Rate of change Definition and 279 Threads

Homework Statement Car A is traveling north on Highway 16 and car B is traveling west on Highway 83. Each car is approaching the intersection of these highways. At a certain moment, car A is 0.3 km from the intersection and traveling at 90km/h while car B is 0.4km from the intersection and...

Please Help! - Integration, Rate of Change, and Volume of Revolution Questions Hi I have completes these following questions but am not sure if I have done them correctly as it is a long time since i studied these topics. I would really appreciate any help. :-) 1 Simplify the following as...

Homework Statement A bathtub with shape semi-circle has radius 5 m is filled with water with rate 2 m^3/minute. How fast will the height of water in the bathtub change when it is 2 m from the bottom? Given that the volume of water when the radius = R and height = y is πy^2(R - y/3)...

Homework Statement Find the irc at X=2 F(x) = \frac{4}{x-1} Homework Equations \stackrel{lim}{h\rightarrow0}\frac{F(a+h)-F(a)}{h} The Attempt at a Solution I end up with \frac{4}{h+h^{2}} or some other form of an h on the bottom. Is there something else i can do to it??

Calculus - please help find average rate of change of the function over a given interval Homework Statement h(t) = sin t, [3pi/4,4pi/3] please help me solve this, try to give me an explanation on every step please. i checked but i can't find anything on this in the book. i am...

Homework Statement 6x^2 - 4 x = -2 Homework Equations n/a The Attempt at a Solution I input -2 for x but i got the wrong answer..the answer is suppose to be -24

Homework Statement The resistance of the loop is 0.55 Ω. At what rate the magnetic field strength increasing or decreasing? (a=8.4 cm, I=148 mA. Give answer in T/s.) The loop is a square, so all the distances around are a=8.4 cm Homework Equations dI=AdB dI=rate of change of the flux...

Homework Statement The Attempt at a Solution Managed part a) just fine, but the trouble comes with part b. Erm, the thing is I've got the answer just fine using the chain rule; i worked out dh/dt = 1/(dV/dh) * dV/dt Giving me 18 * \frac{1}{\frac{pi}{3}(18h-3h^2)} Now, I thought, "Okay...

the height h(x) in meters above the ground of a parachute varies with her horizontal distplacement x in meters from a landing target on the ground as h(x) = 50sin^-1 (0.1x). what is the rate of change of h with respect to x at x = 6m? i was wondering of someone could help me with this question :)

Do physicists ever have to account for the rate of change of acceleration? What about the rate of change of the rate of change of acceleration? This could keep going on forever, but is there some point where it just doesn't matter for a fairly accurate estimate?

Homework Statement Find the average rate of change: g(x)=1/x; x = 1, x = a Homework Equations (f(b)-f(a))/(b-a) = Average rate of change The Attempt at a Solution I've spent far too much time on this problem, but I know I'm making a stupid error and I just can't pin it down. So...

Homework Statement A 0.100A current is charging a capacitor that has square plates 5.00cm on each side. The plate separation is 4.00mm. Find (a) the time rate of change of electric flux between the plates and (b) the displacement current between the plates. Homework Equations I pretty...

Homework Statement For the function f(x)=3x^2-1, for what x values is the instantaneous rate of change equal to the average rate of change on the interval [1,3] Homework Equations The Attempt at a Solution

I am wondering if anybody here can help me with a proof. A particle is moving with velocity \vec{v} in a field \vec{F} (which could be an electric or magnetic field, for example). The velocity can change with time as the particle moves, but the field is static in space. The particle sees the...

A circular wire loop of radius r = 19 cm is immersed in a uniform magnetic field B = 0.690 T with its plane normal to the direction of the field. If the field magnitude then decreases at a constant rate of −1.0×10^-2 T/s, at what rate should r increase so that the induced emf within the loop is...

Homework Statement The mass, m(t), in grams, of a tumor t weeks after it begins growing is given by m(t) = [te^t] / 80 . What is the average rate of change, in grams per week, during the fifth week of growth? a.) 2.730 b.) 3.412 c.) 6.189 d.) 6.546 e.) 11.131 Homework...

Homework Statement A point P (x,y) is moving along the line y=(1/2)x. If x is decreasing at the rate of 3units/s, at wha rate is the distance between P and the fixed point Q (0,11) changing at the instant when P is at (6,3)? Homework Equations Implicit differentation The Attempt...

Homework Statement The cross section of a trough for holding water is an inverted equilateral triangle. The trough is 6m long and 50cm deep. If the water is flowing in a t a rate of 0.6m^3/min, find the rate at which the height is changing when the water is 40cm deep. Homework Equations...

Homework Statement A street light is on top of a 20-foot pole. A person who is 5 feet tall walks away from the pole at the rate of 5 feet per second. At what rate is the tip of the person's shadow moving away from the pole when he is 20 feet from the pole? 2. The attempt at a solution...

Hello again! The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is 100 cm^2? I think I have found the solution, but want to have someone else check it over b/c I am not 100% sure...

Question: A 1.85 m tall man is walking toward a 12 m tall street light at night at a rate of 2.2 m/s. How fast is the length of his shadow changing when he is 12 m from the street light? so, using similar triangles, i got that (x+y)/12 = x/1.85. I can rearrange this into x= or y=, but then I...

Homework Statement A rectangle has a constant area of 200m2 and its length L is increasing at the rate of 4 meters per second. Find the width W at the instant the width is decreasing at the rate of 0.5 meters per second. Homework Equations A=200 dA/dt =0 (since the area is constant)...

A balloon rises at the fate of 8 feet per second from a point on the ground 60 ft. from an observer. Find the rate of change of the angle of elevation when the balloon is 25 feet above the ground I converted 8 ft/s to 2.44 m/s2 to make it easier. I also figured the angle of elevation when the...

Homework Statement Sand is falling into a conical pile at a rate of 10 cubic feet/minute. The diameter of the cone is 3 times the altitude. At what rate is the height of the pile change when the height=15feet. So i was going through and I don't know if i derived it wrong, but i had...

Hi everyone, i am new to this website and i would like to ask one question that i don't quite get. we have started a new topic in class about rates of change Homework Statement An Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10) where currenct is...

Homework Statement A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? Evaluate your answer...

Rate of change problem...very hard...please help! Homework Statement The hands on a clock are of length 5 inches(minute hand) and 4 inches(hour hand). How fast is the distance between the tips of the hands changing at 3:00? The Attempt at a Solution Let the coordinates of the two hands...

Homework Statement The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second? A. -(0.2)piC B. -(0.1)C C. - {(0.1)C}/(2pi) D (0.1)^2C E. (0.1)^2piC...

Homework Statement A balloon is rising vertically from a point on the ground that is 200m from an observer at ground level. The observer determines that the angle of elevation between the observer and the balloon is increasing at a rate of 0.9 degrees/s when the angle of elevation is 45...

hi everyone, i am having trouble with this rate of change question. I need to find the rate of change of a sphere with a volume of V= 4/3*pi*r^3 in respect to it's surface area of A= 4*pi*r^2 can anyone give me a hand? Thanks

Homework Statement A particle moves along the parabola y = 4x^{2} such that it's x coordinate increases at a steady rate of 5 units/minute. How fast is the particle's distance from the origin changing when it is at the point (1,4)? Homework Equations The Attempt at a Solution...

I have been reading a lot about rockets and how the mass flow rate is calculated. If i had a graph of the change in mass with respect to time of a rocket motor throughout its burn. How would i calculate the mass flow rate (change in mass at any given time t) ? Besides using density...

Hello and greetings everyone. 1. A quantity of oil is dropped into water. When the oil hits the water it spreads out as a circle. The radius of the circle is r cm after t seconds and when t = 3 the radius of the circle is increasing at the rate of 0.5 centimetres per second One observer...

Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back. (In case you're wondering, I'm doing my studies by...

Homework Statement A water tank is built in the shape of a circular cone with a height of 6 m and a diameter of 10 m at the top. Water is being pumped into the tank at a rate of 2m^{3} per minute. Find the rate at which the water level is rising when the water is 2 m deep. Homework...

Homework Statement Suppose that t hours after a piece of food is put in the fridge its temperature (in Celsius) is T(t) = 15 - 3t + \frac{4}{t - 1} where 0 \leq t \leq 5. Find the rate of change of temperature after one hour. The Attempt at a Solution Since it's asking for...

Homework Statement Find the instantaneous rate of change of V with respect to r when r=5 micrometers Homework Equations V=4/3pi(r^3) The Attempt at a Solution would you just take the derivative? and if so, wouldn't it just be zero, because it comes out to be a real number, right...

Homework Statement A liquid is being poured onto a level surface making a circular pattern on the surface. Find the rate of change of the area covered on the surface with respect to the radius when the radius is 20cm. Homework Equations Surface area = (Pi)r^2 The Attempt at a...

Tried this problem, but not getting it. Homework Statement A fire hose sends 2528 gallons of water per minute against a building. The water strikes the building at 28 m/s and does not bounce back. What is the magnitude of the rate of change of momentum of the water?Homework Equations The...

[SOLVED] Century Growth Problem: Rate of Change 1. Problem: Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 27 centuries, what is the total (in hours) of the daily...

[SOLVED] Rate of Change - Just checking Homework Statement Sand is poured into a conical pile with the height of the pile equaling the diameter of the pile. If the sand is poured at a constant rate of 5m^3/s at what rate is the height of the pile increasing when height is 2 meters. Homework...

Homework Statement The temparature T of a liquid at a time t minutes is given by the equation T = 30 + 20e-0.05t, for t > 0 (1)Write down the initial tempatature o the liquid, and find the intial rate of change of temparature. (2)Find the time at which the temparature is 40...

First off i'd like to say Hi to the forums, hehe. I didn't really see a new member area but I suppose this will do. Right now I'm kind of struggling with these two problems that I recently took a quiz on and didn't do so well. I've been trying to figure out how to work them out but i just don't...

Homework Statement A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, (A) at what rate is the tip of his shadow moving? (B) at what rate is the length of his shadow changing?Homework...

Homework Statement If I have an equation that describes L in terms of some constants and an angle. e.g. L=C1*\sqrt{(C2-Sin[angle])}+C1*\sqrt{(C2-Cos[angle])} Then, if I take the partial derivative of the above wrt angle, then I would get the unit change in L for a unit change in angle...

The base of a cone-shaped tank is a circle of radius 5 feet, and the vertex of the cone is 12 below the base. The tank is filled to a depth of 7 feet, and water is flowing out of the tank at a rate of 3 cubic feet per minute. Find the rate of change of the depth of the water in the tank.

Rate of change of momentum Homework Statement Hey everybody this is my first post and I really hope you guys can help me out. Ok so here's the problem which is divided into three parts: The first part consists of this: A fire hose sends 1464 gallons of water perminutre against a burning...

I'm having trouble understanding this word problem. A construction worker drops a bolt while woring on a high-rise building 320m above the ground. After t seconds, the bolt has fallen a distance of s metres, where s(t) = 320-5t^2, o < t < 8 a. Find the average velocity during the first...

Homework Statement s is the position of a particle along the s-axis, find an expression for the velocity and acceleration and determine when v=0 s=1-3t^2 Homework Equations v=ds/dt , a=dv/dt The Attempt at a Solution No idea where to begin, my book is not very clear. Do I just...

If the displacement was given by \overrightarrow x (t) ( i.e vector valued function ) . Then the velocity is \overrightarrow v = \frac {d \overrightarrow x}{dt} The speed is the magnitude of v . But .. What is the derivative of the magintude of the displacement \frac {d...