translation makes this coordinate -4,0
The velocity is the derivative of position.
... v(t) = r'(t) = -5sin(t)i +4cos(t)j . . . . velocity
The acceleration is the derivative of velocity.
... a(t) = v'(t) = -5cos(t)i -4sin(t)j . . . . acceleration
The speed is the magnitude of velocity.
... s(t) = ||v(t|| = √((-5sin(t))² +(4cos(t))²)
... = √(25sin(t)² +16(1 -sin(t)²))
... s(t) = √(16 +9sin(t)²) . . . . speed
_____
Of course, derivatives of these functions are found from ...
... (d/dt)(sin(t)) = cos(t); (d/dt)(cos(t)) = -sin(t); (d/dt)(a + b) = da/dt + db/dt.
The answer is D bro ppppppp
ANSWER
The exact value is 24√3
The approximate value is 41.6 to the nearest tenth.
x=52.1 units.
EXPLANATION
Let the blue dotted line be h units.
This line is opposite to the 60° angle.
The side length of the triangle which is 24 units is adjacent to the 60° angle.
So we use the tangent ratio,
![\tan(60 \degree) = \frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%20%5Ctan%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Bopposite%7D%7Badjacent%7D%20)
![\tan(60 \degree) = \frac{h}{24}](https://tex.z-dn.net/?f=%20%5Ctan%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Bh%7D%7B24%7D%20)
![\sqrt{3} = \frac{h}{24}](https://tex.z-dn.net/?f=%20%5Csqrt%7B3%7D%20%3D%20%20%5Cfrac%7Bh%7D%7B24%7D%20)
![h = 24 \sqrt{3}](https://tex.z-dn.net/?f=h%20%3D%2024%20%5Csqrt%7B3%7D%20)
This is the exact value.
![h = 41.6](https://tex.z-dn.net/?f=h%20%3D%2041.6)
This is that approximate value to the nearest tenth.
To find the side length , x, we need to use the second triangle.
![\sin(53\degree) = \frac{h}{x}](https://tex.z-dn.net/?f=%20%5Csin%2853%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Bh%7D%7Bx%7D%20)
![\sin(53\degree) = \frac{41.6}{x}](https://tex.z-dn.net/?f=%20%5Csin%2853%5Cdegree%29%20%20%3D%20%20%5Cfrac%7B41.6%7D%7Bx%7D%20)
![x = \frac{41.6}{\sin(53\degree)}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B41.6%7D%7B%5Csin%2853%5Cdegree%29%7D%20%20)
![x = 52.1](https://tex.z-dn.net/?f=x%20%3D%2052.1)
Answer:
B
Step-by-step explanation: