Answer:
Angle 3 is 65
Angle 8 is 115
Step-by-step explanation:
Answer:
<em>B. The graph of g is the graph of f shifted 2 units down</em>
Step-by-step explanation:
<u>Graph of Functions</u>
We have two functions:
f(x)=3^x
g(x)=3^x-2
Since g(x)=f(x)-2 it will be represented as an identical graph as that for f(x), but vertically displaced 2 units down. Let's check it by plugging some points
f(0)=3^0=1
g(0)=3^0-2=-1
f(1)=3^1=3
g(1)=3^1-2=1
f(3)=3^3=27
g(3)=3^3-2=25
We can notice the values of g(x) are always 2 units below f(x), thus the correct answer is
B. The graph of g is the graph of f shifted 2 units down
Answer:
the distance of the Bird (B) from the plane (P) is = 10779 ft
Step-by-step explanation:
From the given information:
a diagrammatic representation is attached below for better understanding and solution to the question.
From the diagram;
Let the Bird (B) be represent as A
The plane (P) be represented by B
The observer be represented by O
and the tower T be represented by C
we will see that:

Also;

AO = BC = 7000
Let consider the trigonometry of triangle BAO
tan θ = opposite/adjacent
tan 33° = 7000/x
0.6494 = 7000/x
x = 7000/0.6494
x = 10779.18
x = 10779 ft ( to the nearest whole number)
Thus; the distance of the Bird (B) from the plane (P) is = 10779 ft
the solid is made up of 2 regular octagons, 8 sides, joined up by 8 rectangles, one on each side towards the other octagonal face.
from the figure, we can see that the apothem is 5 for the octagons, and since each side is 3 cm long, the perimeter of one octagon is 3*8 = 24.
the standing up sides are simply rectangles of 8x3.
if we can just get the area of all those ten figures, and sum them up, that'd be the area of the solid.
![\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=5\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(5)(24)\implies \stackrel{\textit{just for one octagon}}{A=60} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{two octagon's area}}{2(60)}~~+~~\stackrel{\textit{eight rectangle's area}}{8(3\cdot 8)}\implies 120+192\implies 312](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dap~~%20%5Cbegin%7Bcases%7D%20a%3Dapothem%5C%5C%20p%3Dperimeter%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D5%5C%5C%20p%3D24%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%285%29%2824%29%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bjust%20for%20one%20octagon%7D%7D%7BA%3D60%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Btwo%20octagon%27s%20area%7D%7D%7B2%2860%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Beight%20rectangle%27s%20area%7D%7D%7B8%283%5Ccdot%208%29%7D%5Cimplies%20120%2B192%5Cimplies%20312)