I need help solving these three problems. Thanks

Do three of the following problems. The equation on the right describes a circle. Find the equation of the circle, put it into the standard form (x - h)2 + (y - k)2 = R2, and determine the radius and center of the circle. If the entries in each row of an n times n matrix, A, add up to zero prove that the determinant of A is zero. (Hint: Consider the product AX where X is the n times 1 matrix, each of whose entries is one. ) A company leases rental cars at three Chicago offices (located at Midway Airport, O'Hare Field, and the Loop). Its records show that 60% of the cars rented at Midway are returned there and 20% are returned to each of the other locations. Also, 80% of the cars rented at O'Hare are returned there and 10% are returned to each of the other locations. Finally, 70% of the cars rented at the Loop are returned there, 10% are returned to Midway, and 20% are returned to O'Hare. Assuming that the information above describes a Markov chain, write a transition matrix for this situation. If a car is rented at Midway, what is the probability that it will be returned to the Loop after its second rental? Over the long run, if all of the cars are returned, what proportion of the company's fleet will be located at each office?

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23 Jun 2019

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2.6,#2(a), (b), 13(a), 17(a), 20(a), 25(a), 29, 30

Ed 9th B Blackboarc x h, ed rds.pd Adobe Read Wind 178 1334 100% Tools Sign (b) If 0 is increasing at the rate of radian per minute, find the when rates of change of the area when 0 /6 and 6 m/3 Explain why the rate of change of the area of the triangle is when not constant even though d6/dt is constant. 16. Volume The radius of a sphere is increasing at a rate of when 3 inches per minute a) Find the rates of c hange of the volume when 9 inches when and 36 inches b) Explain why the rate of change of the volume of the sphere when is not constant even though dr/dt is constant. 17. Volume A spherical balloon is inflated with gas at the rate of when 3, y 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is a) 30 centi and (b) 60 centimeters when 4, y 18. Volume All edges of a cube are expanding at a ate of 6 centimeters per second. How fast is e volume c hanging In Exercises 5-8, a point is moving along the graph of the given hen each edge is (a) 2 centimeters and (b) 10 centimeters? function such that dxldt is 2 centimeters per second. Find dyldt for the given values of x 19. Surface Area The conditions are the same as Exercise 18 Determine how fast the surfa changing when each edge is (a) 2 centimeters and (b) 10 centimeter 20. Volume The formula for the volume of a cone is V Find the rates of change of the volume if dr/dt is 2 inches per minute and h 3r when (a 6 inches and (b 7. y 21. Volume At a sand and gravel plant sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately WRITING ABOUT CONCEPTS three times the altitude. At what rate is the heigh of the pile changing when the pile is 15 feet high? 9. Consider th e li near function y b. If changes at a constant rate, does y change at a constant rate? If so, does 22. Depth A conical tank (w th vertex down s 10 feet across th change at the same rate as x? Explain. 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 10. In your ow words, state the guidelines for solving related of the water when th e water is 8 feet rate problems 23. Depth A swimming pool is 12 meters long, 6 meters wide 1 meter deep at the shallow end, and 3 meters deep at the deep 11. Find the rate of change of the distance between the origin end (see figure on next page Water is being pumped nto th f dx/di and a moving point n the graph of y pool at L cubic meter per minute. and there is 1 meter of water centimeters per second the deep end. 12. Find the rate of change of the distance between the origin (a) What percent of the pool is filled? f dx/dt and a moving point on the graph of y b) At what ate is th e water leve sing? centimeters per second 13. Area The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area. when (a 8 centimeters and (b 32 centimeters Comment a A Lueth 18 Research Help 6:30 PM 6/4/2013

Show transcribed image text Ed 9th B Blackboarc x h, ed rds.pd Adobe Read Wind 178 1334 100% Tools Sign (b) If 0 is increasing at the rate of radian per minute, find the when rates of change of the area when 0 /6 and 6 m/3 Explain why the rate of change of the area of the triangle is when not constant even though d6/dt is constant. 16. Volume The radius of a sphere is increasing at a rate of when 3 inches per minute a) Find the rates of c hange of the volume when 9 inches when and 36 inches b) Explain why the rate of change of the volume of the sphere when is not constant even though dr/dt is constant. 17. Volume A spherical balloon is inflated with gas at the rate of when 3, y 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is a) 30 centi and (b) 60 centimeters when 4, y 18. Volume All edges of a cube are expanding at a ate of 6 centimeters per second. How fast is e volume c hanging In Exercises 5-8, a point is moving along the graph of the given hen each edge is (a) 2 centimeters and (b) 10 centimeters? function such that dxldt is 2 centimeters per second. Find dyldt for the given values of x 19. Surface Area The conditions are the same as Exercise 18 Determine how fast the surfa changing when each edge is (a) 2 centimeters and (b) 10 centimeter 20. Volume The formula for the volume of a cone is V Find the rates of change of the volume if dr/dt is 2 inches per minute and h 3r when (a 6 inches and (b 7. y 21. Volume At a sand and gravel plant sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately WRITING ABOUT CONCEPTS three times the altitude. At what rate is the heigh of the pile changing when the pile is 15 feet high? 9. Consider th e li near function y b. If changes at a constant rate, does y change at a constant rate? If so, does 22. Depth A conical tank (w th vertex down s 10 feet across th change at the same rate as x? Explain. 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 10. In your ow words, state the guidelines for solving related of the water when th e water is 8 feet rate problems 23. Depth A swimming pool is 12 meters long, 6 meters wide 1 meter deep at the shallow end, and 3 meters deep at the deep 11. Find the rate of change of the distance between the origin end (see figure on next page Water is being pumped nto th f dx/di and a moving point n the graph of y pool at L cubic meter per minute. and there is 1 meter of water centimeters per second the deep end. 12. Find the rate of change of the distance between the origin (a) What percent of the pool is filled? f dx/dt and a moving point on the graph of y b) At what ate is th e water leve sing? centimeters per second 13. Area The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area. when (a 8 centimeters and (b 32 centimeters Comment a A Lueth 18 Research Help 6:30 PM 6/4/2013

ceruleanbeetle207

PLEASE ANSWER ALL QUESTIONS OR DO NOT ANSWER.

1. The formula

A = P[1 + (r/n)]^nt

describes the accumulated value A of a sum of money P, the principal, after t years at annual percentage rate r (in decimal form) compounded n times a year. How long will it take $25,000 to grow to $500,000 at 9% annual interest compounded monthly

Also:

Solve the logarithmic equation algebraically: Ln (X+5) = Ln (Xâ1) â Ln (X+1)

2. What is the first derivative of the following:

f(x) = ln (2x / x+1)

it is Natural Log of 2x over x+1

3. Please read the article from Money Magazine, posted in our week 8 Module, (one of my favorite financial magazines) that talks about small drop in t-bills will result in a major return in your investments (second paragraph). Why do you think that is? The article is a bit old but the question here is quite relevant about what we cover this week.

Hint: It has to do with the exponential graphs.

ARTICLE: Photo provided

THE ECONOMY: "Though growth averaged 2.5% stock market. says Leuthold, who recently completed a study of the stock market's daily ns over the past 100 years. In fact the stock market's daily swings from 1992 through '95 were less than half the historical average. Recently, however, daily fluctuations BY MICHAEL SIVY prices have cruised frm one high tothe next the stock market's daily swings from 1992 MosT OF THE PAST FOUR YEARS. STOCK ups and dow from one high to the next h, silent ride of a Rolls-Royce. But since March, the market has been lurching at an annual rate invest additional cash in stocks when they're low. If volatili in the first half of oyour Donailene tem dieapsirm ke a broken-down jalopy If you're hesitant to in stock prices have doubled (see the chart be- n't worry. Consider putting some be a sign that we're getting close to a market so jumpy. do of your money in long-term bonds instead. close to a mak t 1996, it will slow likely to beat stocks over the This short-term forecast doesn't change presi- the fact that the five-year outlook for stocks is terrific-thanks to the enormous underlying JTTERY AGAIN Percentage of trading days strength of the U.S. econ- the Dow moved more than 1% omy and the fact that aging -Bonds are next 12 months, says Steve Leuthold, dent of the Leuthold Group. STOCK PRICES ARE GETTING later this year.â nnpolis cuipd AGAIN advisory firm. We couldn't agree more. In fact, the out look for long-term bonds is the best it's been for more omy and the fact that agi baby boomers are continu- ing to sock away more than S20 billion a month in "The Dow couldthan a year. reach 6000 by fall but wil Here's our analysis: We see the economy slowing from its current 2.5% growth rate to only 2% or so late this year. Furthermore, stock mutual funds. Nonetheless, this is atime to restrict any new invest- ments in stocks to conserva- it makes sense to favor issues that are likely to boost their dividends, such as the shares decline ofas much as 15% starting beforea result, long-term-bond year-end." yields could sink from to day's 69% to as low as 6% by year-end. That rate decline would produce total re turns the Wall Street Newsletter n page 58. Stocks with solid around less than growth on bonds and other Income investments could return uping to fall s to 20% in the coming year. Moreover, as you sell By contrast, stocks increasingly look as some of your past year's winners, don't feel hough they are poised for a temporary 15% you have to reinvest all your profits in stocks. Consider putting some money into are likely to 30-year Treasuries (and mutual funds that start worrying that corporate profits are go- hold such long-term. high-quality issues). In hort of analysts' estimates and short, fortify your asset mix with bigger mark down share prices. "Slower earnings holdings of long-term bonds and other in- gains could turn the stock market's ail come investments such as high-yield stocks. portfo- drop in the second half of 1996. Reason: As the economy siows, investors winds into head winds." says economist That will help you keep your overall Michael SivyKathryn J. Lunstrum at Duff & Phelps in lio on track to a double-digit return even if the stock market takes a nasty 15% tumble in The tip-off that a stock market pullback the coming year. may be close is the increasing volatility o share prices over the past three months. Wall Street editor Michad Sivy is a chartered fi Volatility tends to be low in a strong, rising analyst and a former Wall Street researth director. nancia

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