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September 2, 2014

Search: calculus(related rates)

Number of results: 16,279

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 dont ...
December 7, 2006 by Cosmo

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 ...
November 29, 2009 by Joel

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 ...
October 1, 2010 by Calculus

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 ...
November 13, 2011 by Nabiha

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.
May 4, 2013 by Mostafa

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 ...
November 12, 2011 by Nabiha

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 ...
November 12, 2011 by Nabiha

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 ...
November 12, 2011 by Nabiha

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 ...
November 12, 2011 by Nabiha

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 ...
November 13, 2011 by Nabiha

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.
November 13, 2011 by A

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?
October 27, 2009 by drew

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.
December 30, 2010 by elizabeth

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?
August 22, 2014 by PHILLIP

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?
December 30, 2010 by james

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.
October 10, 2013 by Juan

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.
October 10, 2013 by Juan

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.
October 10, 2013 by Juan

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.
October 10, 2013 by Juan

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.
October 10, 2013 by Juan

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.
January 5, 2012 by Mishaka

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 ...
January 9, 2008 by JJ

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...
November 21, 2010 by jahil

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 ...
March 11, 2012 by mary

Business/Economics
What is strengths and weaknesses regarding monetary polcies, and how is related to treasury bill and note rates?
March 2, 2011 by Tanya

math/rates and unit rates
I can't figure out my homework because I don't know what rates & unit rates are.
May 8, 2008 by wyatt christopherson

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...
June 22, 2011 by john

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(...
April 15, 2007 by Anonymous

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 ...
November 5, 2007 by dave

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 ...
March 29, 2012 by Anonymous

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...
April 14, 2011 by Raven

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 ...
May 16, 2010 by Jamie

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...
April 15, 2011 by Raven

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?
December 6, 2013 by Annette

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 ...
January 25, 2012 by Anna

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 ...
May 16, 2011 by needhelp

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 ...
April 17, 2012 by Jason

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, ...
September 9, 2006 by Samantha

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-...
November 3, 2013 by Michelle

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 ...
November 5, 2006 by bobpursley

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...
September 26, 2006 by hannah

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
August 8, 2009 by scooby9132002

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?
November 11, 2010 by Michael

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 ...
October 31, 2013 by Michelle

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 ...
November 2, 2006 by Tracy

math-rates
1,680 kilobytes in 4 minutes ..........how do u get it....... lesson 6-2 ......rates....6th grade pg. 289 ......#2
December 2, 2010 by alex

math-rates
.....rates....6th garde.....lesson6-2 5pounds for $2.49
December 2, 2010 by alex

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 ...
July 8, 2013 by Tony

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!
March 13, 2008 by Anne

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 ...
August 20, 2012 by David

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?
October 24, 2011 by Bernardo

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) ...
November 11, 2012 by Tammy

math
Resolved QuestionShow me another » AP Calculus related rates problem? The volume V or a cone (V = 1/3 š r² h) is increasing at a rate of 28š cubic units per second. At the instant when the radius r of the cone is 3 units, its volume is 12š cubic units and the radius is ...
December 19, 2009 by kelli

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?
December 30, 2010 by elizabeth

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.
January 6, 2009 by Bobby

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?
July 19, 2011 by Anthony

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. (...
November 10, 2009 by Derick

Math
Rates And unit rates 120mi. to 10 gal of gas I'm not sure what you are asking, but this reduces to 12 miles per gallon. Does that help? If not, repost your question in different terms. Thanks for asking.
February 8, 2007 by Ruthie

statistics
Assuming the resting heart rates for a sample of individuals are normal distibuted with a mean of 70 and a standard deviation of 15. Waht percentage of rates less than 70
November 12, 2010 by Darlene Watson

ECO/372
what happens to the monry interrest rates and the economy if the federal reserves is not the seller of government bonds? I know the interest rates go down but not sure what else?
April 27, 2012 by at

Related rates
Sand is being dropped at the rate of 10 cubic meter per minute onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8 meters high?
May 14, 2012 by :)

related rates
A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 8 cm. (Note the answer is a positive number).
October 24, 2011 by james

COM155
Write two paragraphs about how interest rates affect our purchasing decisions. High interest rates make us stop and think, do we need this item? Is it a necessity? When interest rates are high people tend to finance things less. Why pay a lot in interest when you can just ...
August 9, 2011 by Jessica

social problems
Increase in divorce rates over the last century related to :A)rejection of the ideology of the "good"family B) increasing financial independence of woman c)increasing abuse and conflict in families d) change in social norms toward greater acceptance of divorce IS C CORRECT ...
February 23, 2011 by vedrana

Economics
If demand is price elastic, total revenue is a.directly related to quantity demanded b.inversely related to quantity demanded c.directly related to price d.directly related to price and inversely related to quantity demanded e.not related to either price or to quantity demanded
January 19, 2010 by Rosa

geography
I have to put indicators of measuring development in countries in order of importance they are :- literacy rates number of people per doctor, gross national product, % of population access to clean water, population density, % people employed in agriculture, % population ...
May 10, 2010 by sue

Calculus
At a certain factory, output Q is related to inputs u and v by the equation Q= 17u^2+(16u+17v)/(u+v)^2 If the current levels of input are u= 10 and v = 25, use calculus to estimate the change in input v that should be made to offset a decrease of .7 unit in input u so that ...
October 8, 2013 by Rebekah

Environmental Science
How do birth, death, fertility, and migration rates affect population size? What factors can affect these rates?
September 5, 2007 by Patricia

law
Over the past decade, some countries have shown high crime rates while other countries have lower crime rates. For example, the lowest homicide rates in 2000 existed in Saudi-Arabia and Japan, while France and Germany had the highest homicide rates. Their rates, however, were ...
January 2, 2011 by michelle

MATh/UNiT RATES
FIND THE UNIT RATES AND WRITE THEM BOTH IN FRACTION AND WORD FORM. 7.Gabrielle bikes 78 miles in 6 hours.
September 23, 2008 by DEANZA

Chemistry
I haven't calculus in a while. So can someone please help me with this, its for rates: log (base 1/4) 0.25 = m I know that m = 1, but how would I solve for it using the log method.
March 11, 2008 by Raj

sci
How do birth,death,family and migration rates affect the population? What factors can affect these rates
August 22, 2007 by renee

english
Can someone please check my homework for me? · Write two paragraphs about how interest rates affect our purchasing decisions. · Identify the topic sentence in each by underlining it. · Post your paper as an attachment. Interest rates affect the buying of homes in real estate. ...
May 8, 2011 by icelocsgirl

Calculus
Find the Rates of convergence of the following functions as h->0 lim h->0 sin h - hcosh ------------- = 0 h Find the Rates of convergence of the following functions as n->inf lim (Sin (1/n))^2=0 n-> inf
December 11, 2009 by Sammy

Further calculus
1) A price p (in dollars) and demand x for a product are related by 2x^2+6xp+50p^2=10600. If the price is increasing at a rate of 4 dollars per month when the price is 30 dollars, find the rate of change of the demand. 2) a) The price (in dollars) p and the quantity demanded q...
November 2, 2011 by Alison

chemistry
Predict the relative rates for the reaction of butadiene and a)ethene, b)methyl propentanoate, c)maleic anhydride? Please Help!!!How do I determine the relative rates of the reactions?
May 21, 2009 by gizelle

Macroeconomic
1. An example of an automatic stabilizer is A. a temporary tax rebate. B. the progressive income tax.Student Response C. cost of living adjustments to social security payments. 2. Which of the following represent expansionary fiscal policy? A. an increase in average individual...
June 8, 2010 by Bob

calculus(related rates)
Water is leaking out of an inverted conical tank at a rate of 12200 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 15 meters and the diameter at the top is 6.5 meters. If the water level is rising ...
May 5, 2012 by jhon

Criminal Justice
Could someone please help me with this question? What are crime rates? This is what I have so far: Crime rates are the number of offenses reported for each unit of population. How could I expand on this? Thanks for your help!
April 15, 2011 by Helen

SCIENCE/ECOLOGY
I NEED HELP IN PREPARING A DEMOPRAPHIC AND ENVIRONMENTAL TIMELINE WHICH INCLUDES DEATH RATES, BIRTH RATES, POPULATION CHANGES, AND MAJOR HISTORY CHANGES
April 2, 2013 by EVELYN

Calculus
Greetings, This is a question about selecting courses for my semester. I was planning to take Calculus 3 (Mostly 3-Dimensional topics involving calculus) and a C++ programing course. If you have heard of these courses, can you please tell me your thoughts about me taking these...
January 3, 2012 by Simon

Related Rates
A particle moves along a path described by y=x^2. At what point along the curve are x and y changing at the same rate? Find this rate if at time t we have x=sin t and y= sin^2t. I solved the first part and got (1/2, 1/4), but I have no idea how to tackle the second part. Help ...
May 6, 2013 by Shania

Math, Related Rates
Consider the hyperbola y = 1/x and think of it as a slide. A particle slides along the hyperbola so that its x-coordinate is increasing at a rate of f(x) units/sec. If its y-coordinate is decreasing at a constant rate of 1 unit/sec, what is f(x)? -I arrived at the answer f(x...
September 10, 2013 by xavier

Economics
How do you proceed in calculating exchange rates between countries and what data do you need? Exchange rates are simply market prices of foreign currencies. The price can fluxuate on a daily basis. So, are you asking how you would build a model that predicts an exchange rate...
March 22, 2007 by joe

Chemistry
How is water of hydration related to measurement and how it is related to the law of definite composition?
November 3, 2010 by Ash

chemistry
Rates of chemical reactions usually depend on temperature and pressure. However, half-life of all radioactive elements is independent of both T and p. How can these decay rates be independent of T if we beleive in the Arrhenius equation?
July 27, 2010 by Jin

Global science
The ajor reason for the dfamatic increase in human population during the last 100 years is ? a)increasing birthrates,B)decreasing birth rates,c)improved daycare for children,d) decreasing death rates
November 1, 2010 by Anonymous

accounting
the longer the time to maturity: the greater the price increase from an increase in interst rates; the less the price increase from an increase in interest rates; the greater price increase from a decrease in interest rates; the less the price decrease fron a decrease in ...
April 3, 2009 by pookie

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?
November 13, 2011 by Sarah

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 2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5 ft from the wall? Evaluate your answer numerically...
December 2, 2010 by Michael

SS
Rising demand for a certain type of car will probably lead to: a. lower interest rates for all types of vehicles. b. lower interest rates for that type of car. c. higher interest rates for all types of vehicles. d. higher interest rates for that type of car. D
January 23, 2014 by Anonymous

accounting
Plumley Ad Agency contracted with a company to prepare an ad campaign. Plumley uses a job order costing system. Plumley estimates that the job will take 145 designer hours at $90 per hour and 85 staff hours at $45 per hour. Plumley uses two overhead rates in applying overhead ...
December 10, 2011 by Anonymous

physical science
how is subatomic particles related to atomic mass unit how is an electron related t oenergy level
November 3, 2007 by liz

writing
If I could get some help? I was wonderung if I had done this right.Write two paragraphs about how interest rates affect our purchasing decisions. Identify the topic sentence in each by underlining it. I have determined that the first two sentences in each paragrapg are the ...
August 12, 2011 by Anonymous

REC120
Khaldun's hierarchy of desires theory, what element is found at the pinnacle of the pyramid? Desires related to spirituality or Desires related to leisure or Desires for affiliation or Desire for safety or Desire to meet bodily appetites I think it is related to leisure but am...
August 29, 2013 by Jazmyne

Integrals/Related Rates(?)/Volume
Fluid is flowing in a tube that has a radius of 3 centimeters. Water is flowing through a circular cross section at a rate of (9-r^2) cm/s, where r is the distance from the center of the cross section. What is the total amount of water that flows through the cross section in 4...
March 22, 2012 by Alex

calculus
Use the second derivative to determine where the maximum and minimum rates of change occur for a vehicle’s speed modeled by the function v(t) = 0.0591t3 - 0.3399t2 + 0.5019t + 0.00594, where t is the time in minutes after leaving a stoplight.
February 27, 2013 by mark11

calculus
the equation V=U^5=7sqrtW-WZ relates the variables, V,U,W,Z. differentiate with respect to T to get the wquation which relates the rates of change with respect to T?
October 11, 2011 by Anonymous

Math (related rates)
My question is similar to Avik's but with different values. A camera, located 4 km from the launch pad, is tracking the rocket that is fired straight up. When the height of the rocket is 13 km, the camera is rotating at the rate of 3/169 radians per second. What is the speed ...
November 5, 2006 by Sally

Econ
The crowding-out effect arises when: a. govt borrows in the $ market, thus increase % rates and the net investment spending in the economy b. govt borrows in the $ market, thus increasing % rates and decreasing investment spending c. the progressivity of the tax system ...
November 6, 2006 by Amy

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