5Cpi%20%7D%7B180%7D%5C%20radian%5C%5C%5C%5C-51.34%5C%20degree%20%3D%20-0.896%5C%20radian)
Thus
is -0.896 radians
9)
From given,
radius = 15.4 cm
![\theta = \frac{13 \pi }{15}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Cfrac%7B13%20%5Cpi%20%7D%7B15%7D)
<em><u>The length of arc when angle in radians is:</u></em>
![arc\ length = r \times \theta\\\\arc\ length = 15.4 \times \frac{ 13 \pi }{15}\\\\arc\ length = 15.4 \times 2.721\\\\arc\ length = 41.91](https://tex.z-dn.net/?f=arc%5C%20length%20%3D%20r%20%5Ctimes%20%5Ctheta%5C%5C%5C%5Carc%5C%20length%20%3D%2015.4%20%5Ctimes%20%5Cfrac%7B%2013%20%5Cpi%20%7D%7B15%7D%5C%5C%5C%5Carc%5C%20length%20%3D%2015.4%20%5Ctimes%202.721%5C%5C%5C%5Carc%5C%20length%20%3D%2041.91)
Thus length of arc is 41.91 cm