What is Rate of change: Definition and 279 Discussions
In mathematics, a rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable.
One common type of rate is "per unit of time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates, and electric field (in volts per meter).
In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%), fraction, or multiple.
Often rate is a synonym of rhythm or frequency, a count per second (i.e., hertz); e.g., radio frequencies, heart rates, or sample rates.
If xy^2=12 and dy/dt=6, find dx/dt when y=2
The way i thought to do this would be
(1)(y^2)+x(y)(dy/dt)=0 but i don't know x so this isn't working, what am i doing wrong
Homework Statement
A particle is moving along the curve y= 3 \sqrt(4 x + 4). As the particle passes through the point (3, 12), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
Homework...
Homework Statement
For the function g(t) = 1/(3t-2) determine the average rate of change between the values t = 0 and t = a + 1
Homework Equations
ARoC formula : f(b) - f(a) over b-a
The Attempt at a Solution
So I think I am doing it right but can only get so far and then get...
The problem states: sand falls onto a conical pile at a gravel yard at a rare of 10 cubic feet per minute. The base of the pile is approximately three times the altitude. How fast is the pile getting taller when the pile is 15 feet tall?Volume = πr² h/3
dV =...
Hi, I have a problem with an exercise in the book "A First Course in Calculus, fifth edition". The problem is stated as follows:
"A particle moves differentiably on the parabola y=x^2. At what point on the curve are its x- and y-coordinate moving at the same rate? (You may assume dx/dt and dy/dt...
rate of change, derivatives problem...
This table shows the rate of change Canadians who are between 15 and 19 and who smoke...
http://img155.imageshack.us/img155/8915/asdce2.jpg
please answer the questions below it.. thanks in advance
the Volume of a sphere is given by V(r) = \frac{4}{3}\pi(r)^3
Find the average rate of change of volume with respect to radius as the radius changes from 10 cm to 15 cm.
Ok what I tried is: \lim_{r\rightarrow 15} \frac{V(r)-V(a)}{r-a}
P(a,V(a))=(15,14 137)\\ Let\ r=10 \lim_{r\rightarrow 15}...
Hi, I had a question that wanted me to find the instantaneous rate of change of V with respect to h for h = 0.60cm. The equation was V = 1/6*pi*h^3 + 2.00*pi*h and I retrieved an answer of 6.85 cm/s. Could anyone tell me if that is correct? Thanks.
I graphed the function and found the critical points, saddle points, local/absolute max/mins etc.., then i graphed the course parametrically and it resembled a four-leafed rose.
rate of change makes me think of taking the derivative, but course makes me think of integration. which direction...
potential V at the point P(2, -1, 2) in a rectangular
coordinate system is V (x, y, z) =x^2+4y^2+9z^2.
Find the direction that produces the maximum rate of change of V at P.
the max rate of change 37.094.
how to find direction that produces the maximum rate of change ??
2x^2 + 3x
I'm not really sure what to do with the "X"
Form: f(x) - f(c)/ x-c
-2(x)^2 +3(x) - (-2(0)^2 + 3 (0) / x-0
I get
= -2x^2 + 3x + 0 / x - 0
= -2x^2 + 3x / x
that doesn't seem right
I'm taking a break
Find the average rate of change from 1 to 2 for the function f(x)=2x^3 + x
so I did this:
[f(2) – f(1)] – [2x^3 + x] / 2-1
= 2-1-2x^3 + x / 1
= 1-2x^3 + x
= -2x^3 + x
Right?
Two sides of a triangle have lengths a = 5cm and b = 10cm, and the included angle is \theta = \frac{\pi}{3}. If a is increasing at a rate of 2cm/s, b is decreasing at a rate of 1cm/s and \theta remains constant, at what rate os the third side changing? Is it increasing or decreasing?
Just...
Our teacher gave us some extra challenge questions and I've solved them all except for two, which has been really bugging me:
1) Determine the equation of a line that passses through (2,2) and is parallel to the line tangent to y=-3x^3-2x at (-1,5)
2) estimate the instantaneous rate of change...
here is the problem i was trying to do:
A baseball player stands 2 feet from home plate and watches a pitch fly by. Find the rate D(theta)/dt at which his eyes must move to wach a fastball with dx/dt=-130 ft/s as it crosses homeplate at x=0.
now there is a nice diagram of a right...
Hi. I am drawing a complete blank on this calc problem.
Point a moves along the x-axis at the constant rate of 'a' ft/sec
while point b moves along the y-axis at the constant rate of 'b'
ft/sec. Find how fast the distance between them is changing when A is
at the point (x,0)and B is at...
my doubt is what is meant by rate of change of acceleration? how can i measure it in dyanmic condition? if it realated to machene tools, the movement of the slides acceleration has to be changed continuosly for different application . how we can measure it
In a right triangle with sides x,y,z, the theta between leg z and leg y is increasing at a constant rate of 3 rad/min. What is the rate at which x is increasing in units per minute when x equals 3 units and z is 5 units.
so the triangle is basically a 3,4,5 triangle. The theta is between the...
Imagine a trough filled with water (I can't put up a picture).
The water in the tank at time t seconds is given by V = 12x^2. Given that water is flowing into the trough at the rate of 60 cm^3/s, find the rate at which x is increasing when x = 10.
\frac{dV}{dx} = 24x
\frac{d?}{ds} = 60...
How can you caluclate how fast a A/C unit can cool a room? For instance if you had a a/c that can give you 10000Btu/Hr and a room of 1000Cubic Feet, and the tempature is 100F in the room and you want to bring it to 70F. How long would that take? Also how can you find the instintanious temp of...
Hai,
I have the following situation: I have a closed container with a certain gas at a certain temperature(Tg) and pressure(pg). Now I open the container. The gas will escape through the opening to the atmosphere in order to create a pressure balance. There will be no significant...
Our problem is that we measured the rate of change of pressure of a liquid at different length of a pipe, for example, x=0, x=5cm, ... etc, caused by a pump at x=0-15cm=-15cm and got a result that at x=0, dP1/dt1 = -dP2/dt2, where dP1 is the pressure difference over a fixed interval, del t1, and...
URGENTThe rate of change of pressure
Our problem is that we measured the rate of change of pressure of a liquid at different length of a pipe, for example, x=0, x=5cm, ... etc, caused by a pump at x=0-15cm=-15cm and got a result that at x=0, dP1/dt1 = -dP2/dt2, where dP1 is the pressure...
Dear Sir/Madam,
I would like to know if I can apply the conservation of momentum to the rate of change of pressure at a fixed position (for e.g. x=0) as follows:
dP1/dt=-dP2/dt
where dP1 is the pressure changes over a fixed interval of time (del t1) and dP2 is the pressure changes over...
Sorry to bore you all with this rate of change question, I really hate this area of maths and struggle to get my hea round it. Here it is, I'd be greatful for any help you have to offer:
Fluid flows out of a cylindrical tank with constant corss section. At the time t minutes (t is greater...
I'm plotting rate of change of acceleration against time. Acceleration is measured as "g". Time is plotted on the x axis, rate of change of acceleration is plotted on the y axis. Is "dg" a valid label for the "y" axis?
Thanks