Answer:
![$L=\frac{v^2}{2-2\cos(\theta)}$](https://tex.z-dn.net/?f=%24L%3D%5Cfrac%7Bv%5E2%7D%7B2-2%5Ccos%28%5Ctheta%29%7D%24)
Step-by-step explanation:
Solve for
in
![$L-L \cos(\theta)=\frac{v^2}{2} \Longrightarrow L(1-\cos(\theta))=\frac{v^2}{2}$](https://tex.z-dn.net/?f=%24L-L%20%5Ccos%28%5Ctheta%29%3D%5Cfrac%7Bv%5E2%7D%7B2%7D%20%5CLongrightarrow%20L%281-%5Ccos%28%5Ctheta%29%29%3D%5Cfrac%7Bv%5E2%7D%7B2%7D%24)
![$L=\frac{v^2}{2(1-\cos(\theta))}=\frac{v^2}{2-2\cos(\theta)}$](https://tex.z-dn.net/?f=%24L%3D%5Cfrac%7Bv%5E2%7D%7B2%281-%5Ccos%28%5Ctheta%29%29%7D%3D%5Cfrac%7Bv%5E2%7D%7B2-2%5Ccos%28%5Ctheta%29%7D%24)
Answer:
195
Step-by-step explanation:
To find the 23rd term of this sequence, we can use the arithmetic sequence formula
where,
=
term
= first term
= term position
= common difference
![a_{23}=-25+(23-1)10](https://tex.z-dn.net/?f=a_%7B23%7D%3D-25%2B%2823-1%2910)
![a_{23} =195](https://tex.z-dn.net/?f=a_%7B23%7D%20%3D195)
Answer:
Step-by-step explanation:
This is function composition. We will take the g function and plug it into the f function wherever we see an x. That will look like this when it's done but before it's simplified:
and that can be simplified down to
![f(g(x))=\frac{5x-7}{5x-4}](https://tex.z-dn.net/?f=f%28g%28x%29%29%3D%5Cfrac%7B5x-7%7D%7B5x-4%7D)
The domain of this function will be all real numbers EXCEPT for the one(s) that cause the denominator to become undefined. Set the denominator equal to 0 and solve for x:
5x - 4 = 0 so
5x = 4 and
x = 4/5
In other words, D = {x | x ≠ 4/5}
Pytagorean theorem
height10
attached at 10-4=6 yards from bottom
8 yards from base to away
a^2+b^2=c^2
a and b are side legnths and c=hypotonuse
so therfore we are given a and b and we must solve for c
so
6=height
8=base
6^2+8^2=c^2
36+64=c^2
100=c^2
square root
10=c
so therfor the legnth of each cable is 10 yards
3 cables so 3 times 10=30
30 yards needed