Velocity = dy/dx = first derivative of f(x) evaluated at given point. It is the change in position over time.
speed = absolute value of velocity (square your velocity and then square root it)
acceleration = d^2y/dx^2 = second derivative of f(x) evaluated at a given point. It is also the first derivative of your velocity function, or the change in velocity over time.
Both velocity and acceleration are vectors, that is, they are either positive or negative in a direction. Speed is the magnitude of your velocity and has no direction: it is simply the absolute value of your velocity.
2) For multi-variable functions: f(x,y)
velocity = first partial derivative with respect to x + first partial derivative with respect to y. It is the vector sum of these two vectors.
speed = the same as it is for single variable, that is, speed is the absolute value of the velocity. However, in multi-variable functions you must square all your components and then square root it (ie: Pythagorean Theorem: sqrt(i^2+j^2+k^2), with (i,j,k) being the x,y,z, respectively).
acceleration is analogous to single variable acceleration. It is now the 2nd partial with respect to x + 2nd partial with respect to y.
For this case you must first know the definition of density. D = m / v where, m: mass v: volume. You can then write the following hypothesis: IF you know two physical characteristics of an object then you can determine the density. First weigh the object, THEN measure its volume BECAUSE the density is the quotient between the mass and the volume of an object.
Answer: 363 Ω.
Explanation:
In a series AC circuit excited by a sinusoidal voltage source, the magnitude of the impedance is found to be as follows:
Z = √((R^2 )+〖(XL-XC)〗^2) (1)
In order to find the values for the inductive and capacitive reactances, as they depend on the frequency, we need first to find the voltage source frequency.
We are told that it has been set to 5.6 times the resonance frequency.
At resonance, the inductive and capacitive reactances are equal each other in magnitude, so from this relationship, we can find out the resonance frequency fo as follows:
fo = 1/2π√LC = 286 Hz
So, we find f to be as follows:
f = 1,600 Hz
Replacing in the value of XL and Xc in (1), we can find the magnitude of the impedance Z at this frequency, as follows:
Z = 363 Ω