Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYUWhat is the interest due if 500 is borrowed for 6 months at a simple interest rate of 6 per annum? (pp. A67-A68)2AYUThe total amount borrowed (whether by an individual from a bank in the form of a loan or by a bank from an individual in the form of a savings account) is called the _____________________.If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r , expressed as a decimal, the interest I charged is = . Interest charged according to this formula is called ____ _____.5AYU6AYUIn Problems 7-14, find the amount that results from each investment. 100 invested at 4 compounded quarterly after a period of 2 yearsIn Problems 7-14, find the amount that results from each investment. 50 invested at 6 compounded monthly after a period of 3 years900 Invested at 3 compounded semi-annually after a period of 212 years. Invested at compounded monthly after a period of years.
Invested at compounded daily after a period of years.
In Problems 7-14, find the amount that results from each investment. 700 invested at 6 compounded daily after a period of 2 yearsIn Problems 7-14, find the amount that results from each investment. 1000 invested at 11 compounded continuously after a period of 2 yearsIn Problems 7-14, find the amount that results from each investment. 400 invested at 7 compounded continuously after a period of 3 yearsIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 100 after 2 years at 6 compounded monthlyIn Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To got 75 after 3 years at 8 compounded quarterlyIn Problems, find the principal needed now to get each amount; that is, find the present value.
To get after years at compounded daily.
In Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 800 after 3 1 2 years at 7 compound monthlyIn Problems, find the principal needed now to get each amount; that is, find the present value.
To get after years at compounded quarterly.
In Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 300 after 4 years at 3 compounded dailyIn Problems 1522, find the principal needed now to get each amount; that is, find the present value. To get 120 after 314 years at 5 compounded continuously.In Problems 15-22, find the principal needed now to get each amount; that is, find the present value. To get 800 after 2 1 2 years at 8 compounded continuouslyIn Problems 23—26, find the effective rate of interest. For 5 compounded quarterlyIn Problems 2326, find the effective rate of interest. For 6 compounded monthly.In Problems, find the effective rate of interest.
For compounded continuously.
In Problems 23—26, find the effective rate of interest. For 6 compound continuouslyIn Problems 27-30, determine the rate that represents the better deal. 6 compounded quarterly or 6 1 4 compounded annuallyIn Problems 27-30, determine the rate that represents the better deal. 9 compounded quarterly or 9 1 4 compounded annuallyIn Problems 27-30, determine the rate that represents the better deal. 9 compounded monthly or 8.8 compounded dailyIn Problems 27-30, determine the rate that represents the better deal. 8 compounded semiannually or 7.9 compounded dailyWhat rate of interest compounded annually is required to double an investment in 3 years?What rate of interest compounded annually is required to double an investment in 6 years?What rate of interest compounded annually is required to triple an investment in 5 years?What rate of interest compounded annually is required to triple an investment in 10 years?(a) How long does it take for an investment to double in value if it is invested at 8 compounded monthly? (b) How long does it take if the interest is compounded continuously?(a) How long does it take for an investment to triple in value if it is invested at 6 compounded monthly? (b) How long does it take if the interest is compounded continuously?What rate of interest compounded quarterly will yield an effective interest rate of 7 ?What rate of interest compounded continuously will yield an effective interest rate of 6 ?Time Required to Reach a Goal If Tanisha has 100 to invest at 4 per annum compounded monthly, how long will it be before she has 150 ? If the compounding is continuous, how long will it be?Time Required to Reach a Goal If Angela has 100 to invest at 2.5 per annum compounded monthly, how long will it be before she has 175 ? If the compounding is continuous, how long will it be?Time Required to Reach a Goal How many years will it take for an initial investment of 10,000 to grow to 25,000 ? Assume a rate of interest of 6 compounded continuously.Time Required to Reach a Goal how many years will it take for an initial investment of 25,000 to grow to 80,000 ? Assume a rate of interest of 7 compounded continuously.Price Appreciation of Homes What will a 90,000 condominium cost 5 years from now if the price appreciation for condos over that period averages 3 compounded annually?44AYU45AYU46AYUReturn on a Stock George contemplates the purchase of 100 shares of a stock selling for 15 per share. The stock pays no dividends. Tile history of the stock indicates that it should grow at an annual rate of 15 per year. How much should the 100 shares of stock be worth in 5 years?48AYUComparing Savings Plans Jim places 1000 in a bank account that pays 5.6 compounded continuously. After 1 year, will he have enough money to buy a computer system that costs 1060 ? If another bank will pay Jim 5.9 compounded monthly, is this a better deal?Savings Plans On January 1, Kim places 1000 in a certificate of deposit that pays 6.8 compounded continuously and matures in 3 months. Then Kim places the 1000 and the interest in a passbook account that pays 5.25 compounded monthly. How much does Kim have in the passbook account on May 1?Comparing IRA Investments Will invests 2000 in his IRA in a bond trust that pays 9 interest compounded semiannually. His friend Henry invests 2000 in his IRA in a certificate of deposit that pays 8 1 2 compounded continuously. Who has more money after 20 years, Will or Henry?52AYUCollage Costs The average annual cost of college at 4 year private colleges was 34,740 in the 20172018 academic year. This was a 3.6 increase from the previous year. If the cost of college increases by 3.6 each year, what will be the average cost of college at a 4 year private college for the 20372038 academic year? College savings plans, such as a 529 plan, allow individuals to put money aside now to help pay for college later. If one such plan offers a rate of 2 compounded continuously, how much should be put in a college savings plan in 2019 to pay for 1 year of the cost of college at a 4 year private college for an incoming freshmen in 2037? Source: The College Board54AYUComparing Bank Accounts Two bank accounts are opened at the same time. The first has a principal of in an account earning compounded monthly. The second has a principal of in an account earning interest compounded annually. Determine the number of years, to the nearest tenth, at which the account balances will be equal.
Per Capita Federal Debt In 2018, the federal debt was about 21 trillion. In 2018, the U.S. population was about 327 million. Assuming that the federal debt is increasing about 5.5 per year and the U.S. population is increasing about 0.7 per year, determine the per capita debt (total debt divided by population) in 2030.Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the inflation rate averages 3 , how much will 1000 purchase in 2 years?58AYU59AYUInflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the amount that 1000 will purchase is only 930 after 2 years, what was the average inflation rate?Inflation Problems 57-62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3 , then 1000 worth of purchasing power now will have only 970 worth of purchasing power in 1 year because 3 of the original 1000( 0.031000=30 ) has been eroded due to inflation. In general, if the rate of inflation averages r per annum over n years, the amount A that P will purchase after n years is A=P (1r) n where r is expressed as a decimal. Inflation If the average inflation rate is 2 , how long is it until purchasing power is cut in half?62AYUProblems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. Zero-Coupon Bonds A zero-coupon bond can be redeemed in 20 years for 10,000 . How much should you be willing to pay for it now if you want a return of: (a) 5 compounded monthly? (b) 5 compounded continuously?64AYU65AYUProblems 63-66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made. Zero-Coupon Bonds If Pat pays 15,334.65 for a 25,000 face-value, zero-coupon bond that matures in 8 years, what is his annual rate of return?Time to Double or Triple an Investment The formula t= lnm nln( 1+ r n ) can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year. (a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6 ? (b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 5 ? (c) Give a derivation of this formula.68AYU69AYU70AYUProblems 69-72 require the following discussion. The consumer price index (CPI) indicates the relative change in price over time for a fixed basket of goods and services. It is a cost of living index that helps measure the effect of inflation on the cost of goods and services. The CPI uses the base period 1982-1984 for comparison (the CPI for this period is 100). The CPI for March 2015 was 236.12 . This means that 100 in the period 1982-1984 had the same purchasing power as 236.12 in March 2015. In general, if the rate of inflation averages r percent per annum over n years, then the CPI index after n years is CPI=CP I 0 ( 1+ r 100 ) n where CP I 0 is the CPI index at the beginning of the n-year period. Source: U.S. Bureau of Labor Statistics Consumer Price Index If the average annual inflation rate is 3.1 , how long will it take for the CPI index to double? (A doubling of the CPI index means purchasing power is cut in half.)72AYUExplain in your own words what the term compound interest means. What does continuous compounding mean?Explain in your own words the meaning of present value.75AYUGrowth of an Insect Population The size P of a certain insect population at time t (in days) obeys the model P( t )=500 e 0.02t . (a) Determine the number of insects at t=0 days. (b) What is the growth rate of the insect population? (c) Graph the function using a graphing utility. (d) What is the population after 10 days? (e) When will the insect population reach 800? (f) When will the insect population double?Growth of Bacteria The number N of bacteria present in a culture at time t (in hours) obeys the model N(t)= 1000e 0.01t . (a) Determine the number of bacteria at t=0 hours. (b) What is the growth rate of the bacteria? (c) Graph the function using a graphing utility. (d) What is the population after 4 hours? (e) When will the number of bacteria reach 1700? (f) When will the number of bacteria double?Radioactive Decay Strontium-90 is a radioactive material that decays according to the function A(t)= A 0 e 0.0244t , where A 0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 500 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) Graph the function using a graphing utility. (c) How much strontium-90 is left after 10 years? (d) When will 400 grams of strontium-90 be left? (e) What is the half-life of strontium-90?Radioactive Decay Iodine-131 is a radioactive material that decays according to the function A(t)= A 0 e 0.087t , where A 0 is the initial amount present and t is the amount present at time t (in days). Assume that a scientist has a sample of 100 grams of iodine-131. (a) What is the decay rate of iodine-131? (b) Graph the function using a graphing utility. (c) How much iodine-131 is left after 9 days? (d) When w ill 70 grams of iodine-131 be left? (e) What is the half-life of iodine-131?Growth of a Colony of Mosquitoes The population of a colony of mosquitoes obeys the law of uninhibited growth. (a) If N is the population of the colony and t is the time in days, express N as a function of t . (b) If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days? (c) How long is it until there are 10,000 mosquitoes?Bacterial Growth A culture of bacteria obeys the law of uninhibited growth. (a) If N is the number of bacteria in the culture and t is the time in hours, express N as a function of t . (b) If 500 bacteria are present initially and there are 800 after 1 hour, how many will be present in the culture after 5 hours? (c) How long is it until there are 20,000 bacteria?Population Growth The population of a southern city follows the exponential law. (a) If N is the population of the city and t is the time in years, express N as a function of t . (b) If the population doubled in size over an 18-momh period and the current population is 10,000, what will the population be 2 years from now?Ρopulation Decline The population of a midwestern city follows the exponential law. (a) If N is the population of the city and t is the time in years, express N as a function of t . (b) If the population decreased from 900,000 to 800,000 from 2013 to 2015, what will the population be in 2017?Radioactive Decay The half-life of radium is 1690 years, If 10 grams is present now, how much will be present in 50 years?Radioactive Decay The half-life of radioactive potassium is 1.3 billion years. If 10 grams is present now, how much will be present in 100 years? In 1000 years?Estimating the Age of a Tree A Piece of a charcoal is found to contain of the carbon- that is originally had. When did the tree die from which the charcoal came? Use years as the half-life of carbon-.
Estimating Age A fossilized leaf contains 70 of its normal amount of carbon- 14. How old is the fossil?Cooling Time of a Pizza Apizza baked at 450oF is removed from the oven at 5:00 PM and placed in a room that is a constant 70oF. After 5 minutes, the pizza is at 300oF. At what time can you begin eating the pizza if you want its temperature to be 135oF? Determine the time that needs to elapse before the temperature of the pizza is 160oF. What do you notice about the temperature as time passes?Newtons Law of Cooling A thermometer reading 72oF is placed in a refrigerator where the temperature is a constant 38oF. If thermometer reads 60oF after 2 minutes, what will it read after 7 minutes? How long will it take before the thermometer reads 39oF? Determine the time that must elapse before the thermometer reads 45oF. What do you notice about the temperature as time passes?Newton’s Law of Heating A thermometer reading is brought into a room with a constant temperature of. If the thermometer reads after minutes, what will it read after being in the room for minutes? For minutes?
[Hint: You need to construct formula similar to equation]
Equation (4) is,
16AYUDecomposition of Chlorine in a Pool Under certain water conditions, the free chlorine (hypochlorous acid, HOCl) in a swimming pool decomposes according to the law of uninhibited decay. After shocking his pool, Ben tested the water and found the amount of free chlorine to be 2.5 parts per million (ppm). Twenty-four hours later, Ben tested the water again and found the amount of free chlorine to be 2.2 ppm. What will be the reading after 3 days (that is, 72 hours)? When the chlorine level reaches 1.0 ppm, Ben must shock the pool again. How long can Ben go before he must shock the pool again?Decomposition of Dinitrogen Pentoxide At 45 C , dinitrogen pentoxide ( N 2 O 5 ) decomposes into nitrous dioxide ( NO 2 ) and oxygen ( O 2 ) according to the law of uninhibited decay. An initial amount of 0.25 mole of dinitrogen pentoxide decomposes to 0.15 mole in 17 minutes. How much dinitrogen pentoxide will remain after 30 minutes? How long will it take until 0.01 mole of dinitrogen pentoxide remains?19AYUDecomposition of Salt in Water Salt ( NaCl ) decomposes in water into sodium ( Na ) and chloride ( Cl ) ions according to the law of uninhibited decay. If the initial amount of salt is 25 kilograms and, after 10 hours. 15 kilograms of salt is left, how much salt is left after 1 day? How long does it take until 1 2 kilogram of salt is left?21AYU22AYU23AYU24AYU25AYU1AYU2AYU3AYU4AYU5AYU6AYU7AYU8AYU9AYU10AYU11AYU12AYU13AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84RE85RE86RE87RE88RE89RE90RE91RE92RE93RE94RE95RE96RE97REIn Problem, convert each angle in degrees to radius. Express your answer as a multiple of.
1.
In Problem 13, convert each angle in degrees to radius. Express your answer as a multiple of . 400In problem 13, convert each angle in degrees to radians. Express your answer as a multiple of . 13In Problem 46, convert each angle in radius to degrees. 8In Problem, convert each angle in radius to degrees.
5.
In Problem, convert each angle in radius to degrees.
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In Problem 712, find the exact value of each expression. sin6In Problem 712, find the exact value of each expression. cos(56)cos34In Problem 712, find the exact value of each expression. cos(120)In Problem, find the exact value of each expression.
10.
In Problem 712, find the exact value of each expression. sin2tan19412CT13CTIn Problem 1316, use a calculator to evaluate each expression. Round your answer to three decimal places. cos2515CT16CT17. Fill in each table entry with sign of each function.
18. If and, find.
In Problems 1921, find the value of the remaining five trigonometric functions of . sin=57, in quadrant II20CTIn Problems 1921, find the value of the remaining five trigonometric functions of . tan=125, 2In Problems, the point is on the terminal side of angle is standard position. Find the exact value of the given trigonometric function.
22.,
In Problems, the point is on the terminal side of angle is standard position. Find the exact value of the given trigonometric function.
23.,
In Problems 2224, the point (x,y) is on the terminal side of angle is standard position. Find the exact value of the given trigonometric function. (6,3), tanIn Problems and, graph the function.
25.
In Problems and, graph the function.
25.
Write an equation for a sinusoidal graph with the following properties: A=3 Period =23 phase shift =4Logan has a garden in the shape of a sector of a circle; the outer rims of the garden are 25 feet long and the central angle of the sector is 50. She wants to add a 3-foot-wide walk to the outer rim. How many square feet of paving blocks will she need to build the walk?Hungarian Adrian Annus won the gold medal for the hummer throw at the 2004 Olympics in Athens with a winning distance of 83.19 meters*.The event consists of swinging a 16-pound weight attached to a wire 190 centimetres long in a circle and then releasing it. Assuming his release is at a 45 angle to the ground, the hammer will travel a distance of v02g metres, where g=9.8 metres/second 2 and v0 is the linear speed of the hammer when released. At what rate (rpm) was he swinging the hammer upon release? *Annus was stripped of his medal refusing to cooperate with postmedal drug testing.Find the real solutions, if any, of the equation
2. Find an equation for the line with slope containing the point.
3CR4. Describe the equation. Graph it.
5. Describe the equation Graph it.
6. Use the transformation to graph the function
7. Sketch a graph of each of the following functions. Label at least three points on each graph.
Find the inverse function of f(x)=3x29. Find the exact value of.
Graph y=3sin(2x).11. Find the exact value of.
12. Find an exponential function for the following graph. Express your answer in the form.
13. Find a sinusoidal function for the following graph.
14.
(a) Find a linear function that contains the points and. What is the slope? What are the intercepts of the function? Graph the function. Be sure to label the intercepts.
(b) Find a quadratic function with the vertex that contains the point. What are the intercepts of the function? Graph the function.
(c)Show that there is no exponential function of the form that contains the points and.
(a) Find a polynomial function of degree 3 whose y-intercept is 5 and whose x-intercepts are 2, 3 and 5. Graph the function. (b) Find a rational function whose y-intercept 5 and whose x-intercepts are 2, 3 and 5 that has the line x=2 as a vertical asymptote. Graph the function.What is the formula for the circumference C of a circle of radius r ? What is the formula for the area A of a circle of radius r ? (p. A16)If an object has a speed of r feet per second and travels a distance d (in feet) in time t (in seconds), then d= _____ . (pp. A69-A71)An angle is in _____ _____ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis .A _____ _____ is a positive angle whose vertex is at the Center of a circle.If the radius of a circle is r and the length of the arc subtended by a central angle is also r , then the measure of the angle is 1 _____ . a. degree. b. minute. c. second. d. radian.On a circle of radius r , a central angle of radians subtends an arc of length s= _____; the area of the sector formed by this angle is A= _____ .180 = _____ radians a. 2 b. c. 3 2 d. 2An object travels on a circle of radius r with constant speed. If s is the distance traveled in time t on the circle and is the central angle (in radians) swept out in time t , then the linear speed of the object is v= _____ and the angular speed of the object is = _____ .True or False The angular speed of an object traveling on a circle of radius r is the angle (measured in radians) swept out, divided by the elapsed time t .True or False For circular motion on a circle of radius r , linear speed equals angular speed divided by r .In Problems 11-22, draw each angle in standard position. 30In Problems 11-22, draw each angle in standard position. 60In Problems 11-22, draw each angle in standard position. 135In Problems 11-22, draw each angle in standard position. 120In Problems 11-22, draw each angle in standard position. 450In Problems 11-22, draw each angle in standard position. 540In Problems 11-22, draw each angle in standard position. 3 4In Problems 11-22, draw each angle in standard position. 4 3In Problems 11-22, draw each angle in standard position. 6In Problems 11-22, draw each angle in standard position. 2 3In Problems 11-22, draw each angle in standard position. 16 3In Problems 11-22, draw each angle in standard position. 21 4In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 30In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 120In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 240In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 330In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 60In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 30In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 180In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 270In Problems, convert each angle in degrees to radians. Express your answer as a multiple of.
31.
In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 225In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 90In Problems 23-34, convert each angle in degrees to radians. Express your answer as a multiple of . 180