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How do you determine if a rate of change is constant?
You can determine if a rate of change is constant, by taking the instantaneous rate of change at multiple points - if they are all equal to each other, it can be assumed that the rate of change is constant. Alternatively, you can differentiate the function (if there is an associated function) - if this comes to a constant i.e. a number, then the rate of change is constant.
How do you find rate of change if change is not constant?
Find the derivative
What is differential equations as it relates to algebra?
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
What is the unit rate of change of d with respect to t ( That is a change of 1 unit in t will correspond to a change of how many units in d )?
The unit rate of change of d with respect to t is the slope of the line representing the relationship between d and t. It indicates how much d changes for every one unit change in t. Mathematically, it is calculated as the change in d divided by the change in t, often denoted as Δd/Δt. This value represents the instantaneous rate of change at a specific point on the curve.
How do you determine the instantaneous rate of change of compound interest compounded annually?
The derivative is at*ln(a) wheret is the time period, ln is the natural log and a is the multiplier for the annual interest rate: eg if the interest rate is r% then a = (1 + r/100).
What is the rate of change in a position at a given point in time?
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
What is the rate of change in position in a given point of time?
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
What is The rate in change of position at a given point in time?
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
What is application of differentiator?
Finding the rate of change - in particular, the instantaneous rate of change.
What is the difference between a slope and rate of change?
Depends. Slope of tangent = instantaneous rate of change. Slope of secant = average rate of change.
How does average change help find instant rate of change in math?
This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.
Find the instantaneous angular acceleration t5.0 with the instantaneous velocity of 6.0 rads t?
To find the instantaneous angular acceleration, you need to know the time rate of change of the instantaneous angular velocity. Without this information, you cannot calculate the instantaneous angular acceleration at t=5.0s.
The rate of change in position at a given point in time?
Ah, honey, you're talking about velocity! Velocity is the rate of change in position at a specific point in time. It's like speed dating for math - how fast an object is moving at any given moment. So next time someone asks about the rate of change in position, you can confidently say, "Oh, that's just velocity, darling."
What is the purpose of finding derivative?
The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
At a given moment in time instantaneous speed can be though of as the magnitude of instantaneous of what?
At a given moment in time, instantaneous speed can be thought of as the magnitude of the instantaneous velocity of an object. Instantaneous velocity is the rate of change of an object's position at that specific moment in time.
Is the rate at which an object changes velocity?
No, velocity is the instantaneous speed of an object, the rate of change would be the acceleration of the object.
What is the rate of change of position at a specific point in time?
The rate of change of position is the velocity. The velocity at a specific point in time is called the instantaneous velocity.
