Answer:
<4
Step-by-step explanation:
Vertical angles are formed by the same lines and share a vertex but are opposite.
< HEF also called <6 is a vertical angle to < 4
Answer:
The average speed of the object is 18.67 ft/s.
Step-by-step explanation:
Given;
height function, f(t) = -16t² + 42t + 5
The average speed is given by ;
![v = \frac{dx}{dt} \\\\h(t) = -16t^2+42t+5\\\\h(1.5)= -16(1.5)^2 + 42(1.5)+5 = 32 \ ft\\\\](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%5C%5C%5C%5Ch%28t%29%20%3D%20-16t%5E2%2B42t%2B5%5C%5C%5C%5Ch%281.5%29%3D%20-16%281.5%29%5E2%20%2B%2042%281.5%29%2B5%20%20%3D%2032%20%5C%20ft%5C%5C%5C%5C)
from 1.5 s to 2.25 s = 0.75 s,
![h(0.75)= -16(0.75)^2 + 42(0.75)+5 = 27.5 \ ft](https://tex.z-dn.net/?f=h%280.75%29%3D%20-16%280.75%29%5E2%20%2B%2042%280.75%29%2B5%20%20%3D%2027.5%20%5C%20ft)
![h(2.25)= 27.5 +(-16(2.25)^2 + 42(2.25)+5) \\\\h(2.25) = 27.5 + 18.5 = 46 \ ft](https://tex.z-dn.net/?f=h%282.25%29%3D%2027.5%20%2B%28-16%282.25%29%5E2%20%2B%2042%282.25%29%2B5%29%20%5C%5C%5C%5Ch%282.25%29%20%3D%2027.5%20%2B%2018.5%20%3D%2046%20%5C%20ft)
The average speed is given by ;
![v = \frac{h(2.25) - h(1.5)}{2.25-1.5}\\\\v = \frac{46-32}{0.75}\\\\v = 18.67 \ ft/s](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bh%282.25%29%20-%20h%281.5%29%7D%7B2.25-1.5%7D%5C%5C%5C%5Cv%20%3D%20%5Cfrac%7B46-32%7D%7B0.75%7D%5C%5C%5C%5Cv%20%3D%2018.67%20%5C%20ft%2Fs)
Therefore, the average speed of the object is 18.67 ft/s.
Answer:
87,178,291,200 ways
Step-by-step explanation:
Number of songs = 14
To Form an album with the 14 songs, the number of ways at which the 14 songs can be arranged is obtained by calculating the factorial of the number of songs ;
Number of ways in which the 14 songs can be arranged :
14! = (14 * 13 * 12 * 11* 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 87178291200 ways
Answer:
C. 271.44 ![mm^3](https://tex.z-dn.net/?f=mm%5E3)
Step-by-step explanation:
We need to first find the volume of the pipe, then find the volume of the hole and then subtract the volume of the hole from the volume of the pipe.
The diameter of the pipe is 8.4 mm. This means its radius is:
8.4/2 = 4.2 mm
The height of the pipe is 10 mm
The volume of a cylinder is given as:
![V = \pi r^2h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2h)
where r = radius
h - height
Therefore, the volume of the cylinder without the hole is:
![V = \pi * 4.2^2 * 10\\\\V = 554.18 mm^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%2A%204.2%5E2%20%2A%2010%5C%5C%5C%5CV%20%3D%20554.18%20mm%5E3)
The diameter of the hole is 6 mm. Its radius is:
6/2 = 3 mm
The volume of the hole is:
![V = \pi * 3^2 * 10\\\\V = 282.74 mm^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%2A%203%5E2%20%2A%2010%5C%5C%5C%5CV%20%3D%20282.74%20mm%5E3)
The volume is:
554.18 - 282.74 = 271.44 ![mm^3](https://tex.z-dn.net/?f=mm%5E3)
Perimeter: 26
Area: 32
Let me know if you need me to explain in depth!!