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All Textbook Solutions for Precalculus
In Problems graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve.
8AYU9AYU10AYU11AYU12AYU13AYU14AYU15AYU16AYU17AYU18AYUIn Problems 726, graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. x(t)=2cost,y(t)=3sint;0t220AYU21AYUIn Problems graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve.
In Problems graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve.
24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYUIn Problems 39-42, find parametric equations for an object that moves along the ellipse x 2 4 + y 2 9 =1 with the motion described. The motion begins at ( 0,3 ) , is counterclockwise, and requires 1 seconds for a complete revolution.41AYU42AYU43AYU44AYUIn Problems 45-48, use a graphing utility to graph the curve defined by the given parametric equations. x=tsint , y=tcost , t046AYU47AYU48AYU49AYU50AYUCatching a Train Bill’s train leaves at 8:06 AM and accelerates at the rate of 2 meters per second per second. Bill, who can run 5 meters per second, arrives at the train station 5 seconds after the train has left and runs for the train. a. Find parametric equations that model the motions of the train and Bill as a function of time. [Hint: The position s at time t of an object having acceleration a is s= 1 2 a t 2 ]. b. Determine algebraically whether Bill will catch the train. If so, when? c. Simulate the motion of the train and Bill by simultaneously graphing the equations found in part (a).52AYU53AYU54AYU55AYU56AYU57AYUUniform Motion A Cessna (heading south at mph) and a Boeing (heading west at mph) are flying toward the same point at the same altitude. The Cessna is miles from the point where the flight patterns intersect, and the is miles from this intersection point. See the figure.
Find parametric equations that model the motion of the Cessna and the
Find a formula for the distance between the planes as a function of time.
Graph the function in part (b) using the graphing utility.
What is the minimum distance between the planes? When are the planes closest?
Simulate the motion of the planes by simultaneously graphing the equations found in part (a).
The Green Monster The left field wall at Fenway Park is 310 feet from home plate; the wall itself (affectionately named the Green Monster) is 37 feet high. A batted ball must clear the wall to be a home run. Suppose a ball leaves the bat 3 feet off the ground, at an angle of 45 . Use g=32 feet per second2 as the acceleration due to gravity and ignore any air resistance. a. Find parametric equations that model the position of the ball as a function of time. What is the maximum height of the ball if it leaves the bat with a speed of 90 miles per hour? Give your answer in feet. b. How far is the ball from home plate at its maximum height? Give your answer in feet. c. If the ball is hit straight down the left field wall, will it clear the Green Monster? If it does, by how much does it clear the wall?60AYU61AYU62AYU63AYU64AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84RE85RE86RE87RE88RE89RE90RE91RE92RE93RE94RE95RE96RE97RE98RE99RE100RE101RE102RE103RE104RE105RE106RE107RE108RE109RE110REIn problems 14, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. {2x+y=74x+3y=92CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT14CT15CT16CT17CT18CT19CT20CT21CT22CT23CT24CT25CT26CT27CT28CT1CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CRSolve the equation: 3x+4=8x . (pp. A44-A46)(a) Graph the line: 3x+4y=12 . (b) What is the slope of a line parallel to this line? (pp. 29-40)3AYUIf a system of equations has one solution, the system is _____and the equations are ______.If the solution to a system of two linear equations containing two unknowns is x=3,y=2 then the lines intersect at the point _____.If the lines that make up a system of two linear equations are coincident, then the system is __________________ and the equations are ______.{ 2xy=5 5x+2y=8 x=2,y=1;( 2,1 ){ 3x+2y=2 x7y=30 x=2,y=4;( 2,4 ){ 3x4y=4 1 2 x3y= 1 2 x=2,y= 1 2 ;( 2, 1 2 )10AYU11AYU12AYU{ 3x+3y+2z=4 xyz=0 2y3z=8 x=1,y=1;z=2;( 1,1,2 )14AYU15AYU{ 4x5z=6 5yz=17 x6y+5z=24 x=4,y=3;z=2;( 4,3,2 ){ x+y=8 xy=418AYU{ 5xy=21 2x+3y=1220AYU21AYU22AYU{ 3x6y=2 5x+4y=124AYU{ 2x+y=1 4x+2y=326AYU27AYU{ 3x+3y=1 4x+y= 8 329AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU{ x2y+3z=7 2x+y+z=4 3x+2y2z=1044AYU{ xyz=1 2x+3y+z=2 3x+2y=046AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYUOrbital Launches In there was a total of commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was 31 more than half the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches in.
Movie Theater Tickets A movie theater charges 9.00 for adults and 7.00 for senior citizens. On a day when 325 people paid for admission, the total receipts were 2495 . How many who paid were adults? How many were seniors?Mixing Nuts A store sells cashews for 5.00 per pound and peanuts for 1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for 3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately?60AYU61AYUComputing Wind Speed The average airspeed of a single engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?Restaurant Management A restaurant manager wants to purchase 200 sets of dishes. One design costs 25 per set, and another costs 45 per set. If she has only 7400 to spend, how many sets of each design should she order?64AYUComputing a Refund The grocery store we use does not mark prices on its goods. My wife went to this store, bought three 1-pound packages of bacon and two cartons of eggs, and paid a total of 13.45 . Not knowing that she went to the store, I also went to the same store, purchased two 1-pound packages of bacon and three cartons of eggs, and paid a total of 11.45 . Now we want to return two 1-pound packages of bacon and two cartons of eggs. How much will be refunded?66AYUPharmacy A doctor’s prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: One contains 20 vitamin C and 30 vitamin D. the other 40 vitamin C and 20 vitamin D. How many milligrams of each compound should be mixed to fill the prescription?Pharmacy A doctor’s prescription calls for the creation of pills that contain 12 units of vitamin B 12 and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills: One contains 20 vitamin B 1 2 and 30 vitamin E, the other 40 vitamin B 12 and 20 vitamin E. How many units of each powder should be mixed in each pill?Curve Fitting Find real numbers a,b,andc so that the graph of the function y=a x 2 +bx+c contains the points ( 1,4 ),( 2,3 ),and( 0,1 ) .70AYU71AYUIS-LM Model in Economics In economics, the IS curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an equilibrium in the market for goods in the economy. The LM curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an equilibrium in the market for money in the economy. In an economy, suppose that the equilibrium level of income (in millions of dollars) and interest rates satisfy the system of equations { 0.05Y1000r=10 0.05Y+800r=100 Find the equilibrium level of income and interest rates.73AYU74AYU75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU1AYU2AYU3AYU4AYUIn problems 7-18, write the augmented matrix of the given system of equations. { x5y=5 4x+3y=66AYU7AYU8AYU