In Bernoulli's equation, the variable "z" represents the elevation or height of a point above a reference level. It is significant because it accounts for the potential energy of the fluid due to its position in a gravitational field.
The control variable is not manipulated but kept constant to serve as a baseline for comparison. The response variable is the one that is measured and represents the data being recorded to observe any changes or effects caused by manipulating the control variable.
7 pounds
The moment of inertia about the z-axis is given by the equation I = mr^2, where m is the mass and r is the distance from the z-axis. For the moment of inertia to be zero, the mass must be placed at the origin (r=0) along the z-axis. So, the 8.4kg mass must be placed at the origin (0,0,0) to have a moment of inertia of zero about the z-axis.
In statistical mechanics, the Helmholtz free energy is related to the partition function through the equation F -kT ln(Z), where F is the Helmholtz free energy, k is the Boltzmann constant, T is the temperature, and Z is the partition function. This equation describes how the Helmholtz free energy is connected to the microscopic states of a system as described by the partition function.
There is no generic "vibration" equation, as many different things can vibrate with many different boundary conditions. There is, however, a generic wave equation which, as I just hinted at, can be used to formulate equations for specific vibrations.Given a function u(x,y,z,t) where x, y, and z are spatial coordinates in Euclidean space and t is time, the wave equation is given as:∂2u/∂t2 = vp2∇2u,where vp is the phase velocity of the wave and ∇2 is the Laplacian.For the specific example of a vibrating string with a small amplitude, the wave equation becomes:∂2y/∂t2 = v2∂2y/∂x2,where y(x,t) and v is the velocity of the wave.The remarkable thing about the wave equation is how often Mother Nature uses it. The "u(x,y,z,t)" can describe the vibration of a drum head, the electromagnetic fields of light, the ripples on water, the sound of your voice and much more.
To isolate the variable ( z ) in the equation (-15z = 60), you would divide both sides of the equation by (-15). This operation will give you ( z = \frac{60}{-15} ), simplifying to ( z = -4 ).
Z is a constant variable in this equation. A constant variable is a variable, the value of which can never change. In this case, z would be equal to 7.
It is a linear equation in the variable z.
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It multiplies the variable as for example 3z means 3 times z
The variable expression of "z plus 8" is represented as z + 8. In algebra, variables like z can take on different values, while constants like 8 remain the same. When you see "z + 8" in an equation or expression, it means that the variable z is being added to the constant 8.
Given a random variable X with mean M and standard deviation S, Z = (X - M)/S
In the given equation, the relationship between the variables xz and yz is that they are both multiplied by the variable z.
It means that you find the specific value of the equation substituting your specific variables. for example: equation: z=2y+x-3 the evaluatio of the equation for x=1 and y=3 will be: z=2(3)+1-3=4
A function of one variable is of the form y=f(x) where all you need to know in order to get values for y is the value of the independent variable, x. A function of two variables is of the form z=f(x,y) where you need to know the values of both x and y to get a value for z. A linear equation is simply and algebraic equation where all variables, regardless of how many there are, are raised to the power of one.
Z is a variable with mean 0 and variance 1.Z is a variable with mean 0 and variance 1.Z is a variable with mean 0 and variance 1.Z is a variable with mean 0 and variance 1.
a variable