# calculus-rate problem

52,630 results

### calculus

My problem is that a stft above the sidewalk. a man 6ft tall walks away from the light at the rate of 3ft/sec. at what rate is his tip of shadow moving

### calculus

You are letting the air out of a hot air balloon at a steady rate. The volume of the balloon is decreasing at the rate of 10pi m^3/min when the diameter is 45 meters. At what rate is the radius of the balloon changing? I need help! How do I solve this problem? Thank you so ...

### Calculus

Related Rates Problem An isosceles triangle with a base of 20root3 cm long. If the length of the leg decreases at rate 3 cm/h, find the rate of decreasing of the area of the triangle in the instant at which the triange becomes equilateral.

### Timerate problem(calculus)

Sand is being dropped at the rate 10 metercube/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high?

### Calculus

What is the simplest solution to the Brachistochrone problem and the Tautochrone problem involving calculus? (I know that the cycloid is the solution but I need a simple calculus proof as to why this is the case)

### related rates calculus problem

A balloon is being filled with air at a rate of 3 cubic meters per minute. Find the rate at which the radius is changing when the volume is 113.0973355 cubic meters.

### Calculus

1) A telephone company has 10,000 phones in a certain city where the basic rate is $4 per month. The officials have evidence that if the charge is reduced the number of phones will increase at an estimated rate of 1,000 phones for each 25 cent reduction. What rate would yield ...

### related rates problem-calculus

A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi square centimeters?

### calculus-rate problem

A conical tank (with vertex down) is 10 feet acros the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

### Word Problem-Calculus

A spherical balloon is being inflated in such a way that its radius increases at a rate of 3 cm/min. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes? my answer is 45 cm/min. is this right. thanks

### CALCULUS

A plane, flying horizontally at an altitude of 1 km and a speed of 500 km/hr, passes directly over a radar station. find the rate in km/hr at which the distance from the plane to the station is changing when it is 2 km away from the radar station. Hint: this is not a max/min ...

### Calculus

At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but the price is dropping at a rate of $1 per week. I need to know at what rate OHaganBooks' revenue is rising...

### Calculus

At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but the price is dropping at a rate of $1 per week. I need to know at what rate OHaganBooks' revenue is rising...

### Calculus

Sand is being dumped from a conveyor belt at a rate of 20 cubic ft/min into a pile the shape of an inverted come whose diameter and height are always the same. (a) Find the rate of increase of the height when the pile is 10ft high. This is a 2 part problem. Please show me how ...

### Calculus

How would you solve this problem: An airplane is flying in still air with an airspeed of 240 mph. If it is climbing at an angle of 22 degrees, find the rate at which it is gaining altitude.

### calculus

There is a right triangle with x and y legs labeled B and A, respectively. B is increasing at a rate of 1 m/s and A is decreasing at a rate of 2 m/s. At what rate is the angle theta (located on the leg B) changing when A is 10m and B is 20m?

### Calculus

Hi there I am having some troubles trying to do my calculus homework and I really need help trying to do this problem from my homework: Set up the problem and do not solve: The mass of the solid bounded by the surfaces 2x^2 + 2y^2= 9, z=0, z=3 with density function p(x,y)= x^...

### organic chemistry

Hi, I was wondering if somebody could help me out with this problem which says: "Why does changing the base have no effect on the rate of an E1 reaction while it does affect the rate of an E2 reaction?" I would appreciate any help I can get on this problem! Sincerely, Manny

### Calculus

At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for $20 each, but the price is dropping at a rate of $1 per week. I need to know at what rate OHaganBooks' revenue is rising...

### Calculus I

A spherical balloon is inflated at a rate of 10 cm^3/min. How fast does the radius change when the radius is 20 cm? Need help with set up and work through of problem.

### CALCULUS

A 25 ft ladder is leaning against a vertical wall. At what rate (with respect to time) is the angle theta between the ground and the ladder changing, if the top of the ladder is sliding down the wall at the rate of r inches per second, at the moment that the top of the ladder ...

### calculus

the management of a company has decided that the level of its investment should not exceed C dollars. Furthermore, managament has decided that the rate of net investment (the rate of change of the total capital invested) should be proportional to the difference between C and ...

### Calculus

Calculus If V volts are measured across a resistance of R ohms in a circuit carrying a current of I amperes, V=IR. At a certain instant, the voltage is 250 and is increasing at a rate of 4 volts/min, while the current is 0.5 AMP and is increasing at a rate of 0.01 amp/min. ...

### Calculus

A certain calculus student hit Mrs. Evans in the head with a snowball. If the snowball is melting at the rate of 10 cubic feet per minute, at what rate is the radius of the snowball changing when the snowball is 1 foot in radius?

### related rates with work shown

this is a relate rates problem in calculus in a right triangle, the hypotenuse is 5 and the vertical side is x and the angle is theta. so if theta increases at a constant rate of 3 radians per minute, at what rate is x increasing in units per minute when x equals 3 units? d(...

### mathematics

need help badly. this is the math problem. is the rate three-forth's cup of butter/ 3 eggs equivalent to the rate of 3 cups of butter/12 eggs? Please show the work so I can study this equation for my next problem. thanks kindly

### calculus

I have the following problem on a takehome assignment and am stuck. A particular stock has value V(t) at time t where V(t)=Ke^(1/2) where K>0. Assume that alternative investments grow in value to e^(rt). Calculate the instantaneous rate of change in the value of the stock. ...

### Math (Instanttaneous rate of change)

Compute the instantaneous rate of change f'(a) for the function f(x) at x=a using: f'(a)=lim(h->0) (f(a+h)-f(a))/h f(x)=x^2 at x=3 My teacher didn't even go over the problem since class was over but gave us the answer being 6. How do you approach this problem to end up with...

### MATH

Rate Problem: Mr. Stewart rode a distance of 12miles out into the country on a bicycle and returned on foot. His rate on the bicycle was 4 times his rate on foot. He spent 5 hours on the entire trip. Find the rate of walking and on the bicycle.

### Please Help!!!!!!

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, explain your reasoning and use a graphical or numerical approach to ...

### calculus

1. A rocket is fired vertically into the air. Six kilometers away, a telescope tracks the rocket. At a certain moment, the angle between the telescope and the ground is and is increasing at a rate of 0.6 radians per minute. (See the picture. I have defined y to be the height ...

### calculus

Can someone tell me how to do this type of problem? A particle moves along the curve y=sqrt(1+x^3). As it reaches the point (2,3) the y coorindate is increasing at a rate os 4cm/s. How fast is the x coordinate of the point changing at that instant?

### Calculus

(It's a related rate question) A man 6ft tall walks away from a lamp post (15ft) at 5ft/sec. How fast is his shadow lengthening? --- I have the picture, and the constants, the man and the lamp post. I have 5ft/sec as dw/dt, and I know I'm looking for ds/dt, the rate of the ...

### AP Calculus AB

Hello! I'm having trouble with this related rates problem: A 5ft tall person is walking away from a 16ft tall lamppost at a rate of (2/x) ft/sec, where x is the distance from the person to the lamppost. Assume the scenario can be modeled with right triangles. At what rate is ...

### calculus

I need help setting up this problem: A particle moves along the curve y=sqr(1+x^3). As it reaches the point (2,3) the y-cordinate is increasing at a rate of 4cm/s. How fast is the x-coordinate of the point changing at that instant. I could only come up with this: dy/dx=4

### 4 CALCULUS study problem

1. How fast does the radius of a spherical soap bubble change when you blow air into it at the rate of 15 cubic centimeters per second? Our known rate is dV/dt, the change in volume with respect to time, which is 15 cubic centimeters per second. The rate we want to find is dr/...

### Calculus

A spherical balloon a has a diameter 2 m when it is 1500m high . It is observed that the diameter increases at a constant rate of 4cm/min as it continues to rise. At what rate is the volume increasing when the diameter is 4m . At what rate is the surface area imcreasing then?

### calculus

Find the rate of change of the area of a circle with respect to the radius r. What is the rate when r = 12

### calculus

The length l of a rectangle is decrasing at a rate of 5 cm/sec while the width w is increasing at a rate of 2 cm/sec. When l = 15 cm and w = 7 cm, find the following rates of change: The rate of change of the area: Answer = cm^2/sec. The rate of change of the perimeter: Answer...

### calculus

If you are blowing up a balloon at a rate of 3 cubic ft per min, what is the rate of change of the radius after 30 seconds

### Math Finance

Word problem asks to find rate of interest on a monthly deposit for a sinking fund that is needed to produce 130,000 in 20 years. I applied the model, (fv/pv)^1/t -1 I use n/t if compounding yearly, quaterly, etc. No matter what I've tried I can't produce the interest rate ...

### Calculus, bobpursley!

This has to do with my last Calculus problem. I need help on it..The part I replied to after you answered the question.

### calculus

The Voltage v , Current I and Resistance R are related by the equation V=IR. Suppose that V is increasing at a rate of 2 volt/sec, while I is decreasing of the rate of 1/5 (amp/sec ). Let t denote time in seconds. Find the rate at which R is changing when V=40volts and 1=2 amp .

### calculus

The Voltage v , Current I and Resistance R are related by the equation V=IR. Suppose that V is increasing at a rate of 2 volt/sec, while I is decreasing of the rate of 1/5 (amp/sec ). Let t denote time in seconds. Find the rate at which R is changing when V=40volts and 1=2 amp .

### Calculus

Given two problems: Problem A: Tau = Integral(0 to v) v/(q^2 - v^2) dv q = constant Problem B: Tau = Integral(V TO 0) v/(q^2 - v^2) dv q = constant Why is it that, SUBSTITUTION RULE is used in problem A, and QUOTIENT RULE is used in problem B? The two problems are somewhat ...

### calculus

I need help with this calculus problem. H(S)=S/(1+S) If F 1/2, -1/2 & (a+1)? I can't figure out what this mean /?

### Algebra

I hope that I am typing this particular problem right because this algebra problem was provided on a chart. However, I can't copy and paste the chart on here. The problem says "The given graph represents the number of active servicemen in the region who are overweight." Find ...

### Calculus

A woman 5 ft tall walks at the rate of 5.5 ft/sec away from a streetlight that is 16 ft above the ground. At what rate is the tip of her shadow moving?

### Calculus 1

Related Rates Problem: Two cars start moving from the same point. One travels south at 40 mi/h and the other travels west at 30 mi/h. At what rate is the distance between the cars increasing three hours later?

### chemistry

At the instant oxygen is reacting at the rate 5.0 x 10-4 mol/L*s, at what rate is NO reacting and NO2 forming? this is a method of initial rate problem. i don't know what to do the chemical equation is 2 NO(g) + O2 (g) ---> 2 NO2 (g)

### Calculus

for f(x)=-x^2 +1, which value is the largest magnitude? a) average rate of change from x=-1 to x=1 b) instanteneuous rate of change at x=3 c) instanteneous rate of change at x=0 average rate of change from x=-4 to x=0

### calculus

Find the limit of this calculus problem.? (5x-3)/(ln(5+4e^(x)) x=inf

### Calculus

A bead moves on a circular wire x^2 + y^2 = 25. As it passes the point (3,4), the x-coordinate is decreasing at a rate of 2 units per second. At what rate is the y changing?

### maths help calculus

the area of a circle increasing at the rate of 3cm/sec.find the rate of change of the circumference when the radius is 2cm help plz

### Calculus I

Sand falls from a hopper into a conical pile with radius equal to half its height. The sand is poured at a rate of 3 m^3 each minute. How fast is the radius increasing after 10 minutes? Need help with the set up and work through of the problem.

### math word problem

word problem need help: suppose you own a card shop. you buy one line of cards at a rate of 4 cards for $5. you plan to sell the cards at a rate of 3 cards for $5 how may carfds must you sell in order to make a profit of $100.00 i don't understand how to get answer can you help

### Chemistry

The reaction 2NO (g) + 2H2 -> N2 (g) + 2H2O (g) was found to follow the rate law, rate = k[NO]^2[H2]. By what factor will the rate of reaction increase when the pressure of NO gas is increased from 2.0 atm to 3.0 atm? Assume all other conditions are held constant. I'm ...

### Calculus

1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A particle moves along a path described by y=4-...

### Calculus

1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A particle moves along a path described by y=4-...

### Calculus

Show that y= x + sinx-pi satisfies the initial value problem dy/dx=1 + cos x, y(pi)= 0 i don't understand how to do this problem. i don't know where to begin.

### calculus

A woman 5.5 ft tall walks at a rate of 6 ft/sec toward a streetlight that is 22 ft above the ground. At what rate is the length of her shadow changing when she is 15 ft from the base of the light?

### Calculus

A particle moves along the curve y = 3x2 + 1 in such a way that the y value is increasing at the rate of 3 units per second. At what rate is x changing when x = 2?

### Calculus

Determine the maximum sustainable yield (the maximum harvesting and still keep the population stable) of population of logistic growth is Kr/4. I know the logistic equation with constant harvest rate, h, is dx/dt=rx((1-x/k)-h) I do not know how to apply that to the problem...

### math

you have deposited 1000 dollars in your savings account with n annual interest rate of 4 percent compounded monthly. how much money are you going to have in your account after six months? [(1+ 0.04/12)]^6 x 1000 = ?? is the answer 1020.164? You got it. well theres another part...

### chemistry

A first-order reaction is 40% complete at the end of 50 minutes. What is the value of the rate constant (in min^-1)? A. 1.8 x 10^-2 B. 1.0 x 10^-2 C. 1.2 x 10^-2 D. 8.0 x 10^-3 E. none of these how would i approach this problem? i know that to find the rate constant, i could ...

### Math

Please Help!!!! I do not understand and if someone could help that would be great! Thanks !! Problem #1: Find the total amount if you deposit $500 at a rate of 5% for two years using simple interest. Year 1 Year 2 Problem #2: Find the total amount if you deposit $300 at a rate...

### chemistry

Which of the following rate laws suggests that the reaction probably occurs in a single step? why is this problem cant be answer a since it has order of 1 a)(CH3)3CBr + OH- →(CH3)3COH + Br- rate = k[(CH3)3CBr] b)NO(g) + O2(g) → NO2(g) + O(g) rate = k[NO][O2] c)H2O2...

### chemistry

Which of the following rate laws suggests that the reaction probably occurs in a single step? why is this problem cant be answer a since it has order of 1 a)(CH3)3CBr + OH- →(CH3)3COH + Br- rate = k[(CH3)3CBr] b)NO(g) + O2(g) → NO2(g) + O(g) rate = k[NO][O2] c)H2O2...

### Calculus Reposted

A point is moving along the curve xy=12. When the point is at (4,3), the x-coordinate decreases at the rate of 2cm/sec. How fast is the y-coordinate changing at that point? dy/dx=-y/x is my change rate so far, should i substitute the coordinates (x,y) to the equation or just ...

### math

It is projected that t months from now, the average price per unit for gods in a certain sector of the economy will be P(t) = -t3 +7t2 +200t + 300 dollars. c.Use calculus to estimate the change in the rate of price increase during the first half of the 6th month. How can I ...

### Calculus

A payload is released at an elevation of 500m from a hot-air balloon rising at a rate of 14 m/s v(t)=? How would I go about starting this problem? I know that the procedure is relatively simple but I am beyond rusty and second guess myself too much. Any help would be greatly ...

### Math subject Calculus

Hi there I am having some difficulties to solve this problem from my homework package and i don't understand how to approach this problem. Please help me by giving me advice on how to approach this problem. Let z = xsin(x/y), y does not equal zero. Show that the tangent plane ...

### Craig - baloon - calculus moved up

Posted by Craig on Tuesday, November 25, 2008 at 7:54pm. t: 0 2 5 7 11 12 r'(t): 5.7 4.0 2.0 1.2 0.6 0.5 The volume of a spherical hot air balloon expands as the air inside the balloon is heated. The radius of the balloon in feet is modeled by a twice-differentiable function ...

### Math

A Marathon runner runs 10 1/2 miles in 2 hrs. What is her rate? Write an expression to represent the problem. Solve the problem.

### Math

A marathon runner runs 10 1/2 miles in 2 hours. What is her rate? Write an expression to represent the problem. Solve the problem:

### College Algebra Word Problem

I have been racking my head with this one and don't know how to approach it. The question is: A bank loaned out $64,000, part of it at the rate of 13% per year and the rest at a rate of 5% per year. If the interest received was $6000, how much was loaned at 13%. I know the ...

### college algebra

Solve the problem. A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

### college calculus

1) each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square is 16 cm^2? 2)the radius of a sphere is increasing at a rate of 4mm/s.How fast is the volume increasing when the diameter is 80mm? 3)A particle moves along the curve y= (1+x^3)^1/...

### pre-calculus

For groups of 80 or more people, a charter bus company determines the rate per person according to the formula: Rate=8-0.05(n-80),n(greater than or equal to)80 where the rate is given in dollars and 'n' is the number of people. Now, Express the revenue 'R' for the bus company ...

### Math

Hello I am having trouble with a pre-calculus problem. The problem is ln|Sin2X-CosX-1|=0 if you could help by listing the steps to solve that would be great! Thanks!

### Calculus- rates

A man 6ft. tall walks at the rate of 5 ft/sec toward a streelight that is 16 ft. above the ground. At what rate is the length of his shadow changing when he is 10ft. from the base of the light?

### Chemistry

IF the rate of consumption of N2)4 (below) is .0221, what is the rate of production of NO2? N2O4(g)<->2NO2(g) Please help and explain. BC i have to actually understand how to do the problem. Thanks

### Calculus - Rate of Change

Can someone explain how to solve this problem? Sand is being dumped on a conveyor belt onto a pile in such a way that the pile forms in the shape of a cone whose radius is always equal to its height. Assuming that the sand is being dumped at a rate of 10 cubic feet per minute...

### differential calculus

a SECURITY CAMERA is centered 50 feet above a 100-foot hallway. it is easiest to design the camera with a constant angular rate of rotation, but this results in a variable rate at which the images of the surveillance area are recorded. so, it is desirable to design a system ...

### calculus-changing voltage

V = IR V is increasing at the rate of 1 volt/sec while I is decreasing at the rate of 1/3 amp/sec. Let t = time in sec What is dV/dt? What is dI/dt? Find the rate at which R is changing when V = 12 volts and I = 2 amp. Thanks. Please ignore this. I got the answer.

### Math (calculus) (mean values)

A company introduces a new product for which the number of units sold S is given by the equation below, where t is the time in months. s(t)=155(7-9/(2+t)) a) Find the average rate of change of s(t) during the first year. Which my answer was 1395/28 b) During what month of the ...

### Calculus

Hello, I really need help on these two homework problem. >< In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II? So, surely there should be a ln in the solution as well? I would like a step by step process ...

### Calculus

Starting at midnight, a 10 foot radius circular pond freezes inward from the outer edge at a rate of 4 inches per hour. How fast is the open area shrinking at when the radius is 9 feet? (Note: if I'd said "at 3am" instead of "when radius is 9 ft", this would just be a chain ...

### Help meee

Answer from spreadsheet Answer from hand calculation Problem #1: Find the total amount if you deposit $500 at a rate of 5% for two years using simple interest. Year 1 Year 2 Problem #2: Find the total amount if you deposit $300 at a rate of 6% for three years using simple ...

### physics

A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s2 for 14.0s. It runs at a constant speed for 70.0 s and then slows down at a rate of -3.50 m/s2 until it stops at the next station. a) Sketch a position vs. time graph for this problem. b) Sketch...

### Calculus

a sandbag is dropped from a balloon at a height of 60 meteres when the angle of eleveation to the sun is 30 degrees. find the rate at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 35 meters. hint: the position of the sandbag ...

### Calculus Please help!

The altitude of a triangle is increasing at a rate of 2500 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7000 centimeters and the area is 87000...

### calculus

Can you help me solve this problem? I really don't know what to do. I solve problems like for example the rate of change of the elevation but I just encountered this kind of problem so I really don't know what to do. Please help me The endpoints of a movable rod of length 1 ...

### Chemistry

Calculate the rate at which N2O4 is formed in the following reaction at the moment in time when NO2 is being consumed at a rate of 0.0521 M/s. 2NO2(g) <-> N2O4 (g) I am not really sure how to go about this problem. rate = k (N2O4) d(NO2)/dt = -2 d(N2O4)/dt This is what I...

### Calculus

How would i start this problem? The amount that workers contribute monthly for health care insurance premiums can be modeled by A(t)=0.07t^3-3.1t^2 + 54.3t-230, where A is the monthly amount contributed and t is the number of years after 1980. Find the instantaneous rate of ...

### calculus

is average rate of change and average value the same or will you get a different answer for each this is calculus so it's the mean average. it's using the formula and integrating. I don't understand your question, but I can assure you that average rate of change and average ...

### Calculus

Shadow Length A man 6 feet tall walks at a rate of 3 ft per second away from a light that is 16 ft above the ground (see figure). When he is 11 ft from the base of the light find the following. (a) The rate the tip of the shadow is moving. (b) The rate the length of his shadow...

### Calculus

A man of height 1.7 meters walks away from a 5-meter lamppost at a speed of 1.6 m/s. Find the rate at which his shadow is increasing in length. (Round your answer to three decimal places.) This problem is absolutely killing me I see a lot of examples like this on here but I ...

### calculus

Let F(s)=5s2+1s+4. Find a value of d greater than 0 such that the average rate of change of F(s)from 0 to d equals the instantaneous rate of change of F(s)at s=1.