Rate of change Definition and 274 Threads

Hello, I am Primarily a Software Engineer, but have some background knowledge from my A-Level and Uni days. However, I have the following problem. I'd like to find out the rate of change in pressure across a valve. Here are the things I know about the system: Cv at 100% open = 0.004 (I...

Homework Statement [/B] My question is regarding Part B of this problem, I have solved it but I'm wondering if there is another way to solve it since it says dtheta/dt and one of the hints I found online suggested that I use the chain rule. Homework Equations Q = mc(deltaT) Q/t = P The...

Homework Statement The Attempt at a Solution As far as I know those are correct. Could I have some assistance on how to solve for the rate of change? I know the formula is f(b)-f(a)/b-a but not sure how to go about it

Homework Statement Homework Equations Rate of change formula: y2-y1/x2-y2 The Attempt at a Solution If this is a rate of change problem so I use the rate of change formula: y2-y1/x2-y2 and since it's from 2 to 4 I think that would be (2,0) (4,0) and thus (0-0)/(4-2) = 0/2 = 0 I don't...

Im having trouble with this problem to do with applictions of calculus. If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms (Ω), is given by 1R=1R1+1R2. If R1 and R2 are increasing at rates of 0.4Ω/s and 0.6Ω/s respectively, how...

Homework Statement I didn't know if this was considered "advanced" physics, but it's an intermediate classical mechanics course so I'll just post my question here. Basically, if you have a cardioid ##r(\theta)=k(1+\cos(\theta))##, you can show that the ##\dot{\theta}=\frac{v}{\sqrt{2kr}}##...

For a situation where we have two infinite flat parallel plates with a viscous fluid in between if the upper plate if acted upon by a constant force then the plate should accelerate. The fluid layer adjacently below the upper plate should have the same acceleration as this plate (due to no-slip...

Homework Statement A vertical jet of water of 3cm in diameter impinges upon a horizontal flat plate with a velocity of 4m/s, and all of the water spreads out horizontally. Find the force exerted on the plate. Homework EquationsThe Attempt at a Solution I am not 100% sure how to tackle this...

Homework Statement [/B] I need to differentiate the exponential function i = 12.5 (1-e^-t/CR) and I need to plot a table so that I can do a graph of i against t but I'm not sure how. (CR is the equivelant of Capacitance 20 Micro Fards and Resistance 300 Kilo Ohms)Homework Equations [/B] How do...

Determine the average rate if change of the function y = 2cos(x - $\pi$/3) + 1 for the interval $\pi$/3 $\le$ x $\le$ $\pi$/2 I tried finding the exact values of the two (0 and 0.5) and subbing them into the AROC equation but I keep getting the wrong answer (1.4)

In the integration of Force with respect to displacement (W=∫F.dx), is that true if the rate of change of displacement approaches to zero? My teacher said the one which approaches to zero is the rate of change of time. But If I arrange the formula, I will get F=dW/dx then F= lim Δx→0 ΔW/Δx...

Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...

Air pressure decreases at a rate of 2.5 pascals per kilometer in the eastward direction. In addition, the air pressure is increasing at a constant rate with respect to time everywhere. A ship sailing eastward at 10 km/hour past an island takes barometer readings and records a pressure drop of 30...

The ans is 4. Could someone please help..thanks in advance. :)

Homework Statement mtan for f(x) = 5/√ 3x ... at x=1 Homework Equations msec = y2-y1 / x2-x1 The Attempt at a Solution The two points I got from the equation: (1, 5/√ 3) and (1+h, 5/√ 3+h) msec = f(1+h) - f(1) / h = (5/√ 3+h - 5/√ 3) / h ... multiply top and bottom by denominators (√ 3+h)...

Homework Statement Hi everyone, I am new to calculus. I was recently assigned some homework and am having a difficult time with it. Please help me out. Thank you! A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x - x^2), where x and f(x) are measured in miles. Find the...

https://www.physicsforums.com/attachments/2883 It was found earlier that $ \frac{dx}{dt}=\frac{\pi}{30} \frac{rad}{sec} $ and $\frac{dy}{dx}=\frac{\pi}{60} \frac{rad}{sec}$ (C) since $s$ and $x$ and are related by the Law of Cosines; What is the rate of change of with respect to time...

Homework Statement The Wikipedia article on spatial rigid body dynamics derives the equation of motion \boldsymbol\tau = [I]\boldsymbol\alpha + \boldsymbol\omega\times[I]\boldsymbol\omega from \sum_{i=1}^n \boldsymbol\Delta\mathbf{r}_i\times (m_i\mathbf{a}_i). But, there is another way to...

Homework Statement The space shuttle Endeavor is moving at a speed of 27870 Km / h. At takeoff, its mass is 2, 28 * 10 ^ 6 kg, however, its mass decreases as it uses its fuel: the engine burns liquid oxygen which has a density of 1141 kg / m^3, at a rate of 1340 liters per second. Calculate...

Point $$P$$ moves at $a$ constant rate along the semicircle centered at $$O$$ from $$M$$ to $$N$$. The radius of the semicircle is $10cm$, and it takes $30s$ for $P$ to move from $M$ to $N$. $∠POM$ has measure $x$ radians, $∠OPM$ has measure $y$ radians, and $MP=S$ cm as indicated in the...

I wanted to see how the rate of change of rate constant with temperature (dk/dT) changes with activation energy. I tried to do this with differentials: k=A*e-EA/RT so \frac{dk}{dT} = \frac{A E_A \cdot e^{-\frac{E_A}{RT}} } {RT^2} and then \frac{d(\frac{dk}{dT})}{dE_A} = A \cdot...

Is possible to compute the rate of change of x wrt sin(x)? ##\frac{dx}{d \sin(x)}##

A helicopter is flying to the right (in the +x direction) with a constant speed v, carrying a package of mass M suspended below it using a cable as shown in the figure (you can assume that H and L are not changing with time). Choose the package as your system. What is its rate of change of...

One plane is flying due east straight and level at 30000 feet and at 420 mi/h. A second plane flies due north at 40560 feet and at 480 mi/h. The second plane crosses above the flight path of the first plane 2 minutes after the first plane passes that point. How fast were they approaching each...

What is the Rate of change of area of circle in respect to radius when radius is 3in I know that that dA/dr is equal to the circumference of the circle But where does that come from? Also the formula for the circumference of the circle is 2(pi)r But the answer is 6 (pi)in^2/in. I understand...

Homework Statement (This problem concerns an electron orbiting a proton. Ultimately we are trying to find the time for a classical electron to spiral into the nucleus of an atom, which will lead us to a discussion of why classical mechanics gives way to quantum mechanics when discussing things...

Here is the question: I have posted a link there to this thread so the OP may view my work.

The function for attitude vs air pressure is f(x) = 2100/x 1. Approximate the instantaneous rate of change at 100 millibars a) Use the equation to calculate the point (100,___) I found the y-value to be 21. b) We need two points to calculate a slope, so to approximate the tangent line we use...

Homework Statement A balloon is being tracked from an observation point 0.42 mi from its launch site. Both the launch site and observation point are on level ground. How fast is the angle of elevation to the top of the balloon increasing at the instant it is 20°, if the balloon is rising...

1. A ladder 10 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when...

Hi, I am working on a rate of change problem and appear stumped with my calculations. S(T) = (-0.03T^2 + 1.6T - 13.65)^-1 S'(T) = (-1)((-0.03T^2 + 1.6T - 13.65)^-2 (-0.03 (2T) + 1.6)) S'(T) = - (-0.06T + 1.6) / (-0.03T^2 + 1.6T - 13.65)^2 S'(T) = (0.06T-1.6) / (-0.03T^2+1.6T-13.65)^2 = 0...

A conical tank (with the vertex down) is $10 \text{ ft}$ across the top and $12 \text{ ft}$ deep. If water is flowing into the tank at rate of $\displaystyle\frac{10 \text{ ft}^3}{\text{min}}$ Find the rate of change of the depth of the water when the water is $8 \text{ ft}$ deep...

Find the rate of change of the distance between the origin and a moving point on the graph of $$y=\sin{x} \text{ if } \frac{dx}{dt}=\frac{2 \text{cm}}{\text {sec}}$$

on b) I think this is the point they wanted us to get hope answers are correct its an even problem # so no ans in bk.

if correct? wasn't sure if $$\pi$$ should be in answer since answer is in$$\frac{\text{in}^3}{min}$$

I am just a hobbyist and try to learn for myself. I understand that the value of a field and its rate of change play the same role of position and momentum of a particle with respect to Uncertainty Principle, i.e. both pairs are conjugate variables. My question is: does the rate of change of...

Equation of standing waves→ y=Asinkxcosωt What do i get if i differentiate the above equation with respect to "x" ? Do i get the rate of change of amplitude when i put t=0?

Here is the question: I have posted a link there to this topic so the OP can see my work.

Hi everyone Firstly this is not a homework question, i work in transport engineering. ( i do study part time which is why i sometimes post in the homework section) Now to the problem. I am trying to understand how to solve this problem, i already know the answer. A train is traveling...

Homework Statement Write a simplified algebraic expression, in terms of a and h, to estimate the instantaneous rate of change of the profit for each numeber of athletic shirts sold. Use h = 0.1. The Attempt at a Solution { -0.25(1000+h)^2 + 4(1000+h) + 12 - [ -0.25(1000)^2 + 4(1000)...

Homework Statement A soccer ball is kicked into the air from a platform. The height of the ball, in metres, t seconds after it is kicked is modeled by h(t) = -4.9t^2 + 13.5t + 1.2. I solved for the expression that represents the average rate of change of height over the interval 2<= t <=...

Hello! I was wondering if somebody could help me develop an answer to the question below. I would like to calculate a rate of change of the following function: θ = arctan (a * (tan β)) where "a" is a constant. By the way, the shape of the curve -- angle alpha as a function of angle...

https://www.khanacademy.org/math/calculus/derivative_applications/rates_of_change/v/falling-ladder-related-rates Homework Statement Essentially, the question states that a ladder, with length 10ft, is laid up against a wall with its bottom 8ft out. The ladder begins to slip, on a...

https://www.khanacademy.org/math/calculus/derivative_applications/rates_of_change/v/falling-ladder-related-rates Essentially, the question states that a ladder, with length 10ft, is laid up against a wall with its bottom 8ft out. The ladder begins to slip, on a friction-less surface, at a...

oops I meant "Rate of change of area of a square with respect to its side length" Ok I have to use this annoying Stewart textbook for my Calc class in college. Most of the questions require what I like to call "Monkey Math," where you just memorize a set of steps and then follow them rigidly...

A=\pir^{2} therfore, \frac{dA}{dt}=2\pi\frac{dr}{dt} The question is if \frac{dr}{dt} is constant is \frac{dA}{dt} constant? To me, I know that if the change in radius with respect to time is constant, The rate of change of the are with respect to time still depends on the radius of...

Homework Statement In an experiment an individual throws a rock with an initial horizontal velocity of v0 = 20 ft/s at time t=0. The rock is thrown from the edge of a cliff (directly above the base of the cliff) at height h=50 ft from the ground. The origin is assigned at the base of the...

Homework Statement The demand function for a certain product is given by pq=4000, where p is the price charged per item and q is the quantity which can be sold at that price. If the product currently sells for $3.50 per item, what would be the rate of change of quantity over time if the rate...

Magnetism of a bar magnet -- maximum rate of change? If a bar magnet is placed along the x-axis with (0,0) at its center, along which axis does the magnetic field fall off faster and why?

Here is the question: Here is a link to the question: Calculus Parallel Resistors Question Help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.