Answer:
it could be 372 adults with one kid or 426 kids with no adults but that isn't logical
Step-by-step explanation:
i don't really know how to explain it sorry
Answer:
2
Step-by-step explanation:
Diagonals of a parallelogram bisects each other.
Therefore,
4x = 8
x = 8/4
x = 2
Or
5x = 3x + 4
5x - 3x = 4
2x = 4
x = 4/2
x = 2
Answer:
The golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of
.
Step-by-step explanation:
The formula from the maximum distance of a projectile with initial height h=0, is:
![d(\theta)=\frac{v_i^2sin(2\theta)}{g}](https://tex.z-dn.net/?f=d%28%5Ctheta%29%3D%5Cfrac%7Bv_i%5E2sin%282%5Ctheta%29%7D%7Bg%7D)
Where
is the initial velocity.
In the closed interval method, the first step is to find the values of the function in the critical points in the interval which is
. The critical points of the function are those who make
:
![d(\theta)=\frac{v_i^2\sin(2\theta)}{g}\\d'(\theta)=\frac{v_i^2\cos(2\theta)}{g}*(2)\\d'(\theta)=\frac{2v_i^2\cos(2\theta)}{g}](https://tex.z-dn.net/?f=d%28%5Ctheta%29%3D%5Cfrac%7Bv_i%5E2%5Csin%282%5Ctheta%29%7D%7Bg%7D%5C%5Cd%27%28%5Ctheta%29%3D%5Cfrac%7Bv_i%5E2%5Ccos%282%5Ctheta%29%7D%7Bg%7D%2A%282%29%5C%5Cd%27%28%5Ctheta%29%3D%5Cfrac%7B2v_i%5E2%5Ccos%282%5Ctheta%29%7D%7Bg%7D)
![d'(\theta)=0\\\frac{2v_i^2\cos(2\theta)}{g}=0\\\cos(2\theta)=0\\2\theta=\pi/2,3\pi/2,5\pi/2,...\\\theta=\pi/4,3\pi/4,5\pi/4,...](https://tex.z-dn.net/?f=d%27%28%5Ctheta%29%3D0%5C%5C%5Cfrac%7B2v_i%5E2%5Ccos%282%5Ctheta%29%7D%7Bg%7D%3D0%5C%5C%5Ccos%282%5Ctheta%29%3D0%5C%5C2%5Ctheta%3D%5Cpi%2F2%2C3%5Cpi%2F2%2C5%5Cpi%2F2%2C...%5C%5C%5Ctheta%3D%5Cpi%2F4%2C3%5Cpi%2F4%2C5%5Cpi%2F4%2C...)
The critical value inside the interval is
.
![d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\d(\pi/4)=\frac{v_i^2sin(2(\pi/4))}{g}\\d(\pi/4)=\frac{v_i^2sin(\pi/2)}{g}\\d(\pi/4)=\frac{v_i^2(1)}{g}\\d(\pi/4)=\frac{(200)^2}{32}\\d(\pi/4)=\frac{40000}{32}\\d(\pi/4)=1250ft](https://tex.z-dn.net/?f=d%28%5Ctheta%29%3D%5Cfrac%7Bv_i%5E2sin%282%5Ctheta%29%7D%7Bg%7D%5C%5Cd%28%5Cpi%2F4%29%3D%5Cfrac%7Bv_i%5E2sin%282%28%5Cpi%2F4%29%29%7D%7Bg%7D%5C%5Cd%28%5Cpi%2F4%29%3D%5Cfrac%7Bv_i%5E2sin%28%5Cpi%2F2%29%7D%7Bg%7D%5C%5Cd%28%5Cpi%2F4%29%3D%5Cfrac%7Bv_i%5E2%281%29%7D%7Bg%7D%5C%5Cd%28%5Cpi%2F4%29%3D%5Cfrac%7B%28200%29%5E2%7D%7B32%7D%5C%5Cd%28%5Cpi%2F4%29%3D%5Cfrac%7B40000%7D%7B32%7D%5C%5Cd%28%5Cpi%2F4%29%3D1250ft)
The second step is to find the values of the function at the endpoints of the interval:
![d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\\theta=0\\d(0)=\frac{v_i^2sin(2(0))}{g}\\d(0)=\frac{v_i^2(0)}{g}=0ft\\\theta=\pi/2\\d(\pi/2)=\frac{v_i^2sin(2(\pi/2))}{g}\\d(\pi/2)=\frac{v_i^2sin(\pi)}{g}\\d(\pi/2)=\frac{v_i^2(0)}{g}=0ft](https://tex.z-dn.net/?f=d%28%5Ctheta%29%3D%5Cfrac%7Bv_i%5E2sin%282%5Ctheta%29%7D%7Bg%7D%5C%5C%5Ctheta%3D0%5C%5Cd%280%29%3D%5Cfrac%7Bv_i%5E2sin%282%280%29%29%7D%7Bg%7D%5C%5Cd%280%29%3D%5Cfrac%7Bv_i%5E2%280%29%7D%7Bg%7D%3D0ft%5C%5C%5Ctheta%3D%5Cpi%2F2%5C%5Cd%28%5Cpi%2F2%29%3D%5Cfrac%7Bv_i%5E2sin%282%28%5Cpi%2F2%29%29%7D%7Bg%7D%5C%5Cd%28%5Cpi%2F2%29%3D%5Cfrac%7Bv_i%5E2sin%28%5Cpi%29%7D%7Bg%7D%5C%5Cd%28%5Cpi%2F2%29%3D%5Cfrac%7Bv_i%5E2%280%29%7D%7Bg%7D%3D0ft)
The biggest value of f is gived by
, therefore
is the absolute maximum.
In the context of the problem, the golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of
.
Answer:
(x-1)^5 (x+1)
Step-by-step explanation:
2 (x-1)^5 + (x-1)^6
Factor out (x-1)^5
2 (x-1)^5 + (x-1)^5 (x-1)
(x-1)^5( 2 + x-1)
Combine like terms
(x-1)^5 (x+1)
(0, 56)
hope this helps :D