Answer:
≈ 82 feet
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to calculate distance (d)
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Here the hypotenuse is the distance (d) between the 2 poles, hence
d² = 80² + 45² = 6400 + 2025 = 8425 ( take the square root of both sides )
d =
≈ 82 feet ( to the nearest foot )
Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
Answer:
Alternative C is the correct answer
Step-by-step explanation:
The first step is to determine the composite function;
![f[g(x)]](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D)
![f[g(x)]=cos[cot(x)]](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D%3Dcos%5Bcot%28x%29%5D)
We then employ a graphing utility to determine the range and the domain of the new function.
The range is the set of y-values for which the function is defined. In this case it is;
![[-1,1]](https://tex.z-dn.net/?f=%5B-1%2C1%5D)
On the other hand, the domain refers to the set of the x-values for which the function is real and defined. In this case; it is the set of real numbers x except x does not equal npi for all integers n.
Yup! We're all pretty good here. :)
So i think here you would FOIL. so -5x^2+10x-5x+10 and then combine like terms :)