Solutions for Precalculus
Problem 1SP:
Franz borrowed a total of $10,000 . Part of the money was borrowed from a lending institution that...Problem 2SP:
How much 4 acid solution should be mixed with 200mL of a 12 acid solution to make a 9 acid solution?Problem 3SP:
A fishing boat can travel 60km with a 2.5-km/hr current in 2 hr less time than it can travel 60 km...Problem 4SP:
Sheldon and Penny were awarded a contract to paint 16 offices in the new math building at a...Problem 5SP:
A sail on a sailboat is in the shape of two adjacent right triangles. The hypotenuse of the lower...Problem 6SP:
A fireworks mortar is launched straight upward from a pool deck 2 m off the ground at an initial...Problem 2PE:
Suppose that 8 of a solution is fertilizer by volume and the remaining 92% is water. How much...Problem 3PE:
If d=rt,thent=Problem 4PE:
If d=rt,thenr=Problem 5PE:
Rocco borrowed a total of $5000 from two student loans. One loan charged 3% simple interest and the...Problem 6PE:
Laura borrowed a total of $22,000 from two different banks to start a business. One bank charged the...Problem 7PE:
Fernando invest money in a 3-yr CD (certificate of deposit) that returned the equivalent of 4.4%...Problem 8PE:
Ebony bought a 5-yr Treasury note that paid the equivalent of 2.8% simple interest. she invested...Problem 9PE:
Ethanol fuel mixture have "E" number that indicate the percentage of ethanol in the mixture by...Problem 10PE:
A nurse mixes 60 cc of a 50 saline solution with a 10% saline solution to produce a 25% saline...Problem 11PE:
The density and strength of concrete are determined by the ratio of cement and aggregate (aggregate...Problem 12PE:
Antifreeze is a compound added to water to reduce the freezing point of a mixture. In extreme cold...Problem 13PE:
Jesse takes a 3-day kayak trip and travels 72 km south from Everglades City to a camp area in...Problem 14PE:
A plane travels 800 mi from Dallas, Texas, to Atlanta, Georgia, with a prevailing west wind of 40...Problem 15PE:
Jean runs 6 mi and then rides 24 mi on her bicycle in a biathlon. She rides 8 mph faster than she...Problem 16PE:
Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear...Problem 17PE:
Two passengers leave the airport at Kansas City, Missouri. One flies to Los Angeles, California, in...Problem 18PE:
Two planes leave from Atlanta Georgia. One makes a 5.2-hr flight to Seattle, Washington, and the...Problem 19PE:
Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon...Problem 20PE:
Peggy competes in a biathlon by running and bicycling around a large loop through a city. She runs...Problem 21PE:
Joel can run around a 14mi track in 66 sec, and Jason can run around the track in 60 sec. If the...Problem 22PE:
Marta can vacuum the house in 40 min. It takes her daughter 1 hr to vacuum the house. How long would...Problem 23PE:
One pump can fill a pool in 10 hr. Working with a second slower pump, the two pumps together can...Problem 24PE:
Brad and Angelina can mow their yard together with two lawn mowers in 30 min. When Brad works alone,...Problem 25PE:
A patio is configured from a rectangle with two right triangles of equal size attached at the two...Problem 26PE:
The front face of a house is in the shape of a rectangle with a Queen post roof truss above. The...Problem 27PE:
A baseball diamond is in the shape of a square with 90-ft sides. How far is it from home plate to...Problem 28PE:
The figure is a cube with 6-in. sides. Find the extract length of the diagonal through the interior...Problem 29PE:
The sail on a sailboat is in the shape of two adjacent right triangles. In the lower triangle, the...Problem 30PE:
A portion of a roof truss is given in the figure. The tringle on the left is configured such that...Problem 31PE:
The display area on a cell phone has a 3.5-in. diagonal. a. If the aspect ratio of length to width...Problem 32PE:
The display area on a computer has a 15-in. diagonal. If the aspect ratio of length to width is 1.6...Problem 33PE:
NBA basketball legend Michael Jordan had a 48-in. vertical leap. Suppose that Michael jumped from...Problem 34PE:
At the time of this printing, the highest vertical leap on record is 60 in., held by Kadour Ziani....Problem 35PE:
A bad punter on a football team kicks a football approximately straight upward with an initial...Problem 36PE:
In a classic Seinfeld episode, Jerry tosses a loaf of bread (a marble rye) straight upward to his...Problem 37PE:
Suppose that 40 deer are introduced in a protected wilderness area. The population of the herd P can...Problem 38PE:
Starting from rest, an automobile's velocity v (in ft/sec) is given by v=180t2t+10r , where t is the...Problem 39PE:
Brianna's SUV gets 22 mpg in the city and 30 mpg on the highway. The amount of gas she uses A (in...Problem 40PE:
Dexter's truck gets 32 mpg on the highway and 24 mpg in the city. The amount of gas he uses A (in...Problem 41PE:
At a construction site, cement sand, and gravel are mixed to make concrete. The ratio of cement to...Problem 42PE:
The property tax on a $180,000 house is $1296 . At this rate, what is the property tax on a house...Problem 43PE:
In addition to measuring a person's individual HDL and LDL cholesterol levels, doctors also compute...Problem 44PE:
For a recent Congress, there were 10 more Democrats than Republicans in the U.S. Senate. This...Problem 45PE:
When studying wildlife populations, biologists sometimes use a technique called "mark-recapture."...Problem 46PE:
To estimate the number of bass in a lake, a biologist catches and tags 24 bass. Several weeks later,...Problem 47PE:
Seismographs can record two types of wave energy (P waves and S waves) that travel through the Earth...Problem 48PE:
Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel...Problem 49PE:
Henri needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $110...Problem 50PE:
After a hurricane, repairs to a roof will cost $2400 for materials and $80/hr in labor. a. Write a...Problem 51PE:
On moving day, Guyton needs to rent a truck. The length of the cargo space is 12 ft and the height...Problem 52PE:
Lorene Plans to make several open-topped boxes in which to carry plants. She makes the boxes from...Problem 53PE:
The population P of a culture of Pseudomonas aeruginoso bacteria is given by P=1718t2+82,000t+10,000...Problem 54PE:
The distance d (in ft) required to stop a car that was traveling at speed v (in mph) before the...Problem 55PE:
Is it possible for the measures of the angles in a tringle to be represented by three consecutive...Problem 56PE:
Bob wants to change a $100 bill into an equal number of $20 bills, $10 bills, and $5 bills. Is this...Problem 57PE:
A golden rectangle is a rectangle in which the ratio of its length to its width is equal to the...Problem 58PE:
An artist has been commissioned to make a stained glass window in the shape of a regular octagon....Problem 59PE:
A farmer has 160 yd of fencing material and wants to enclose three rectangular pens. Suppose that x...Problem 60PE:
At noon, a ship leaves a harbor and sails south at 10 knots. Two hours later, a second ship leaves...Browse All Chapters of This Textbook
Chapter R - Review Of PrerequisitesChapter R.1 - Sets And The Real Number LineChapter R.2 - Exponents And RadicalsChapter R.3 - Polynomials And FactoringChapter R.4 - Rational Expressions And More Operations On RadicalsChapter R.5 - Equations With Real SolutionsChapter R.6 - Complex Numbers And More Quadratic EquationsChapter R.7 - Applications Of EquationsChapter R.8 - Linear, Compound, And Absolute Value InequalitiesChapter 1 - Functions And Relations
Chapter 1.1 - The Rectangular Coordinate System And Graphing UtilitiesChapter 1.2 - CirclesChapter 1.3 - Functions And RelationsChapter 1.4 - Linear Equations In Two Variables And Linear FunctionsChapter 1.5 - Applications Of Linear Equations And ModelingChapter 1.6 - Transformations Of GraphsChapter 1.7 - Analyzing Graphs Of Functions And Piecewise-defined FunctionsChapter 1.8 - Algebra Of Functions And Function CompositionChapter 2 - Polynomial And Rational FunctionsChapter 2.1 - Quadratic Functions And ApplicationsChapter 2.2 - Introduction To Polynomial FunctionsChapter 2.3 - Division Of Polynomials And The Remainder And Factor TheoremsChapter 2.4 - Zeros Of PolynomialsChapter 2.5 - Rational FunctionsChapter 2.6 - Polynomial And Rational InequalitiesChapter 2.7 - VariationChapter 3 - Exponential And Logarithmic FunctionsChapter 3.1 - Inverse FunctionsChapter 3.2 - Exponential FunctionsChapter 3.3 - Logarithmic FunctionsChapter 3.4 - Properties Of LogarithmsChapter 3.5 - Exponential And Logarithmic Equations And ApplicationsChapter 3.6 - Modeling With Exponential And Logarithmic FunctionsChapter 4 - Trigonometric FunctionsChapter 4.1 - Angles And Their MeasureChapter 4.2 - Trigonometric Functions Defined On The Unit CircleChapter 4.3 - Right Triangle TrigonometryChapter 4.4 - Trigonometric Functions Of Any AngleChapter 4.5 - Graphs Of Sine And Cosine FunctionsChapter 4.6 - Graphs Of Other Trigonometric FunctionsChapter 4.7 - Inverse Trigonometric FunctionsChapter 5 - Analytic TrigonometryChapter 5.1 - Fundamental Trigonometric IdentitiesChapter 5.2 - Sum And Difference FormulasChapter 5.3 - Double-angle, Power-reducing, And Half-angle FormulasChapter 5.4 - Product-to-sum And Sum-to-product FormulasChapter 5.5 - Trigonometric EquationsChapter 6 - Applications Of Trigonometric FunctionsChapter 6.1 - Applications Of Right TrianglesChapter 6.2 - The Law Of SinesChapter 6.3 - The Law Of CosinesChapter 6.4 - Harmonic MotionChapter 7 - Trigonometry Applied To Polar Coordinate Systems And VectorsChapter 7.1 - Polar CoordinatesChapter 7.2 - Graphs Of Polar EquationsChapter 7.3 - Complex Numbers In Polar FormChapter 7.4 - VectorsChapter 7.5 - Dot ProductChapter 8 - Systems Of Equations And InequalitiesChapter 8.1 - Systems Of Linear Equations In Two Variables And ApplicationsChapter 8.2 - Systems Of Linear Equations In Three Variables And ApplicationsChapter 8.3 - Partial Fraction DecompositionChapter 8.4 - Systems Of Nonlinear Equations In Two VariablesChapter 8.5 - Inequalities And Systems Of Inequalities In Two VariablesChapter 8.6 - Linear ProgrammingChapter 9 - Matrices And Determinants And ApplicationsChapter 9.1 - Solving Systems Of Linear Equations Using MatricesChapter 9.2 - Inconsistent Systems And Dependent EquationsChapter 9.3 - Operations On MatricesChapter 9.4 - Inverse Matrices And Matrix EquationsChapter 9.5 - Determinants And Cramer’s RuleChapter 10 - Analytic GeometryChapter 10.1 - The EllipseChapter 10.2 - The HyperbolaChapter 10.3 - The ParabolaChapter 10.4 - Rotation Of AxesChapter 10.5 - Polar Equations Of ConicsChapter 10.6 - Plane Curves And Parametric EquationsChapter 11 - Sequences, Series, Induction, And ProbabilityChapter 11.1 - Sequences And SeriesChapter 11.2 - Arithmetic Sequences And SeriesChapter 11.3 - Geometric Sequences And SeriesChapter 11.4 - Mathematical InductionChapter 11.5 - The Binomial TheoremChapter 11.6 - Principles Of CountingChapter 11.7 - Introduction To Probability
Book Details
Julie Miller wrote her developmental math series because students were coming into her Precalculus course underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. She began her developmental mathematics offerings with intermediate algebra to help bridge that gap. The Precalculus series is a carefully constructed end to that bridge that uses the highly effective pedagogical features from her fastest growing developmental math series. What sets Julie Miller’s series apart is that it addresses course issues through an author-created digital package that maintains a consistent voice and notation throughout the program. This consistency--in videos, PowerPoints, Lecture Notes, and Group Activities--coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Precalculus and can carry them through to the calculus sequence.
Sample Solutions for this Textbook
We offer sample solutions for Precalculus homework problems. See examples below:
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