# calculus: related rates

21,872 results

### differential calculus

ADIABATIC EXPANSION when a certain polyatomic gas undergoes adiabatic expansion,its pressure p and volume V satisfy the equation pV^1.3 =k,where k is constant.Find the relationship between the related rates dp/dt and dV/dt. this is a problem of related rates please show all ...

### Math - Calculus

Im trying to understand related rates here and im getting stuck at this word problem. It says if V is the volume of a sphere with radius r, and the volume of the sphere decreases as the time passes. express dV/dt in terms of dr/dt. Describe the relationship in words. I don't ...

### Calculus (related rates)

Find dy/dt when y = 2x2 + 2x + 4 and dx/dt = 14 when x = 7.

### Calculus (related rates)

Find dy/dt where y = 2 sqrt(x)-4 and dx/dt = 9 when x = 4.

### Calculus - Related Rates

Bacteria are growing in a circular colony one bacterium thick. The bacteria are growing at a constant rate, thus making the area of the colony increase at a constant rate of 12 mm sq. per hour. Find an equation expressing the rate of change of the radius as a function of the ...

### Calculus Related Rates

A balloon is 70 feet from an observer which is rising at 15 ft/sec. At 5 seconds after lift off, how fast is the angle of elevation changing?

### Calculus Related Rates

Mulch is dumped into a pile with height always 1/3 the diameter at a rate of 30 ft^3/hr. How fast is the height increasing when it is 6 ft tall?

### Calculus Related Rates

Two people leave from the same spot and walk at 4 ft/sec going north and 5 ft/sec northwest. At 30 seconds, how fast is the distance between them changing??

### Related Rates Problem

A runner sprints around a circular track of radius 150 m at a constant speed of 7 m/s. The runner's friend is standing at a distance 300 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 300 m? (Round to 2 ...

### Calculus

Related rates: The volume of a cube is increasing at the rate of 40 mm^3/s. How fast is the surface area of the cube increasing when each edge is 10 mm?

### Calculus Related Rates

If a spherical balloon is inflated and its volume is increasing at a rate of 6 in^3/min. What is the rate of change of the radius when the radius is 3 inches??

### math

This is actually maths homework but the question sounds like geography: 1)Why do you think the UK is so high up in the list for mortality rates due to drug-related diseases. What do you think we can do to lower drug-related deaths in the UK? 2)Why do you think the UK is so ...

### Related Rates Calculus

A man 1.8 m tall is walking at a rate of 1.5 m/s away from a streetlight. It is found that the length of his shadow is increasing at a rate of 0.9 m/s. How high above the ground is the streetlight?

### 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.

### Calculus Related Rates

Two people leave from the same spot and walk at 4ft/sec going north and 5ft/sec going northwest. At 30 seconds, how fast is the distance between them changing?

### maths

This is actually maths homework but the question sounds like geography: 1)Why do you think the UK is so high up in the list for mortality rates due to drug-related diseases. What do you think we can do to lower drug-related deaths in the UK? 2)Why do you think the UK is so ...

### maths

This is actually maths homework but the question sounds like geography: 1)Why do you think the UK is so high up in the list for mortality rates due to drug-related diseases. What do you think we can do to lower drug-related deaths in the UK? 2)Why do you think the UK is so ...

### maths

This is actually maths homework but the question sounds like geography: 1)Why do you think the UK is so high up in the list for mortality rates due to drug-related diseases. What do you think we can do to lower drug-related deaths in the UK? 2)Why do you think the UK is so ...

### Maths

This is actually maths homework but the question sounds like geography: 1)Why do you think the UK is so high up in the list for mortality rates due to drug-related diseases. What do you think we can do to lower drug-related deaths in the UK? 2)Why do you think the UK is so ...

### maths

This is actually maths homework but the question sounds like geography: 1)Why do you think the UK is so high up in the list for mortality rates due to drug-related diseases. What do you think we can do to lower drug-related deaths in the UK? 2)Why do you think the UK is so ...

### 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?

### Calculus 1

Related Rates: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.

### Related rates-calculus

You are eating soup from a hemispherical bowl of radius 6cm at a constant rate of 40ml/min. Find the rate at which the soup level is going down in depth of the soup is 2cm.

### Calculus- Related rates

A spherical balloon is inflated at the rate of 1 cm^3 per minuter. At the instant when the radius r=1.5, (a.) how fast is the radius increasing? (b.) how fast is the surface area increasing?

### calculus (related rates)

A particle moves in the plane along the curve y=xln(x). At what rate is the distance from the origin increasing at the moment its x-coordinate is 2 cm and its x-coordinate is increasing at a rate of 17 cm/sec?

### Calculus - Related Rates

Suppose that you are watching a spaceship take off. You are 100 meters from the launch pad, and you measure the angle made by the rocket and the ground to be increasing at a rate of (d)(theta)/dt = 0.1 radians per second. What is the velocity of the rocket when theta = pi/4?

### 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

Related Rates: The minute hand on a watch is 9 mm long and the hour hand is 6 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

### Related rates math in calculus

A square sheet of cardboard has sides 18cm. Four equal portions are cut away from the corner and discard. The sides are then twiced up to form a restangular box. What are the dimension of the box formed that will have max volume?

### Calculus 1

Related Rates: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one ...

### 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 related rates

Boyle’s law for the expansion of a gas is PV = k, where P is the pressure (in pounds per unit of area), V is the volume of the gas, and k is a constant. Find the expression that shows the rate of change of the pressure as related to the rate of change of the volume. dP/dt...

### Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.

### Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.

### Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.

### Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.

### Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between the ships changing at 4:00pm.

### Calculus Related Rates

Two sides of a triangle are 5 and 8 and the angle between them is increasing at .05 rad/sec. how fast is the distance between the tips of the sides increasing when the angle is pi/4

### Calculus Related Rates

A hot air balloon, 50 feet from an observer, is rising at 20 ft/sec. At 5 seconds after lift off 1. How fast is the distance between the observer and the balloon changing? 2. How fast is the angle of elevation changing?

### related rates calculus 1

gravel is being dumped from a conveyor belt at a rate of 15 ft^3/hr and its coarseness is such that it forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of 10ft

### Calculus 1

Related Rates: 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 0.9 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?

### Calculus Related Rates

A balloon, 50 feet from an observer, is rising at 20 ft/sec. At 5 seconds after lift off 1. How fast is the distance between the observer and the balloon changing? 2. How fast is the angle of elevation changing? I need help on both questions. Thanks in advance smart people!!

### Calculus (related rates)

A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the ladder is 5 m from the wall?

### Sociology

What is the effect of industrialization on population growth rates? A. It decreases growth rates B. It stabilizes growth rates C. It increases growth rates D. There is no correlation between industrialization and growth rates My text says that industrialization decreases birth...

### Calculus ~ Related Rates

A man 2 meters tall walks at the rate of 2 meters per second toward a streetlight that's 5 meters above the ground. At what rate is the tip of his shadow moving?We've already set this up part of the way. We know that dx/dt = - 2 meters per second, and we're looking for dy/dt.

### Calculus

For the function f(x) = x^2 - 4x +5, x>= 2, which is equal to d/dx (f-1 this is the inverse)(x)) ? 1/(2y-4) where x and y are related by the equation (satisfy the equation) x=y^2-4y+5 x>= 1 2y-4 where x and y are related by the equation y= = x^2 - 4x +5, x>= 2 1/2x-4 ...

### Calculus

related rates: a ladder, 12 feet long, is leaning against a wall. if the foot of the ladder slides away from the wall along level ground,what is the rate of change of the top of the ladder with respect to the distance of the foot of the ladder from the wall when the foot is 6 ...

### Calculus 1 Related Rates

Water is discharged from a pipeline at a velocity v(in ft/sec) given by v=1240p^(1/2), where p is the pressure (in psi). I f the water pressure is changing at a rate of 0.406 psi/sec, find the acceleration(dv/dt) of the water when p=33.0 psi. I know the answer is suppose to be...

### calculus: related rates

hello, please help me. A cylindrical can is being heated with its height increasing at the rate of 0.01cm/min and its diameter at the rate of 0.005cm/min. At what rate is the volume increasing when the can has a diameter of 15cm and a height of 20cm. this is how i'm going ...

### Business/Economics

What is strengths and weaknesses regarding monetary polcies, and how is related to treasury bill and note rates?

### math/rates and unit rates

I can't figure out my homework because I don't know what rates & unit rates are.

### calculus

Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to over­ come the centrifugal force, the road is banked at an angle of magnitude 0 from the horizontal. The banking angle must satisfy the equation rg tan 0 = v^2 where v is...

### calculus ( related rates )

a paper cup in the shape of a cone has a diameter of 10cm across the top, and is 8cm deep. if the cup is leaking out the bottom at 2pi cm^3/min, at what rate is thet area of the water surface ( only the top surface of the water) changing, when the cup has a the water depth of ...

### differetial calculus-related rates

LINEAR VS ANGULAR SPEED A wheel of a radius 30 centimeters revolves at a rate of 10 revolutions per second.A dot is painted at a point P on the rim of the wheel. a)find dx/dt as a function of ϴ. b)use a graphing utility to graph a function in part (a) c)when is the ...

### 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(...

### calculus : related rates

a balloon rises at a rate of 3 meters per second from a point on the ground 30 meters from an observer. find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the ground... so i drew a small picture depicting it ...

### 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 (Related Rates)

The position of a particle moving in a straight line is given by s(t) = (e^(-t))(cos(5t)) for t>0, where t is in seconds. If the particle changes direction at time T seconds, then T must satisfy the equation: cos(5T) = 0 5T = arctan(-1/5) 5e^(-t) sin(5t) = 0 tan(5T) = -1/5 ...

### social studies

1)An interest rate is a special type of? a. loan b. price c. bank d. service 2) How does a compound interest rate differ from a simple interest rate? a. Compound interest rates pay more interest over time b. Compound interest rates are calculated only once a year c. Compound ...

### Calculus, Related Rates

At 12 noon ship A is 60 miles west of point P steaming east at 15 knots and ship B is 36 miles south of P steaming north at 10 knots. If the ships continue their courses and speed. how is the distance between them changes at 2pm? At what time the ships are closest? The answers...

### Business

Recently, it was observed that people have started saving more rather than spending. This has impacted the demand for luxury goods and services. The decline in the demand led to unemployment in the related sectors. What can be a primary solution to reduce the unemployment ...

### AP CALCULUS!!! HELPP

related rates: the base of a pyramid-shaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate of 2 cubic meters er second. find the rate...

### AP CALCULUS!! HELPPP URGENT

related rates: the base of a pyramid-shaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate of 2 cubic meters er second. find the rate...

### Riddle

How are these two people related to each other? If a man's mother's nephew is a woman's father's cousin, how closely related are the man and woman related? I think they would be related by marriage?

### Chemistry

Just a few questions about rates of reaction. A) Why are the units for average and instantaneous rates the same? -because they are both measures of how quickly a reaction is occuring per unit time B) For a given set of data, two students determined different average reaction ...

### Social studies

How die a compound interest rate differ from a simple interest rate? Compound interest rates pay more interest over time Compound interest rates are calculated only once a year Compound interest rates ideally lower than simple interest rates•• Compound interest rates apply...

### related rates word problems

"A man of height 2.2 meters walk away from a 5-meter lamppost at a speed of 1.2 m/s. Find the rate at which his shadow is increasing in length. " what is the answer to this? if anyone can help that would be great

### Chemistry 152

to obtain the rate of the reaction 5Br-(aq) +BrO3- (aq) + 6H+ (aq) ---3Br2(aq) + 3H2O(l) you might follow the Br concentration or the BrO concentration.How are the rates in terms of these species related?

### Calculus-Related Rates

Three elementry kids are at a field day hula hoop contest. They were the last one standing of the heated competition. They have been hula hooping for 10minutes. Student1 (S1) is at point (6,5); Student2 (S2) is at point (6,1) while student 3(S3) is at (1,1). Finally, the gym ...

### comp

can you help me Underline the topic sentence for this paragraph??? Interest rates have a decidedly large impact on purchasing decisions. Interest rates affect our purchases in a couple different ways. Interest rates are what you pay for the use of someone else's money. When ...

### Math (related rates) help?

A 13ft ladder slides down a wall at 2ft/sec when it is 12 ft above the ground. Find the rate at which the angle it makes with the ground changes at this moment?

### Calculus, Related Rates

A particle at point A is 50 mm away from a second particle at point B. The first particle is moving toward point B at a constant rate and the second particle is moving at a right angle to the line AB at a rate that is 1/3 of the rate of the first particle. The particles get ...

### Macroeconomics - inflation vs unemployment!!!!

I had to graph both the U.S. inflation and unemployment rates on the same graph between the years 1990-2004. I need to analyze the data. How are the two rates related? How does one affect the other, if so? One way to analyze the data is to put the inflation data on one axis, ...

### finance

Which of the following is true with regards to rising interest rates. A. Use long-term loans to take advantage of current low rates. B. The term of the loan is ot impacted by rising interst rates. C. Use short term loans to take advantage of low iterest rates. D. Select long-...

### Help! Urgent!

You know tangentTheta=h/4 take the derivative sec^2 Theta * dTheta/dt= 1/4 dh/dt you know dtheta/dt solving for dh/dt You know sec Theta from the right triangle: sec theta = sqrt(h^2 +16) /h check me. Georgina: in the future, please put the title in the subject box, in this ...

### math/unit rate

please help me find the definition for unit rate. It depends upon what kind of unit. Go to www.google.com and type in unit rate. There is one source there for hotel unit rates, another for unit rates for the medical field, etc. You may also go to www.dictionary.com and type in...

### Calculus - Related Rates

A road perpendicular to a highway leads to a farmhouse located 5 miles away. An automobile traveling on the highway passes through this intersection at a speed of 65mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 1 miles...

### Math (Calculus) (Related Rates)

A boat pulls away from a dock at 2 m/s, but the operator has neglected to remove the tow rope used to pull the boat up to the dock. This rope runs thru a pulley which is attached to the dock at a point 1 m higher than the point at which the rope is attached to the boat. A) How...

### Related rates

Two people start from the same point. One walks east at 1 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes?

### Introduction to Finance: Harvesting the Money Tree

7) The problem in stretching out the maturity of marketable securities is that A. long-term rates higher than short-term rates. B. interest rates are generally lower. C. you are legally locked in until the maturity date. D. there is greater possibility of loss. I think B

### Finance

which of the following is true with regards to rising interest rates? A. Use Long-term loans to take advantage of current low rates. B. The term of the loan option is not impacted by rising interest rates. c. Use Short-term to take advantage of low interst rates. D. Select ...

### calcus

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

### Related rates

Hey, I have a question on related rates and I'm a little rusty at them. I have an idea how to do this one but at a certian point i get stuck. The question is: Two cars leave the intersection, the first travelling south at 40 km/hr and another travelling west at 90 km/hr. How ...

### Science

What conclusion can be drawn about the relationship between the arrangement of elements on the periodic table and the patterns observed in their priorities? A. Properties of elements are related to atomic numbers. B. Properties of elements are related to ductility. C. ...

### science

1) What conclusions can be drawn about the relationship between the arrangement of elements on the periodic table and the patterns observed in their properties? :Properties of elements are related to atomic numbers.*** :Properties of elements are related to ductility. :...

### Calculus

two complex numbers Z and W are related by the formula W=(Z+1)/(1-Z) what is W if Z=1.5i? thanks for the help!

### math-rates

1,680 kilobytes in 4 minutes ..........how do u get it....... lesson 6-2 ......rates....6th grade pg. 289 ......#2

### statistics

Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predicted by the prime ...

### math

A medical researcher wants to determine whether male pulse rates vary more or less than female pulse rates. Using the sample pulse rates in Data Set 1 in Appendix B, the male pulse rates can be summarized with the statistics 40=n,69.4=x,11.3=s. For females, the statistics are,...

### math

Resolved QuestionShow me another » AP Calculus related rates problem? The volume V or a cone (V = 1/3 ð r² h) is increasing at a rate of 28ð cubic units per second. At the instant when the radius r of the cone is 3 units, its volume is 12ð cubic units and the radius is ...

### math-rates

.....rates....6th garde.....lesson6-2 5pounds for \$2.49

### calc related rates

A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

### Stats

Question 3 Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predicted by the ...

### related rates problems

Water pours out of a conical tank of height 10 feet and radius 4 feet at a rate of 10 cubic feet per minute. How fast is the water level changing when it is 5 feet high?

### Sociology

What does the author think best explains the number of lower-class offenders in the criminal justice system? a) They have higher offending rates. b) They have higher rates of recidivism. c) There are both disparities in crime rates and discrimination in the system. d) ...

### geography

In which country have death rates declined markedly even as infant mortality rates are the highest in the world?

### 6th grade

Hello, I need help in trying to figure out rates (as in ratios and rates). What is a formula that I would use? Thanks in advance.

### Calc

How do I do this related rates problem? A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. (...

### Government

1. Both corporate and individual income tax rates are set at ______ rates. a. high b. low c. progressive d. regressive I think it's C?

### Related Rates

A street light is at the top of a 10.5 ft. tall pole. A man 5.4 ft tall walks away from the pole with a speed of 3.5 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 47 feet from the pole?