Rate Definition and 1000 Threads

Homework Statement [10marks] A water tank has the shape of a vertex-down right circular cone. The depth of the tank is 9 meters, and the top of the tank has radius 6 meters. Water flows into the tank from a hose at a constant rate of 14 cubic metres per hour, and leaks out of a hole at...

Homework Statement The nuclide (32,15)P undergoes Beta - decay with a half-life of 14.3 d. It is used as a tracer isotope in biochemical analysis. What is the initial decay rate of a 1.2mg sample? Homework Equations T1/2 = Ln 2 / λ Ro = λN0 The Attempt at a Solution I first...

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 A rocket is moving into the air with a height function given by h(t) = 200t^2. A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after liftoff? Homework...

Relation between Cooling rate and Viscosity Hi all I have a situation where i have a molten Aluminium Copper alloy melt poured in a mould to be solidified. This means, the mould temperature is lower than than than the poured melt. I am thinking about a relation which associates temperature...

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...

Homework Statement Work out the mass flow rate of Nitrogen traveling through a at 0.3m^3/s if the pressure is 1 bar and the temperature is 18°C and the ideal gas constant is 8314 J/Kg K Homework Equations m=ρ*V*A m = mass flow rate ρ= density V = velocity A = flow area PV =...

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.

Homework Statement I've attached the problem sheet and my attempt at the problem. I've completed all the parts except for the last part, where I have to calculate the count rate of the radioactive source. The answers should be 6000 counts for 185MeV and 4650 counts for 1MeV. I'm not sure...

Homework Statement An equilateral triangle with side length x sits atop a rectangle with a base length of x, with the base of the triangle coinciding with the top base of the rectangle. the height of the rectangle is 7 times the length of its base. If the combined area of the figures is...

Q. Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function: (cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h) A. cos(x+h) = cosxcosh - sinxsinh subtitute this to...

Homework Statement In Attachment Homework Equations The Attempt at a Solution Second Attachment. - I have only attempted part (i) so far, because I am not sure if I am doing it correctly. I was thinking since the value of the latent heat of pentane is given, surely it has to be...

I'm trying to get the transfer function of this rigid control system that uses rate feedback to stabilize it. Using k=1 and kv=0 Attempt at a solution. When kv=0, the rate feedback is removed. In the block diagram, I moved the pickoff point and used the cascade rule to get 1/s^2 and...

Homework Statement Find all the points at which the direction of the fastest rate of change of the function f(x,y)=x^{2}+y^{2}-2x-4y is i+j Homework Equations The Attempt at a Solution The direction of the fastest change is \nabla f(x,y)=(2x-2)i+(2y-4)j, so we need to find all...

Hi all, i have to use an air pump to create a flow rate in a pipe system. My pump model is hta100h-304 which i have attach the spec below. From actual air delivery data(871.2lpm@10 kg/cm2G,762.3lpm@12kg/cm2G), i try to convert to mass flow rate unit and it is around 0.19 kg/s. Is this mean...

A potential difference of 50 mV is maintained between the ends of a 9.70 m length of wire whose cross section area is 25.0mm^2. The conductivity of the wire is 6.80 x 10^6 (ohm.m)^-1. Determine the rate at which the energy in the wire is transformed into kinetic to thermal energy. 2. Homework...

I know that incandescent bulbs are filled with some inert gas to reduce the rate at which the filament decays. If the filament was to be exposed to ambient air, how long before it evaporated? How long can a mesh of light bulb filaments (or other material with as high a melting point that can be...

Homework Statement A potential difference of 50 mV is maintained between the ends of a 9.70 m length of wire whose cross section area is 25.0mm^2. The conductivity of the wire is 6.80 x 10^6 (ohm.m)^-1. Determine the rate at which the energy in the wire is transformed into kinetic to...

Homework Statement Suppose you are climbing a hill whose shape is given by the equation: z = 1400 − 0.005x^2 − 0.01y^2 where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1264). The positive x-axis points east and the positive y-axis points...

Homework Statement The total amount of oil in a well is 24000 barrels. The present rate of consumption is 100 barrels per year. How long will the gas supply last if the present yearly rate of consumption increases by 1% per year? Homework Equations We can use the approximation (1+x)^i =...

Homework Statement a 5 kg block with a 10cm length sits at the top of a frictionless, 6.0m 12kg uniform ramp. This ramp is held up by a rope of tension T at a 35* angle to the ground. The block is released and allowed to accelerate. What is the rate at which the tension in the supporting...

One of the main points of cosmology is that the Hubble rate of distance expansion is not constant. In the standard cosmic model it evolves according to the Friedman equation. Recently I've been noticing more professional cosmologists referring to it as a rate, like these people (Roy Maartens is...

Homework Statement Let Q(t)=t2. Find a formula for the average rate of change (ROC) of Q over the interval [1, t] and use it to estimate the instantaneous ROC at t = 1.Homework Equations For x1 ≠ x0, the average rate of change of y with respect to x over [x0, x1] is the ratio Average ROC =...

Can Anybody help to code this in matlab A->B --- A is Sbbstrate here and B is Product Y[b][/a]=stiochimetric Initial values are A[0] and B[0] Q= reaction quotient R=active if Q<k ----- R is reaction R=Stops if Q=k t=...

Hi, Im stuck: I found this example in which they calculate the rate of reaction: the title is "calculating the average reaction rate" Now how the hell is this average reaction rate if they didnt use stoichiometric coefficients!? (in this case it should be 2. Thanks in advance.

Hi guys, Just doing a few calculations on a homeloan and comparison rate calculation has got me stumped. Loan Amount: $320,000 Loan Time: 30 years Interest Rate:5.55% Initial Costs:$4463 Monthly Fee: $15 So from this, with a fortnightly compounding frequency, I calculate the total...

B.F. Skinner's law of effect said when a response is followed by a reinforcing stimulus, the rate of response increases. So when a response produces a reinforcing stimulus, responses per unit of time (rate) increases. He said the response strengthens. He said when the rate increases, the...

Homework Statement A 3000lb car with a wheelbase of 100 inches and track of 50 inches sits on level ground with equal weight on each wheel. The effective spring rate is 700 lb/in at each wheel. One wheel is now raised by 1 inch and the car is allowed to settle to a new equilibrium. What is the...

Heat Transfer Qts Engine oil at 60 oC flows over flat plate whose temperature is at 20 oC with a velocity of 2 m s-1. The length of the plate is 5m. What is the film temperature and the rate of heat transfer per unit width of the entire plate? Additional information (at the film temperature)...

Homework Statement 120 mol/min of Propane (C3H8) is burned in the presence of air (21% O2 and 79% N2) in a furnace, two reactions occur: Complete Combustion: 67%, propane is burned to CO2 and H2O Incomplete Combustion: 18%, propane is burned to CO and H2O Oxygen is supplied at 70%...

Homework Statement 32) A stone dropped into a pond at time t=0 seconds causes a circular ripple that ravels out from the point of impact at 5 metres per second. At what rate (in square metres per second) is the area within the circle increasing when t=10? Homework Equations I need to use...

Homework Statement I am given this question: what is the monthly payment necessary to ammortize a loan of $100 000 at 2.3% compounded monthly for 20 years. I know the answer to the above: it is done by using the ammortization payment formula, in this case: R = 100 000...

Let a monochromatic plane wave impinge on a collector of area A, delivering power P. Let the average photon rate of arrival on the collector be B. Now make the collector move toward the source at velocity v. By the Doppler effect, the frequency, and hence the energy, of the photons will...

I'd like to get images at a frequency of at least 100 frames/sec to measure servo arm speeds (including acceleration from rest) under various torque loads. This is for personal research associated with RC helicopter accessories, but as a high school physics teacher it seems it would be good for...

Does the spring constant of a piece of rubber affect its rate of cooling constant 'k' ? 1) Is there any formula, any proven relationship? 2) If there isn't, would investigating it make any sense? Or would it end up being a waste of time as the two variables are totally unrelated? Is there...

I am calculating the time it takes for an object to fall 90° about an axis of rotation in the x-y plane. I have managed to calculate the rate of change of angular acceleration, which will be represented by the symbol ψ. Unfortunately it is not rad/s^3, but (rad/s^2)/θ or \alpha/θ. The value of ψ...

Homework Statement A power plant generates 1300MW and operates at 315 °C a 20°C heat sink is available. what is the minimum rate at which heat must be discarded? Homework Equations not really sure how to begin this one, have a feeling it is related to dq=Tds at constant pressure giving...

Looking at the steam table below, if I understand things correctly, it will take 419kJ to bring a kg of water to the boil at 100°C and a further 2257kJ to turn all of that boiling water into steam. I assume that would have to be in an open boiler, as the pressure inside of a closed vessel would...

The concept of a "rate" Here's another question from good ol square :| I was hoping to get some clarification about the concept of a rate of two quantities, with different units, like speed \frac{a-units}{b-units}. How does the expression for division \frac{a-units}{b-units} arise from the...

Why do gradient show rate of maximum increase not decrease always?

Homework Statement surface of mountain is modeled by h(x,y)=5000-0.001x^2-.004y^2. Climber is at (500,300,4390) and he drops bottle which is at (300,450,4100) What is his elevation rate of change if he heads for the bottle? In what direction should he proceed to reach z=4100 feet the...

Homework Statement Water runs into a cylindrical tank at the rate of 0.6m^3/s. The tank has a heigh of 2.5m and a base radius of 1.2m. How fast is the water level rising when the water level is 1.6m deep. Homework Equations V=∏ x r^2 x h The Attempt at a Solution I know that...

Task: A steady flow boiler takes in feed water at 1.5kg/s, at a temperature of 30 °C. The water is heated and turned into wet steam. This leaves at 1.5kg/s, with a pressure of 10 bar and a dryness fraction of 0.97 to the superheater, where it receives heat at a constant pressure and emerges...

Homework Statement Find the units of k1, k2, k3, k4, and k5. Write rate reactions for dA/dt a. A\leftrightarrowB k1 (forward) k2 (backward) b. A + B \rightarrow C k3 (forward) c. A + R \rightarrow 2R k4 (forward) d. A \rightarrow B k5 (forward) Homework Equations...

A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 59.5E5 kg, of which 7.39E5 kg is fuel. The rocket engine is then fired for 300 s, during which fuel is consumed at the rate of 480 kg/s. The speed of the exhaust products relative to the...

Hello Forum, Battery chargers are devices to put energy into a secondary (rechargable) bttery by forcing an electric current through it. The charge current depends on the technology and capacity of the battery being charged. The capacity of a battery represent the amount of electric charge...

[b]1. Consider an ocean current flowing at 2.5m/s a) How much kinetic energy is contained in a cubic volume of water that measures 1m on each side? The density of seawater is about 1030kg/m3 b) If the flow is perpendicular to one of the cube faces, what is the rate at which the current carries...

I have a motorcycle engine on a test stand and I need a way to measure the mass flow rate into the engine. It is currently carburated. I had two ideas off the top of my head. 1) build a venturi, and measure the pressure drop to figure out the velocity and therefore the mass flow rate...