F(2y + 1) is 2
+
for this question
Answer:
½ ln 3
Step-by-step explanation:
∫ sec²x / tan x dx
If u = tan x, then du = sec²x dx.
∫ du / u
ln|u| + C
ln|tan x| + C
Evaluate between π/4 and π/3.
ln|tan(π/3)| + C − (ln|tan(π/4)| + C)
ln|√3| + C − ln|1| − C
ln(√3)
½ ln 3
2.3 is the other length
Hope this helps :)
The length of one side of the octagon is given by:
![L = 72/8 L = 9](https://tex.z-dn.net/?f=L%20%3D%2072%2F8%0A%0AL%20%3D%209)
Then, the apothem can be determined using the Pythagorean theorem in the following way:
![11.8 ^ 2 = (9/2) ^ 2 + a ^ 2 ](https://tex.z-dn.net/?f=11.8%20%5E%202%20%3D%20%289%2F2%29%20%5E%202%20%2B%20a%20%5E%202%0A)
Clearing to have:
![a = 10.91](https://tex.z-dn.net/?f=a%20%3D%2010.91)
Then, the area is given by:
![A = (8) * (1/2) * (L) * (a) ](https://tex.z-dn.net/?f=A%20%3D%20%288%29%20%2A%20%281%2F2%29%20%2A%20%28L%29%20%2A%20%28a%29%0A)
Where,
L: length of the octagon sides
a: apotema
Substituting values:
Answer:
the approximate length of the apothem is:
a = 10.91 feet
The approximate area of the floor of the gazebo is:
A = 392.76 feet ^ 2