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What does the constant rate of change mean in math?
The change in y over the change in x
How does the constant rate of change show up in the table?
You have already assumed the information in the table is linear in nature. Given that information, the constant rate of change is the ratio of the amount of change in the dependent variable compared to the amount of change of the independent variable. Put a simpler way, it is change in y divided by change in x.
How do you find the average rate of change for a linear function?
A linear function has a constant rate of change - so the average rate of change is the same as the rate of change.Take any two points, A = (p,q) and B = (r, s) which satisfy the function. Then the rate of change is(q - s)/(p - r).If the linear equation is given:in the form y = mx + c then the rate of change is m; orin the form ax + by + c = 0 [the standard form] then the rate is -a/b.
How is slope and constant rate of change the same?
Slope is known as rise over run. Rise means the amount of units the y-value (or second dimension) has traveled up the y-axis or down the y-axis. Run means the amount of units the x-value (the first dimension) has traveled forwards or backwards on the x-axis. Take a slope of 2 (can also be written as 2/1) that means it goes up two units as it goes over 1 unit for the whole entire graph. A slope of 5/7 means it goes with a y-value of 5 up and an x-value of 7 over. This can be done for any number even negative numbers. Ok... so now to relate it to a constant rate of change. Imagine the dimensions (x and y values) go on for an infinite amount. The slope will be constant throughout infinity. It will always have the same rise over run... It will always be constant. The rate of change is equivalent to the saying "rise over run". Since the slope is constant over infinity the constant rate of change is the same thing across infinity.
What is the integral of f prime divided by the quantity f times the square root of the quantity f squared minus a squared with respect to x where f is a function of x and a is a constant?
∫ f'(x)/[f(x)√(f(x)2 - a2)] dx = (1/a)arcses(f(x)/a) + C C is the constant of integration.
Why is the slope called the rate of change?
On a graph, the slope does tell you the rate of change of y with respect to x. If the slope is steep, that means that there is a high rate of change of y with respect to x. If the slope is shallow, then y is not changing that rapidly with respect to x.
What is the rate of change for -21x plus 9?
The rate of change, with respect to x, is -21.
What does the constant rate of change mean in math?
The change in y over the change in x
Chain rule in calculus?
If y is a differentiable function of u, and u is a differentiable function of x. Then y has a derivative with respect to x given by the formula : dy/dx = dy/du. du/dx This formula is known as the Chain Rule and says, " The rate of change of y with respect to x is the rate of change of y with respect to u multiplied by the rate of change of u with respect to x."
What units are used for rate of change?
Suppose Y is a variable which is dependent on another variable X. Then the units used for the rate of change in Y, with respect to X, will be the units of Y divided by the units of X. For example, if x is the length of a side of a cube (in cm), and Y is its volume (in cm3), then the rate of change of Y, with respect to X, is measures in cm3/cm.
What is the rate of change in the equation x equal 9?
0. Differentiation of a constant gives f'(x)=0.
What is the third derivative of the function x with respect to time, denoted as d3x/dt3?
The third derivative of the function x with respect to time is the rate of change of the acceleration of x with respect to time. It is denoted as d3x/dt3.
What would be the rule with a constant rate of change of 1 on the x-axis and with a constant rate of change of 2 on the y-axis?
-1
What is an example of constant rate of change?
A constant rate of change is anything that increases or decreases by the same amount for every trial. Therefore an example could be driving down the highway at a speed of exactly 60 MPH. If your speed doesn't change you are driving at a constant rate. Here's another: your cell phone company charges you $0.55 for every minute you use. The rate that you are charged always stays the same so it is a constant rate of change. Anything that goes up by X number of units for every Y value every time is a constant rate of change.
What is the rate of change of the quantity represented by the function d3x/dt3?
The rate of change of the quantity represented by the function d3x/dt3 is the third derivative of x with respect to t.
Can a rate change and the slope of the line be different quantities?
The instantaneous rate change of the variable y with respect to x must be the slope of the line at the point represented by that instant. However, the rate of change of x, with respect to y will be different [it will be the x/y slope, not the y/x slope]. It will be the reciprocal of the slope of the line. Also, if you have a time-distance graph the slope is the rate of chage of distance, ie speed. But, there is also the rate of change of speed - the acceleration - which is not DIRECTLY related to the slope. It is the rate at which the slope changes! So the answer, in normal circumstances, is no: they are the same. But you can define situations where they can be different.
How does the constant rate of change show up in the table?
You have already assumed the information in the table is linear in nature. Given that information, the constant rate of change is the ratio of the amount of change in the dependent variable compared to the amount of change of the independent variable. Put a simpler way, it is change in y divided by change in x.
