The position of the particle is given by:
x(t) = t³ - 12t² + 21t - 9
Differentiate x(t) with respect to t to find the velocity x'(t):
x'(t) = 3t² - 24t + 21
Differentiate x'(t) with respect to t to find the acceleration x''(t):
x''(t) = 6t - 24
Answer:
B) Angular velocity
Explanation:
The equivalent of Newton's second law for the rotational motions can be written as:
where
is the net torque applied to the object
I is the moment of inertia
is the angular acceleration
From the formula we see that when a constant net torque is applied, then the object also has a constant angular acceleration, .
But we also know that
where 
is the angular velocity: so, a constant angular acceleration means that the angular velocity of the object is changing, so the correct answer is
B) Angular velocity
(moment of inertia and center of gravity do not change since they only depend on the mass and the geometry/shape of the object, which do not change)
Answer:
3 times louder
Explanation:
The Loudness in decibel Db L = 10㏒(I/I₀) where I = sound intensity level and I₀ = threshold of hearing = 10⁻¹² W/m².
Now, for Jessica, I₁ = sound intensity level of Jessica's music = 10⁻⁹
and I₂ = sound intensity level of Braylee's music = 10⁻³
So, substituting the variables into the equation, we have
L₁ = 10㏒(I₁/I₀)
L₁ = 10㏒(10⁻⁹/10⁻¹²)
L₁ = 10㏒(10³)
L₁ = 3 × 10㏒10
L₁ = 30㏒10
L₁ = 30 dB
Now, for Braylee, I₂ = sound intensity level of Braylee's music = 10⁻³
So, substituting the variables into the equation, we have
L₂ = 10㏒(I₁/I₀)
L₂ = 10㏒(10⁻³/10⁻¹²)
L₂ = 10㏒(10⁹)
L₂ = 9 × 10㏒10
L₂ =90㏒10
L₂ = 90 dB
So, the number of times Braylee's music is louder than Jessica's music is L₂/L₁ = 90 dB/30 dB = 3
So, Braylee's music is 3 times louder than Jessica's music
Answer:
(C) 15 Feet
Explanation:
You must park at lest 15 Feet away from a fire hydrant.
If you disobey this law, you could be fined up to $115 dollars.
Answer:
They host three or more distinct ecosystems at different elevations.
Explanation:
I checked it, and its right.
