
	Where results make sense

Topic: Related Rates

Related Topics

Implicit function

Product rule

Lists of integrals

Derivative

List of integrals of area functions

Solid of revolution

Calculus

Relation (mathematics)

List of integrals of exponential functions

Propitiation

Cultivar

Book of Judges

Red Sox Nation

Fat fetishism

Thunderstorm

In the News (Thu 16 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Related Rates
		Related rate problems often involve a situation in which you are asked to calculate the rate at which one quantity changes with respect to time from the rate at which a second quantity changes with respect to time.
		Related rate problems can be recognized because the rate of change of one or more quantities with respect to time is given and the rate of change with respect to time of another quantity is required.
		The rate of change of the volume of the pile is given, the constant multiplier is specified, and there is a request to find the rate of change of the height of the pile when the height is a specified value.
	astro.ocis.temple.edu /~dhill001/relatedrates/relatedrates.html (1959 words)

	PlanetMath: related rates
		The rates of change are no longer scalars, but rather velocity vectors, and therefore the derivative must be regarded as a linear transformation that changes one vector into another.
		The above is the multi-dimensional and coordinate-free generalization of the related rates relation (1).
		This is version 3 of related rates, born on 2002-06-06, modified 2005-11-27.
	planetmath.org /encyclopedia/RelatedRates.html (599 words)

	RELATED RATES APPLICATIONS
		In related rate applications one tries to find the rate at which one quantity is changing by relating it to other quantities with known rates of change.
		Related rates applications can be used to answer the focusing problem as well as the elevation problem.
		A typical related rate application would calculate the rate at which they were separating at a later point in time.
	www.usna.edu /MathDept/website/courses/calc_labs/relatedrates/Application.html (601 words)

	Firearm-Related Fatality Rates - West Virginia and United States
		West Virginia's rate of suicide firearm deaths from 1993-98 was 10.8 deaths per 100,000 population, compared to a U.S. rate of 6.9.
		The rate among fl residents, on the other hand, was lower than the comparable national rate, with an overall rate of 16.9 deaths per 100,000 fl population compared to a U. rate of 24.0.
		While the highest rates of firearm-related suicide by age were found among persons aged 65 and older both nationally and statewide, West Virginia residents had higher rates than their national counterparts in all age groups.
	www.wvdhhr.org /bph/oehp/hsc/briefs/five/default.htm (940 words)

	Rates of Homicide, Suicide, and Firearm-Related Death Among Children -- 26 Industrialized Countries
		The firearm-related homicide rate in the United States was nearly 16 times higher than that in all of the other countries combined (0.94 compared with 0.06); the firearm-related suicide rate was nearly 11 times higher (0.32 compared with 0.03); and the unintentional firearm-related death rate was nine times higher (0.36 compared with 0.04).
		The rate for firearm-related deaths among children in the United States (1.66) was 2.7-fold greater than that in the country with the next highest rate (Finland, 0.62) (Figure_1).
		Although specific reasons for the differences in rates among countries are unknown, previous studies have reported on the associations between rates of violent childhood death and low funding for social programs (6), economic stress related to participation of women in the labor force (7,8), divorce, ethnic-linguistic heterogeneity, and social acceptability of violence (9).
	www.cdc.gov /mmwr/preview/mmwrhtml/00046149.htm (1508 words)

	Related Rates Problems (Site not responding. Last check: 2007-09-10)
		A screen saver displays the outline of a 3 cm by 2 cm rectangle and then expands the rectangle in such a way that the 2 cm side is exanpanding at the rate of 4 cm/sec and the proportions of the rectangle never change.
		Assuming the shoreline is straight and that the gangster is walking at the rate of 2 km/hr, how fast must the FBI agent rotate the spyglass to track the gangster when the gangster is 1 km from the point on the shore nearest to the boat.
		Suppose that the receptacle is being filled with water at the rate of.2 cubic inches per second.
	oregonstate.edu /instruct/mth251/cq/Stage9/Practice/ratesProblems.html (342 words)

	Related Rates
		On the other hand, we find some problems in which there are two variables, x and y, related by an equation that does not involve t, but it can be understood that both x and y are functions of t.
		Find the rate of change of its radius when its radius is 10 centimeters.
		2- The rate at which the radius of the liquid surface is increasing at this moment.
	library.thinkquest.org /C006002/Pages/Related_Rates.htm (319 words)

	Nonfatal and Fatal Firearm-Related Injuries -- United States, 1993-1997
		To examine trends in nonfatal firearm-related rates by intent of injury, sample weights for cases with unknown intent (i.e., 13.4% of nonfatal injuries during the 5-year period) were allocated to one of the three known categories--assault/legal intervention, intentionally self-inflicted, or unintentional injury.
		This decline was accompanied by a decrease of 21.1% in the annual death rate from 15.4 per 100,000 (95% CI=15.2-15.5) in 1993 to 12.1 per 100,000 (95% CI=12.0-12.3) in 1997 (Table 2).
		The declines in nonfatal and fatal injury rates were similar for males (40.7% for nonfatal, 20.9% for fatal) and for females (42.1% for nonfatal, 23.2% for fatal).
	www.cdc.gov /mmwr/preview/mmwrhtml/mm4845a1.htm (1875 words)

	RELATED RATES REVIEW
		In the preceding applet you were able to make observations about the rate of change of distance between two ships given their respective rates of change of position or velocities.
		In general, a related rate problem involves the determination of the rate of change of a given quantity by relating it to other quantities whose rates of change are known.
		Furthermore, suppose it is known that the volume of the sphere is increasing at the rate of 10 cubic feet per minute.
	www.usna.edu /MathDept/cdp/relatedrates/MathReview.html (617 words)

	IRS Announces 2006 Standard Mileage Rates
		The standard mileage rates for business, medical and moving purposes are based on an annual study of the fixed and variable costs of operating an automobile.
		For the first eight months of 2005, the standard rate for miles driven for medical or moving purposes was 15 cents per mile, and, except for special Hurricane Katrina rates, the standard rate for miles driven in service of a charitable organization was 14 cents per mile.
		For the period Aug. 25 to Aug. 31, 2005, the rate for miles driven for charities providing Hurricane Katrina relief is 29 cents, for deduction purposes, and 40.5 cents, for reimbursement purposes.
	www.irs.gov /newsroom/article/0,,id=151226,00.html (448 words)

	math 505, lecture on related rates
		This is a lesson on related rates, one of the topics in differentiation that first-year calculus students seem to find hardest.
		The rate at which the light of an offshore lighthouse revolves determines the rate at which the light moves along the shoreline.
		The rate at which a balloon is filled determines the rate at which the radius increases (for a spherical balloon).
	www.math.utk.edu /~rdavis/Rates/Lecture.htm (950 words)

	Karl's Calculus Tutor - The Dance of the Derivatives (Related Rates)
		Furthermore, the rate at which the roll spins is related to the radius.
		We see "rate" and "radius" in the same phrase, and that indicates that the problem is asking for the derivative of radius with respect to the independent variable, which in this case is time.
		In the doggie problem it stated the thickness of the paper, the rate the paper was being pulled, and the radius at which you were to establish the rate (observe that the thickness is neither a dependent nor an independent variable -- it is a constant.
	www.karlscalculus.org /calc8_1.html (6009 words)

	Instantaneous velocity. Related rates. - An approach to calculus
		For, the slope of that line, which is 22, is rate of change of s with respect to t, which by definition is the velocity.
		The second derivative is the rate of change of the velocity with respect to time.
		A boy is walking at the rate of 5 miles per hour toward the foot of a flag pole 60 feet high.
	www.themathpage.com /aCalc/motion.htm (1162 words)

	Related Rates : Exercises for Calculus I at the Library of Math (Site not responding. Last check: 2007-09-10)
		In this topic we show how implicit differentiation and the chain rule can be used to calculate the rate of change of one variable in terms of the rate of change of another variable (which may be more easily measured).
		The procedure of solving a related rates problem is to find an equation that relates two quantities and then use the chain rule to differentiate both sides with respect to time.
		Then, from knowing the rate of change of one value at a point in time, we can calculate the rate of change of another quantity at that moment in time.
	www.libraryofmath.com /Calculus_I_Exercise_Related_Rates.html (617 words)

	Related Rate Problems (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)
		The base of the ladder is pulled away from the side of the house at the rate of 2 feet per second.
		Find the rate of change of the radius of a sphere at the point in time when the radius is 6 feet if the volume is increasing at the rate of 8 pi cubic feet per second.
		Find the rate of change of the volume of a cylinder when its radius is 6 feet if its height is always (3/2) times its radius and its radius is increasing at the rate of 2 feet per minute.
	www2.scc-fl.edu.cob-web.org:8888 /lvosbury/CalculusI_Folder/RelatedRateProblems.htm (1777 words)

	Related Rates
		A "related rates" problem is a problem which involves at least two changing quantities and asks you to figure out the rate at which one is changing given sufficient information on all of the others.
		Differentiate this relation with respect to the underlying independent variable, usually making heavy use of the chain rule.
		The relation among the variable x, y, and z, using the Pythagorean theorem, is that
	oregonstate.edu /instruct/mth251/cq/Stage9/Lesson/relatedRates.html (460 words)

	Related rates - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)
		In differential calculus, related rates problems involve finding the rate at which a quantity is changing by relating that quantity to other quantities whose rates of change are known.
		Identify the known rates of change and the rate of change that is to be found.
		Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found.
	en.wikipedia.org.cob-web.org:8888 /wiki/Related_rates (422 words)

	related rates - The rates Spot (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)
		The staff at The rates Spot has gone through the web and has gathered a list of links that offer the most information on related rates.
		Important Introduction: The basic idea behind related rates is that each of the variables is now a...
		A "related rates" problem is a problem which involves at least two changing quantities and asks you to figure out the rate at which one is changing given sufficient information on all...
	www.brockbankinvestment.com.cob-web.org:8888 /rates/related-rates.html (375 words)

	related rates
		The problem asked for the rate at which the tip of the shadow is moving away from the light post.
		The text does that by finding the rate of change of (x+ y) which is the total distance from the light post to the tip of the shadow.
		You determined the rate of change of y, the length of the shadow, and then added on the rate at which the distance of the person from the light post, x, is changing.
	www.physicsforums.com /showthread.php?t=114901 (631 words)

	Qrhetoric Calculus - Related Rates
		The basic idea behind related rates is that each of the variables is now a function of time, or t.
		Here, in related rates, you will take a derivative of a function that will give you as many variables as are in the equation.
		This is the rate of change of r with respect to t, and you can now solve for it.
	www.qcalculus.com /cal07.htm (1099 words)

	Related Rate Problems
		Initially there are 30 feet of rope out and the rope is taught and being reeled in by a circular device the top of which is 10 feet higher than the point where the rope is attached to the boat.
		A large red balloon is rising at the rate of 20 ft/sec.
		The end of a pulley (at point C in the picture) is being pulled down at the rate of 1 ft/sec.
	www2.scc-fl.com /lvosbury/CalculusI_Folder/RelatedRateProblems.htm (1777 words)

	Calculus I Notes, Section 4-1
		To do so, we write an equation that relates the variables involved and differentiate it to get an equation that relates the rate we seek to the rate we know.
		Since the line is reeled in at the rate of 2 feet per second, and s is shrinking.
		Write an equation that relates the variables: You may have to combine two or more equations to get a single equation that relates the variable whose rate you want to the variable whose rate you know.
	www.blc.edu /fac/rbuelow/calc/nt4-1.htm (544 words)

	[No title]
		Find the rates at which the box's (a) volume, (b) surface area, and (c) diagonal length s are changing at the instant when x = 4, y = 3, and z = 2.
		A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away from her at a rate of 25 ft/sec.
		Since the ladder is in feet, and the rate the ladder is sliding down would make more sense in ft/ sec we must convert 1 mi /hr to ft /sec.
	faculty.eicc.edu /bwood/math150supnotes/supplemental12.htm (626 words)

	Calculus I (Math 2413) - Derivatives - Related Rates
		/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.
		Note that the rate is negative since the distance from the wall, x, is decreasing. We always need to be careful with signs with these problems.
		In this section we’ve seen three related rates problems. They all work in essentially the same way. The main difference between them was coming up with the relationship between the known and unknown quantities. This is often the hardest part of the problem.
	tutorial.math.lamar.edu /AllBrowsers/2413/RelatedRates.asp (1031 words)

	Related rates
		Excepting R of course, anywhere from two to all four of the quantities related by this formula may vary with time.
		Thus the rate of change of the left-hand side of the Ideal Gas Equation with respect to time will always equal the rate of change of the right-hand side of the Ideal Gas Equation with respect to time, and we have
		Suppose that a rubber ball of is being inflated at a rate of 5 cubic centimeters per second.
	www.uwm.edu /Dept/Math/Resources/Calculus/Key/node59.htm (430 words)

	Related Rates (Site not responding. Last check: 2007-09-10)
		A key part of solving related rates problems is translating the word problem to mathematical terms.
		A gear is revolving at the rate of 30 revolutions per minute (1 rev = 2pi rad).
		Write an equation involving the variables whose rates of change either are given or are to be found.
	library.thinkquest.org /3616/Calc/S2/RR.html (319 words)

	Related Rates Of Change (Site not responding. Last check: 2007-09-10)
		These are questions that depend upon related rates of change.
		To consider the case of the oil slick, we first have to assume that the thickness of the slick is constant.
		So we have an expression for the rate at which the oil slick grows, in terms of the current radius.
	www.mathsyear2000.org /alevel/pure/purtutdifrel.htm (274 words)

	Method for Solving Related Rate Problems (Site not responding. Last check: 2007-09-10)
		Note which quantities have rates that are given and which quantities have rates which are desired.
		State the rates (in terms of derivatives) and any other values given in the problem.
		Find an equation relating the quantity with the unknown rate to the quantity (or quantities) with the known rate.
	www.gpc.edu /~jcraig/calc1_ch4/4s1_related_rates.htm (132 words)

	2.17 Related Rates
		By relating the rates in this way, we often can answer interesting questions about the model that we use to specify the original problem.
		Suppose that an inflating balloon is spherical in shape, and its radius is changing at the rate of 3 centimeters per second.
		A baseball diamond is 90 feet square, and the pitcher's mound is at the center of the square.
	www.math.dartmouth.edu /~klbooksite/2.17/217.html (355 words)

Try your search on: Qwika (all wikis)